TSTP Solution File: ITP230^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP230^1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 03:22:36 EDT 2023
% Result : Timeout 299.68s 300.16s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.48/2.50 % Problem : ITP230^1 : TPTP v8.1.2. Released v8.1.0.
% 2.48/2.51 % Command : do_cvc5 %s %d
% 2.53/2.73 % Computer : n007.cluster.edu
% 2.53/2.73 % Model : x86_64 x86_64
% 2.53/2.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.53/2.73 % Memory : 8042.1875MB
% 2.53/2.73 % OS : Linux 3.10.0-693.el7.x86_64
% 2.53/2.73 % CPULimit : 300
% 2.53/2.73 % WCLimit : 300
% 2.53/2.73 % DateTime : Sun Aug 27 12:02:29 EDT 2023
% 2.53/2.73 % CPUTime :
% 4.98/5.19 %----Proving TH0
% 4.98/5.19 %------------------------------------------------------------------------------
% 4.98/5.19 % File : ITP230^1 : TPTP v8.1.2. Released v8.1.0.
% 4.98/5.19 % Domain : Interactive Theorem Proving
% 4.98/5.19 % Problem : Sledgehammer problem VEBT_Insert 00815_052383
% 4.98/5.19 % Version : [Des22] axioms.
% 4.98/5.19 % English :
% 4.98/5.19
% 4.98/5.19 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 4.98/5.19 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 4.98/5.19 % Source : [Des22]
% 4.98/5.19 % Names : 0066_VEBT_Insert_00815_052383 [Des22]
% 4.98/5.19
% 4.98/5.19 % Status : Theorem
% 4.98/5.19 % Rating : 1.00 v8.1.0
% 4.98/5.19 % Syntax : Number of formulae : 11144 (6175 unt; 893 typ; 0 def)
% 4.98/5.19 % Number of atoms : 25886 (11863 equ; 0 cnn)
% 4.98/5.19 % Maximal formula atoms : 71 ( 2 avg)
% 4.98/5.19 % Number of connectives : 104359 (2549 ~; 552 |;1511 &;91255 @)
% 4.98/5.19 % ( 0 <=>;8492 =>; 0 <=; 0 <~>)
% 4.98/5.19 % Maximal formula depth : 39 ( 5 avg)
% 4.98/5.19 % Number of types : 72 ( 71 usr)
% 4.98/5.19 % Number of type conns : 3230 (3230 >; 0 *; 0 +; 0 <<)
% 4.98/5.19 % Number of symbols : 825 ( 822 usr; 59 con; 0-8 aty)
% 4.98/5.19 % Number of variables : 24105 (2023 ^;21501 !; 581 ?;24105 :)
% 4.98/5.19 % SPC : TH0_THM_EQU_NAR
% 4.98/5.19
% 4.98/5.19 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 4.98/5.19 % from the van Emde Boas Trees session in the Archive of Formal
% 4.98/5.19 % proofs -
% 4.98/5.19 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 4.98/5.19 % 2022-02-17 20:21:48.351
% 4.98/5.19 %------------------------------------------------------------------------------
% 4.98/5.19 % Could-be-implicit typings (71)
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% 4.98/5.19 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
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% 4.98/5.20 finite_card_set_nat: set_set_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 4.98/5.20 finite_card_char: set_char > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 4.98/5.20 finite3207457112153483333omplex: set_complex > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 4.98/5.20 finite_finite_int: set_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 4.98/5.20 finite_finite_nat: set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.98/5.20 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 4.98/5.20 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 4.98/5.20 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Ocomp_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Oid_001_Eo,type,
% 4.98/5.20 id_o: $o > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 4.98/5.20 id_nat: nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__String__Ochar,type,
% 4.98/5.20 inj_on_nat_char: ( nat > char ) > set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Oinj__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.98/5.20 inj_on_real_real: ( real > real ) > set_real > $o ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 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 ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 4.98/5.20 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 4.98/5.20 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.98/5.20 the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 4.98/5.20 gcd_Gcd_int: set_int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 4.98/5.20 gcd_Gcd_nat: set_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_GCD_Obezw,type,
% 4.98/5.20 bezw: nat > nat > product_prod_int_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_GCD_Obezw__rel,type,
% 4.98/5.20 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 4.98/5.20 gcd_gcd_int: int > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 4.98/5.20 gcd_gcd_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_GCD_Ogcd__nat__rel,type,
% 4.98/5.20 gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 abs_abs_Code_integer: code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 4.98/5.20 abs_abs_complex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 4.98/5.20 abs_abs_int: int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 4.98/5.20 abs_abs_rat: rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 4.98/5.20 abs_abs_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
% 4.98/5.20 minus_minus_complex: complex > complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
% 4.98/5.20 minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 4.98/5.20 minus_minus_int: int > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 4.98/5.20 minus_minus_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 4.98/5.20 minus_minus_rat: rat > rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 4.98/5.20 minus_minus_real: real > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.98/5.20 minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
% 4.98/5.20 minus_minus_set_int: set_int > set_int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 minus_minus_set_nat: set_nat > set_nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 minus_minus_set_real: set_real > set_real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.98/5.20 minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oone__class_Oone_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 one_one_Code_integer: code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex,type,
% 4.98/5.20 one_one_complex: complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oone__class_Oone_001t__Extended____Nat__Oenat,type,
% 4.98/5.20 one_on7984719198319812577d_enat: extended_enat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 4.98/5.20 one_one_int: int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 4.98/5.20 one_one_nat: nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oone__class_Oone_001t__Rat__Orat,type,
% 4.98/5.20 one_one_rat: rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal,type,
% 4.98/5.20 one_one_real: real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oplus__class_Oplus_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oplus__class_Oplus_001t__Complex__Ocomplex,type,
% 4.98/5.20 plus_plus_complex: complex > complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oplus__class_Oplus_001t__Extended____Nat__Oenat,type,
% 4.98/5.20 plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oplus__class_Oplus_001t__Int__Oint,type,
% 4.98/5.20 plus_plus_int: int > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat,type,
% 4.98/5.20 plus_plus_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oplus__class_Oplus_001t__Num__Onum,type,
% 4.98/5.20 plus_plus_num: num > num > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oplus__class_Oplus_001t__Rat__Orat,type,
% 4.98/5.20 plus_plus_rat: rat > rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal,type,
% 4.98/5.20 plus_plus_real: real > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Osgn__class_Osgn_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 sgn_sgn_Code_integer: code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Osgn__class_Osgn_001t__Int__Oint,type,
% 4.98/5.20 sgn_sgn_int: int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Osgn__class_Osgn_001t__Rat__Orat,type,
% 4.98/5.20 sgn_sgn_rat: rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Osgn__class_Osgn_001t__Real__Oreal,type,
% 4.98/5.20 sgn_sgn_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Otimes__class_Otimes_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex,type,
% 4.98/5.20 times_times_complex: complex > complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Otimes__class_Otimes_001t__Extended____Nat__Oenat,type,
% 4.98/5.20 times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Otimes__class_Otimes_001t__Int__Oint,type,
% 4.98/5.20 times_times_int: int > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat,type,
% 4.98/5.20 times_times_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Otimes__class_Otimes_001t__Num__Onum,type,
% 4.98/5.20 times_times_num: num > num > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Otimes__class_Otimes_001t__Rat__Orat,type,
% 4.98/5.20 times_times_rat: rat > rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal,type,
% 4.98/5.20 times_times_real: real > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 uminus1351360451143612070nteger: code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Complex__Ocomplex,type,
% 4.98/5.20 uminus1482373934393186551omplex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 4.98/5.20 uminus_uminus_int: int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Rat__Orat,type,
% 4.98/5.20 uminus_uminus_rat: rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Real__Oreal,type,
% 4.98/5.20 uminus_uminus_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.98/5.20 uminus8566677241136511917omplex: set_complex > set_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Int__Oint_J,type,
% 4.98/5.20 uminus1532241313380277803et_int: set_int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 uminus5710092332889474511et_nat: set_nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 uminus612125837232591019t_real: set_real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.98/5.20 uminus613421341184616069et_nat: set_set_nat > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ozero__class_Ozero_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 zero_z3403309356797280102nteger: code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex,type,
% 4.98/5.20 zero_zero_complex: complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ozero__class_Ozero_001t__Extended____Nat__Oenat,type,
% 4.98/5.20 zero_z5237406670263579293d_enat: extended_enat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 4.98/5.20 zero_zero_int: int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 4.98/5.20 zero_zero_nat: nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ozero__class_Ozero_001t__Rat__Orat,type,
% 4.98/5.20 zero_zero_rat: rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal,type,
% 4.98/5.20 zero_zero_real: real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 4.98/5.20 groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Groups__Big_Ocomm__monoid__add__class_Osum_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 4.98/5.20 groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).
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% 4.98/5.20 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 4.98/5.20 distinct_int: list_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 4.98/5.20 distinct_nat: list_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 4.98/5.20 linord2614967742042102400et_nat: set_nat > list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 4.98/5.20 cons_int: int > list_int > list_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 4.98/5.20 cons_nat: nat > list_nat > list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 4.98/5.20 nil_int: list_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 4.98/5.20 nil_nat: list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 4.98/5.20 hd_nat: list_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 4.98/5.20 set_o2: list_o > set_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 4.98/5.20 set_complex2: list_complex > set_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 4.98/5.20 set_int2: list_int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 4.98/5.20 set_nat2: list_nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 4.98/5.20 set_real2: list_real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 set_set_nat2: list_set_nat > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 4.98/5.20 tl_nat: list_nat > list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist__update_001_Eo,type,
% 4.98/5.20 list_update_o: list_o > nat > $o > list_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 4.98/5.20 list_update_complex: list_complex > nat > complex > list_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 4.98/5.20 list_update_int: list_int > nat > int > list_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 4.98/5.20 list_update_nat: list_nat > nat > nat > list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 4.98/5.20 list_update_real: list_real > nat > real > list_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001_Eo,type,
% 4.98/5.20 nth_o: list_o > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 4.98/5.20 nth_complex: list_complex > nat > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 4.98/5.20 nth_int: list_int > nat > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 4.98/5.20 nth_nat: list_nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 4.98/5.20 nth_num: list_num > nat > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 4.98/5.20 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 4.98/5.20 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 4.98/5.20 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 4.98/5.20 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 4.98/5.20 nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 4.98/5.20 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 4.98/5.20 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 4.98/5.20 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 4.98/5.20 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 4.98/5.20 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 4.98/5.20 nth_real: list_real > nat > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 nth_set_nat: list_set_nat > nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 4.98/5.20 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 4.98/5.20 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 4.98/5.20 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 4.98/5.20 produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 4.98/5.20 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 4.98/5.20 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 4.98/5.20 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 4.98/5.20 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 4.98/5.20 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 4.98/5.20 remdups_nat: list_nat > list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oreplicate_001_Eo,type,
% 4.98/5.20 replicate_o: nat > $o > list_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 4.98/5.20 replicate_complex: nat > complex > list_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 4.98/5.20 replicate_int: nat > int > list_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 4.98/5.20 replicate_nat: nat > nat > list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 4.98/5.20 replicate_real: nat > real > list_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 replicate_set_nat: nat > set_nat > list_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 4.98/5.20 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 4.98/5.20 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oupt,type,
% 4.98/5.20 upt: nat > nat > list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oupto,type,
% 4.98/5.20 upto: int > int > list_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oupto__aux,type,
% 4.98/5.20 upto_aux: int > int > list_int > list_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_List_Oupto__rel,type,
% 4.98/5.20 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_OSuc,type,
% 4.98/5.20 suc: nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.98/5.20 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 4.98/5.20 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 4.98/5.20 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 4.98/5.20 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Onat_Opred,type,
% 4.98/5.20 pred: nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 4.98/5.20 semiring_1_Nats_int: set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 semiri4939895301339042750nteger: nat > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 4.98/5.20 semiri8010041392384452111omplex: nat > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 4.98/5.20 semiri1314217659103216013at_int: nat > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 4.98/5.20 semiri1316708129612266289at_nat: nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 4.98/5.20 semiri681578069525770553at_rat: nat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 4.98/5.20 semiri5074537144036343181t_real: nat > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 4.98/5.20 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 4.98/5.20 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 4.98/5.20 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 4.98/5.20 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 4.98/5.20 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 4.98/5.20 size_size_list_o: list_o > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 4.98/5.20 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 4.98/5.20 size_s3451745648224563538omplex: list_complex > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 4.98/5.20 size_size_list_int: list_int > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 4.98/5.20 size_size_list_nat: list_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 4.98/5.20 size_size_list_num: list_num > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 4.98/5.20 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 4.98/5.20 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 4.98/5.20 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 4.98/5.20 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 4.98/5.20 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 4.98/5.20 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 4.98/5.20 size_size_list_real: list_real > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.98/5.20 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 4.98/5.20 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 4.98/5.20 size_size_num: num > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
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% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
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% 4.98/5.20 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 4.98/5.20 nat_list_encode: list_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 4.98/5.20 nat_list_encode_rel: list_nat > list_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 4.98/5.20 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 4.98/5.20 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 4.98/5.20 nat_prod_encode: product_prod_nat_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 4.98/5.20 nat_set_decode: nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 4.98/5.20 nat_set_encode: set_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Nat__Bijection_Otriangle,type,
% 4.98/5.20 nat_triangle: nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_NthRoot_Oroot,type,
% 4.98/5.20 root: nat > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_NthRoot_Osqrt,type,
% 4.98/5.20 sqrt: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_OBitM,type,
% 4.98/5.20 bitM: num > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oinc,type,
% 4.98/5.20 inc: num > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 4.98/5.20 neg_nu7009210354673126013omplex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 4.98/5.20 neg_numeral_dbl_rat: rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 4.98/5.20 neg_numeral_dbl_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 4.98/5.20 neg_nu6511756317524482435omplex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 4.98/5.20 neg_nu3179335615603231917ec_rat: rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 4.98/5.20 neg_nu6075765906172075777c_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 4.98/5.20 neg_nu5219082963157363817nc_rat: rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 4.98/5.20 neg_nu8295874005876285629c_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 4.98/5.20 neg_numeral_sub_int: num > num > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onum_OBit0,type,
% 4.98/5.20 bit0: num > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onum_OBit1,type,
% 4.98/5.20 bit1: num > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onum_OOne,type,
% 4.98/5.20 one: num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 4.98/5.20 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onum_Osize__num,type,
% 4.98/5.20 size_num: num > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onum__of__nat,type,
% 4.98/5.20 num_of_nat: nat > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 4.98/5.20 numeral_numeral_rat: num > rat ).
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% 4.98/5.20 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
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% 4.98/5.20
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% 4.98/5.20 thf(sy_c_Num_Opred__numeral,type,
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% 4.98/5.20
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
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% 4.98/5.20 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
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% 4.98/5.20 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
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% 4.98/5.20 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
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% 4.98/5.20 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
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% 4.98/5.20 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Num__Onum_J,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
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% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.98/5.20 ord_less_set_complex: set_complex > set_complex > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 4.98/5.20 ord_less_set_int: set_int > set_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 ord_less_set_nat: set_nat > set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Num__Onum_J,type,
% 4.98/5.20 ord_less_set_num: set_num > set_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Rat__Orat_J,type,
% 4.98/5.20 ord_less_set_rat: set_rat > set_rat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 ord_less_set_real: set_real > set_real > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.98/5.20 ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Code____Numeral__Ointeger_M_062_I_Eo_M_Eo_J_J,type,
% 4.98/5.20 ord_le2162486998276636481er_o_o: ( code_integer > $o > $o ) > ( code_integer > $o > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 4.98/5.20 ord_le4573692005234683329plex_o: ( complex > $o ) > ( complex > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 4.98/5.20 ord_le6741204236512500942_int_o: ( int > int > $o ) > ( int > int > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_Eo_J,type,
% 4.98/5.20 ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 4.98/5.20 ord_le2646555220125990790_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_062_It__Num__Onum_M_Eo_J_J,type,
% 4.98/5.20 ord_le3404735783095501756_num_o: ( nat > num > $o ) > ( nat > num > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_Eo_J,type,
% 4.98/5.20 ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J,type,
% 4.98/5.20 ord_le6124364862034508274_num_o: ( num > num > $o ) > ( num > num > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Real__Oreal_M_Eo_J,type,
% 4.98/5.20 ord_less_eq_real_o: ( real > $o ) > ( real > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 4.98/5.20 ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Extended____Nat__Oenat,type,
% 4.98/5.20 ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 4.98/5.20 ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 4.98/5.20 ord_less_eq_int: int > int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 4.98/5.20 ord_less_eq_nat: nat > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 4.98/5.20 ord_less_eq_num: num > num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 4.98/5.20 ord_less_eq_rat: rat > rat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 4.98/5.20 ord_less_eq_real: real > real > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 4.98/5.20 ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.98/5.20 ord_le211207098394363844omplex: set_complex > set_complex > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
% 4.98/5.20 ord_less_eq_set_int: set_int > set_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 4.98/5.20 ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
% 4.98/5.20 ord_less_eq_set_num: set_num > set_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_J,type,
% 4.98/5.20 ord_le8980329558974975238eger_o: set_Pr448751882837621926eger_o > set_Pr448751882837621926eger_o > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 4.98/5.20 ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.98/5.20 ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 4.98/5.20 ord_le8085105155179020875at_num: set_Pr6200539531224447659at_num > set_Pr6200539531224447659at_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J_J,type,
% 4.98/5.20 ord_le880128212290418581um_num: set_Pr8218934625190621173um_num > set_Pr8218934625190621173um_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Rat__Orat_J,type,
% 4.98/5.20 ord_less_eq_set_rat: set_rat > set_rat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 ord_less_eq_set_real: set_real > set_real > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 4.98/5.20 ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 4.98/5.20 ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 ord_max_Code_integer: code_integer > code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
% 4.98/5.20 ord_max_int: int > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
% 4.98/5.20 ord_max_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
% 4.98/5.20 ord_max_num: num > num > num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
% 4.98/5.20 ord_max_rat: rat > rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
% 4.98/5.20 ord_max_real: real > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Int__Oint_J,type,
% 4.98/5.20 ord_max_set_int: set_int > set_int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 ord_max_set_nat: set_nat > set_nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 ord_max_set_real: set_real > set_real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oord__class_Omin_001t__Nat__Onat,type,
% 4.98/5.20 ord_min_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 4.98/5.20 order_Greatest_nat: ( nat > $o ) > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 order_mono_nat_nat: ( nat > nat ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 4.98/5.20 top_top_set_o: set_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Int__Oint_J,type,
% 4.98/5.20 top_top_set_int: set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 top_top_set_nat: set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 4.98/5.20 top_to1996260823553986621t_unit: set_Product_unit ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 top_top_set_real: set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
% 4.98/5.20 top_top_set_char: set_char ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 power_8256067586552552935nteger: code_integer > nat > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
% 4.98/5.20 power_power_complex: complex > nat > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 4.98/5.20 power_power_int: int > nat > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
% 4.98/5.20 power_power_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
% 4.98/5.20 power_power_rat: rat > nat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
% 4.98/5.20 power_power_real: real > nat > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 4.98/5.20 produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Num__Onum_Mt__Num__Onum_J_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J_J,type,
% 4.98/5.20 produc851828971589881931at_num: ( nat > num > num ) > produc2963631642982155120at_num > produc3368934014287244435at_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
% 4.98/5.20 product_Pair_o_o: $o > $o > product_prod_o_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001_Eo_001t__Int__Oint,type,
% 4.98/5.20 product_Pair_o_int: $o > int > product_prod_o_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
% 4.98/5.20 product_Pair_o_nat: $o > nat > product_prod_o_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001_Eo,type,
% 4.98/5.20 produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 4.98/5.20 product_Pair_int_int: int > int > product_prod_int_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 4.98/5.20 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.98/5.20 produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 4.98/5.20 produc1195630363706982562at_num: nat > product_prod_nat_num > produc2963631642982155120at_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 4.98/5.20 product_Pair_num_num: num > num > product_prod_num_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 4.98/5.20 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 4.98/5.20 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 4.98/5.20 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_OSigma_001t__Nat__Onat_001t__Nat__Onat,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001_Eo,type,
% 4.98/5.20 produc7828578312038201481er_o_o: ( code_integer > $o > $o ) > produc6271795597528267376eger_o > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.98/5.20 produc1043322548047392435omplex: ( code_integer > $o > set_complex ) > produc6271795597528267376eger_o > set_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Int__Oint_J,type,
% 4.98/5.20 produc1253318751659547953et_int: ( code_integer > $o > set_int ) > produc6271795597528267376eger_o > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 produc5431169771168744661et_nat: ( code_integer > $o > set_nat ) > produc6271795597528267376eger_o > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001_Eo_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 produc242741666403216561t_real: ( code_integer > $o > set_real ) > produc6271795597528267376eger_o > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 4.98/5.20 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 4.98/5.20 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 4.98/5.20 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 4.98/5.20 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 4.98/5.20 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 4.98/5.20 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 4.98/5.20 produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 4.98/5.20 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 4.98/5.20
% 4.98/5.20 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,
% 4.98/5.20 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 4.98/5.20 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 4.98/5.20 produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001_Eo,type,
% 4.98/5.20 produc4927758841916487424_num_o: ( nat > num > $o ) > product_prod_nat_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 4.98/5.20 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.98/5.20 produc6231982587499038204omplex: ( nat > num > set_complex ) > product_prod_nat_num > set_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 produc1435849484188172666t_real: ( nat > num > set_real ) > product_prod_nat_num > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001_Eo,type,
% 4.98/5.20 produc5703948589228662326_num_o: ( num > num > $o ) > product_prod_num_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 4.98/5.20 produc2866383454006189126omplex: ( num > num > set_complex ) > product_prod_num_num > set_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Int__Oint_J,type,
% 4.98/5.20 produc6406642877701697732et_int: ( num > num > set_int ) > product_prod_num_num > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 produc1361121860356118632et_nat: ( num > num > set_nat ) > product_prod_num_num > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Num__Onum_001t__Num__Onum_001t__Set__Oset_It__Real__Oreal_J,type,
% 4.98/5.20 produc8296048397933160132t_real: ( num > num > set_real ) > product_prod_num_num > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 4.98/5.20 product_fst_int_int: product_prod_int_int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 4.98/5.20 product_snd_int_int: product_prod_int_int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rat_OFract,type,
% 4.98/5.20 fract: int > int > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rat_OFrct,type,
% 4.98/5.20 frct: product_prod_int_int > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 4.98/5.20 field_5140801741446780682s_real: set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rat_Onormalize,type,
% 4.98/5.20 normalize: product_prod_int_int > product_prod_int_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rat_Oof__int,type,
% 4.98/5.20 of_int: int > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rat_Oquotient__of,type,
% 4.98/5.20 quotient_of: rat > product_prod_int_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 4.98/5.20 real_V2521375963428798218omplex: set_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.98/5.20 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 4.98/5.20 real_V1022390504157884413omplex: complex > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 4.98/5.20 real_V7735802525324610683m_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 4.98/5.20 real_V4546457046886955230omplex: real > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 4.98/5.20 real_V2046097035970521341omplex: real > complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 4.98/5.20 real_V1485227260804924795R_real: real > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 4.98/5.20 divide1717551699836669952omplex: complex > complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
% 4.98/5.20 divide_divide_int: int > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 4.98/5.20 divide_divide_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 4.98/5.20 divide_divide_rat: rat > rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 4.98/5.20 divide_divide_real: real > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 4.98/5.20 dvd_dvd_complex: complex > complex > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 4.98/5.20 dvd_dvd_int: int > int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 4.98/5.20 dvd_dvd_nat: nat > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 4.98/5.20 dvd_dvd_rat: rat > rat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 4.98/5.20 dvd_dvd_real: real > real > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 4.98/5.20 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 4.98/5.20 modulo_modulo_int: int > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 4.98/5.20 modulo_modulo_nat: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 4.98/5.20 zero_n1201886186963655149omplex: $o > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 4.98/5.20 zero_n2684676970156552555ol_int: $o > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
% 4.98/5.20 zero_n2687167440665602831ol_nat: $o > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 4.98/5.20 zero_n2052037380579107095ol_rat: $o > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 4.98/5.20 zero_n3304061248610475627l_real: $o > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osuminf_001t__Int__Oint,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osuminf_001t__Nat__Onat,type,
% 4.98/5.20 suminf_nat: ( nat > nat ) > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osummable_001t__Complex__Ocomplex,type,
% 4.98/5.20 summable_complex: ( nat > complex ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osummable_001t__Int__Oint,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osummable_001t__Nat__Onat,type,
% 4.98/5.20 summable_nat: ( nat > nat ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 4.98/5.20 summable_real: ( nat > real ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osums_001t__Int__Oint,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
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% 4.98/5.20
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
% 4.98/5.20 collect_list_nat: ( list_nat > $o ) > set_list_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
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% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Num__Onum,type,
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% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.98/5.20 collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
% 4.98/5.20 collect_rat: ( rat > $o ) > set_rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Real__Oreal,type,
% 4.98/5.20 collect_real: ( real > $o ) > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 collect_set_nat: ( set_nat > $o ) > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 4.98/5.20 pow_nat: set_nat > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 4.98/5.20 image_int_int: ( int > int ) > set_int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 4.98/5.20 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 4.98/5.20 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 4.98/5.20 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.98/5.20 image_real_real: ( real > real ) > set_real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 4.98/5.20 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 4.98/5.20 insert_complex: complex > set_complex > set_complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 4.98/5.20 insert_int: int > set_int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 4.98/5.20 insert_nat: nat > set_nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 4.98/5.20 insert_real: real > set_real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 4.98/5.20 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 4.98/5.20 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 4.98/5.20 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 4.98/5.20 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 4.98/5.20 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 4.98/5.20 set_or1266510415728281911st_int: int > int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 4.98/5.20 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 4.98/5.20 set_or7049704709247886629st_num: num > num > set_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 4.98/5.20 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 4.98/5.20 set_or1222579329274155063t_real: real > real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 4.98/5.20 set_or4662586982721622107an_int: int > int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 4.98/5.20 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 4.98/5.20 set_ord_atLeast_nat: nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 4.98/5.20 set_ord_atLeast_real: real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 4.98/5.20 set_ord_atMost_int: int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 4.98/5.20 set_ord_atMost_nat: nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 4.98/5.20 set_ord_atMost_num: num > set_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
% 4.98/5.20 set_ord_atMost_rat: rat > set_rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 4.98/5.20 set_ord_atMost_real: real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 set_or4236626031148496127et_nat: set_nat > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 4.98/5.20 set_or6656581121297822940st_int: int > int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 4.98/5.20 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 4.98/5.20 set_or5832277885323065728an_int: int > int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 4.98/5.20 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 4.98/5.20 set_or1633881224788618240n_real: real > real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 4.98/5.20 set_or1210151606488870762an_nat: nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 4.98/5.20 set_or5849166863359141190n_real: real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 4.98/5.20 set_ord_lessThan_int: int > set_int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 4.98/5.20 set_ord_lessThan_nat: nat > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 4.98/5.20 set_ord_lessThan_num: num > set_num ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 4.98/5.20 set_ord_lessThan_rat: rat > set_rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 4.98/5.20 set_or5984915006950818249n_real: real > set_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_String_Oascii__of,type,
% 4.98/5.20 ascii_of: char > char ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_String_Ochar_OChar,type,
% 4.98/5.20 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_String_Ochar_Osize__char,type,
% 4.98/5.20 size_char: char > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 4.98/5.20 comm_s629917340098488124ar_nat: char > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_String_Ointeger__of__char,type,
% 4.98/5.20 integer_of_char: char > code_integer ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 4.98/5.20 unique3096191561947761185of_nat: nat > char ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.98/5.20 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 4.98/5.20 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 4.98/5.20 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 4.98/5.20 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 4.98/5.20 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 4.98/5.20 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 4.98/5.20 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 topolo7278393974255667507et_nat: ( nat > set_nat ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 4.98/5.20 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 4.98/5.20 topolo2815343760600316023s_real: real > filter_real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 4.98/5.20 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oarccos,type,
% 4.98/5.20 arccos: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 4.98/5.20 arcosh_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oarcsin,type,
% 4.98/5.20 arcsin: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oarctan,type,
% 4.98/5.20 arctan: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 4.98/5.20 arsinh_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 4.98/5.20 artanh_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 4.98/5.20 cos_complex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 4.98/5.20 cos_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Ocos__coeff,type,
% 4.98/5.20 cos_coeff: nat > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 4.98/5.20 cosh_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
% 4.98/5.20 cot_complex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 4.98/5.20 cot_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 4.98/5.20 diffs_complex: ( nat > complex ) > nat > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 4.98/5.20 diffs_int: ( nat > int ) > nat > int ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Odiffs_001t__Rat__Orat,type,
% 4.98/5.20 diffs_rat: ( nat > rat ) > nat > rat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 4.98/5.20 diffs_real: ( nat > real ) > nat > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 4.98/5.20 exp_complex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 4.98/5.20 exp_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 4.98/5.20 ln_ln_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Olog,type,
% 4.98/5.20 log: real > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Opi,type,
% 4.98/5.20 pi: real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 4.98/5.20 powr_real: real > real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 4.98/5.20 sin_complex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 4.98/5.20 sin_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Osin__coeff,type,
% 4.98/5.20 sin_coeff: nat > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 4.98/5.20 sinh_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 4.98/5.20 tan_complex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 4.98/5.20 tan_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 4.98/5.20 tanh_complex: complex > complex ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 4.98/5.20 tanh_real: real > real ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 4.98/5.20 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 4.98/5.20 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 4.98/5.20 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 4.98/5.20 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 4.98/5.20 vEBT_VEBT_high: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 4.98/5.20 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 4.98/5.20 vEBT_VEBT_low: nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 4.98/5.20 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 4.98/5.20 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 4.98/5.20 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 4.98/5.20 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 4.98/5.20 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 4.98/5.20 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 4.98/5.20 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 4.98/5.20 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 4.98/5.20 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 4.98/5.20 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 4.98/5.20 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 4.98/5.20 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 4.98/5.20 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 4.98/5.20 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 4.98/5.20 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 4.98/5.20 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 4.98/5.20 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 4.98/5.20 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 4.98/5.20 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.98/5.20 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.98/5.20 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 4.98/5.20 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001_Eo,type,
% 4.98/5.20 member_o: $o > set_o > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 4.98/5.20 member_complex: complex > set_complex > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Int__Oint,type,
% 4.98/5.20 member_int: int > set_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 4.98/5.20 member_list_nat: list_nat > set_list_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Nat__Onat,type,
% 4.98/5.20 member_nat: nat > set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Num__Onum,type,
% 4.98/5.20 member_num: num > set_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 4.98/5.20 member1379723562493234055eger_o: produc6271795597528267376eger_o > set_Pr448751882837621926eger_o > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 4.98/5.20 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 4.98/5.20 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Num__Onum_J,type,
% 4.98/5.20 member9148766508732265716at_num: product_prod_nat_num > set_Pr6200539531224447659at_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 4.98/5.20 member7279096912039735102um_num: product_prod_num_num > set_Pr8218934625190621173um_num > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Rat__Orat,type,
% 4.98/5.20 member_rat: rat > set_rat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Real__Oreal,type,
% 4.98/5.20 member_real: real > set_real > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 4.98/5.20 member_set_nat: set_nat > set_set_nat > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 4.98/5.20 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_deg____,type,
% 4.98/5.20 deg: nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_m____,type,
% 4.98/5.20 m: nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_ma____,type,
% 4.98/5.20 ma: nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_mi____,type,
% 4.98/5.20 mi: nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_na____,type,
% 4.98/5.20 na: nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_summary____,type,
% 4.98/5.20 summary: vEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_treeList____,type,
% 4.98/5.20 treeList: list_VEBT_VEBT ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_xa____,type,
% 4.98/5.20 xa: nat ).
% 4.98/5.20
% 4.98/5.20 thf(sy_v_ya____,type,
% 4.98/5.20 ya: nat ).
% 4.98/5.20
% 4.98/5.20 % Relevant facts (10209)
% 4.98/5.20 thf(fact_0__C5_Ohyps_C_I3_J,axiom,
% 4.98/5.20 ( m
% 4.98/5.20 = ( suc @ na ) ) ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(3)
% 4.98/5.20 thf(fact_1_both__member__options__def,axiom,
% 4.98/5.20 ( vEBT_V8194947554948674370ptions
% 4.98/5.20 = ( ^ [T: vEBT_VEBT,X: nat] :
% 4.98/5.20 ( ( vEBT_V5719532721284313246member @ T @ X )
% 4.98/5.20 | ( vEBT_VEBT_membermima @ T @ X ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % both_member_options_def
% 4.98/5.20 thf(fact_2_valid__0__not,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT] :
% 4.98/5.20 ~ ( vEBT_invar_vebt @ T2 @ zero_zero_nat ) ).
% 4.98/5.20
% 4.98/5.20 % valid_0_not
% 4.98/5.20 thf(fact_3_valid__tree__deg__neq__0,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT] :
% 4.98/5.20 ~ ( vEBT_invar_vebt @ T2 @ zero_zero_nat ) ).
% 4.98/5.20
% 4.98/5.20 % valid_tree_deg_neq_0
% 4.98/5.20 thf(fact_4_even__odd__cases,axiom,
% 4.98/5.20 ! [X2: nat] :
% 4.98/5.20 ( ! [N: nat] :
% 4.98/5.20 ( X2
% 4.98/5.20 != ( plus_plus_nat @ N @ N ) )
% 4.98/5.20 => ~ ! [N: nat] :
% 4.98/5.20 ( X2
% 4.98/5.20 != ( plus_plus_nat @ N @ ( suc @ N ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % even_odd_cases
% 4.98/5.20 thf(fact_5__C5_Ohyps_C_I1_J,axiom,
% 4.98/5.20 vEBT_invar_vebt @ summary @ m ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(1)
% 4.98/5.20 thf(fact_6_deg__deg__n,axiom,
% 4.98/5.20 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N2 )
% 4.98/5.20 => ( Deg = N2 ) ) ).
% 4.98/5.20
% 4.98/5.20 % deg_deg_n
% 4.98/5.20 thf(fact_7__C5_Ohyps_C_I7_J,axiom,
% 4.98/5.20 ord_less_eq_nat @ mi @ ma ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(7)
% 4.98/5.20 thf(fact_8__C5_Ohyps_C_I4_J,axiom,
% 4.98/5.20 ( deg
% 4.98/5.20 = ( plus_plus_nat @ na @ m ) ) ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(4)
% 4.98/5.20 thf(fact_9_False,axiom,
% 4.98/5.20 ( ( vEBT_VEBT_high @ mi @ na )
% 4.98/5.20 != ( vEBT_VEBT_high @ ya @ na ) ) ).
% 4.98/5.20
% 4.98/5.20 % False
% 4.98/5.20 thf(fact_10__C5_Ohyps_C_I6_J,axiom,
% 4.98/5.20 ( ( mi = ma )
% 4.98/5.20 => ! [X3: vEBT_VEBT] :
% 4.98/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 4.98/5.20 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(6)
% 4.98/5.20 thf(fact_11_both__member__options__equiv__member,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT,N2: nat,X2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 4.98/5.20 => ( ( vEBT_V8194947554948674370ptions @ T2 @ X2 )
% 4.98/5.20 = ( vEBT_vebt_member @ T2 @ X2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % both_member_options_equiv_member
% 4.98/5.20 thf(fact_12_valid__member__both__member__options,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT,N2: nat,X2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 4.98/5.20 => ( ( vEBT_V8194947554948674370ptions @ T2 @ X2 )
% 4.98/5.20 => ( vEBT_vebt_member @ T2 @ X2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % valid_member_both_member_options
% 4.98/5.20 thf(fact_13__C000_C,axiom,
% 4.98/5.20 vEBT_vebt_member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ya @ na ) ) @ ( vEBT_VEBT_low @ ya @ na ) ).
% 4.98/5.20
% 4.98/5.20 % "000"
% 4.98/5.20 thf(fact_14_deg__SUcn__Node,axiom,
% 4.98/5.20 ! [Tree: vEBT_VEBT,N2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N2 ) ) )
% 4.98/5.20 => ? [Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 4.98/5.20 ( Tree
% 4.98/5.20 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N2 ) ) @ TreeList2 @ S ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % deg_SUcn_Node
% 4.98/5.20 thf(fact_15__092_060open_062x_A_060_Ami_092_060close_062,axiom,
% 4.98/5.20 ord_less_nat @ xa @ mi ).
% 4.98/5.20
% 4.98/5.20 % \<open>x < mi\<close>
% 4.98/5.20 thf(fact_16__C001_C,axiom,
% 4.98/5.20 ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ya @ na ) ) @ na )
% 4.98/5.20 & ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ya @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % "001"
% 4.98/5.20 thf(fact_17_mi__eq__ma__no__ch,axiom,
% 4.98/5.20 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg )
% 4.98/5.20 => ( ( Mi = Ma )
% 4.98/5.20 => ( ! [X3: vEBT_VEBT] :
% 4.98/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.20 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) )
% 4.98/5.20 & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % mi_eq_ma_no_ch
% 4.98/5.20 thf(fact_18__C5_Oprems_C_I3_J,axiom,
% 4.98/5.20 vEBT_vebt_member @ ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa ) @ ya ).
% 4.98/5.20
% 4.98/5.20 % "5.prems"(3)
% 4.98/5.20 thf(fact_19__C5_Ohyps_C_I8_J,axiom,
% 4.98/5.20 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(8)
% 4.98/5.20 thf(fact_20__C5_Oprems_C_I2_J,axiom,
% 4.98/5.20 ord_less_nat @ ya @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 4.98/5.20
% 4.98/5.20 % "5.prems"(2)
% 4.98/5.20 thf(fact_21__C004_C,axiom,
% 4.98/5.20 ( ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ya @ na ) ) @ ( vEBT_VEBT_low @ ya @ na ) )
% 4.98/5.20 => ( vEBT_V5719532721284313246member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ ya ) ) ).
% 4.98/5.20
% 4.98/5.20 % "004"
% 4.98/5.20 thf(fact_22_not__min__Null__member,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT] :
% 4.98/5.20 ( ~ ( vEBT_VEBT_minNull @ T2 )
% 4.98/5.20 => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T2 @ X_12 ) ) ).
% 4.98/5.20
% 4.98/5.20 % not_min_Null_member
% 4.98/5.20 thf(fact_23__C5_Ohyps_C_I5_J,axiom,
% 4.98/5.20 ! [I: nat] :
% 4.98/5.20 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.98/5.20 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X4 ) )
% 4.98/5.20 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(5)
% 4.98/5.20 thf(fact_24__C5_Oprems_C_I1_J,axiom,
% 4.98/5.20 ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 4.98/5.20
% 4.98/5.20 % "5.prems"(1)
% 4.98/5.20 thf(fact_25_VEBT_Oinject_I1_J,axiom,
% 4.98/5.20 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 4.98/5.20 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 4.98/5.20 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 4.98/5.20 = ( ( X11 = Y11 )
% 4.98/5.20 & ( X12 = Y12 )
% 4.98/5.20 & ( X13 = Y13 )
% 4.98/5.20 & ( X14 = Y14 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % VEBT.inject(1)
% 4.98/5.20 thf(fact_26_option_Oinject,axiom,
% 4.98/5.20 ! [X22: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 4.98/5.20 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 4.98/5.20 = ( some_P7363390416028606310at_nat @ Y2 ) )
% 4.98/5.20 = ( X22 = Y2 ) ) ).
% 4.98/5.20
% 4.98/5.20 % option.inject
% 4.98/5.20 thf(fact_27_option_Oinject,axiom,
% 4.98/5.20 ! [X22: num,Y2: num] :
% 4.98/5.20 ( ( ( some_num @ X22 )
% 4.98/5.20 = ( some_num @ Y2 ) )
% 4.98/5.20 = ( X22 = Y2 ) ) ).
% 4.98/5.20
% 4.98/5.20 % option.inject
% 4.98/5.20 thf(fact_28_prod_Oinject,axiom,
% 4.98/5.20 ! [X1: code_integer,X22: $o,Y1: code_integer,Y2: $o] :
% 4.98/5.20 ( ( ( produc6677183202524767010eger_o @ X1 @ X22 )
% 4.98/5.20 = ( produc6677183202524767010eger_o @ Y1 @ Y2 ) )
% 4.98/5.20 = ( ( X1 = Y1 )
% 4.98/5.20 & ( X22 = Y2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % prod.inject
% 4.98/5.20 thf(fact_29_prod_Oinject,axiom,
% 4.98/5.20 ! [X1: num,X22: num,Y1: num,Y2: num] :
% 4.98/5.20 ( ( ( product_Pair_num_num @ X1 @ X22 )
% 4.98/5.20 = ( product_Pair_num_num @ Y1 @ Y2 ) )
% 4.98/5.20 = ( ( X1 = Y1 )
% 4.98/5.20 & ( X22 = Y2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % prod.inject
% 4.98/5.20 thf(fact_30_prod_Oinject,axiom,
% 4.98/5.20 ! [X1: nat,X22: num,Y1: nat,Y2: num] :
% 4.98/5.20 ( ( ( product_Pair_nat_num @ X1 @ X22 )
% 4.98/5.20 = ( product_Pair_nat_num @ Y1 @ Y2 ) )
% 4.98/5.20 = ( ( X1 = Y1 )
% 4.98/5.20 & ( X22 = Y2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % prod.inject
% 4.98/5.20 thf(fact_31_prod_Oinject,axiom,
% 4.98/5.20 ! [X1: nat,X22: nat,Y1: nat,Y2: nat] :
% 4.98/5.20 ( ( ( product_Pair_nat_nat @ X1 @ X22 )
% 4.98/5.20 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 4.98/5.20 = ( ( X1 = Y1 )
% 4.98/5.20 & ( X22 = Y2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % prod.inject
% 4.98/5.20 thf(fact_32_prod_Oinject,axiom,
% 4.98/5.20 ! [X1: int,X22: int,Y1: int,Y2: int] :
% 4.98/5.20 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 4.98/5.20 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 4.98/5.20 = ( ( X1 = Y1 )
% 4.98/5.20 & ( X22 = Y2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % prod.inject
% 4.98/5.20 thf(fact_33_old_Oprod_Oinject,axiom,
% 4.98/5.20 ! [A: code_integer,B: $o,A2: code_integer,B2: $o] :
% 4.98/5.20 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 4.98/5.20 = ( produc6677183202524767010eger_o @ A2 @ B2 ) )
% 4.98/5.20 = ( ( A = A2 )
% 4.98/5.20 & ( B = B2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % old.prod.inject
% 4.98/5.20 thf(fact_34_old_Oprod_Oinject,axiom,
% 4.98/5.20 ! [A: num,B: num,A2: num,B2: num] :
% 4.98/5.20 ( ( ( product_Pair_num_num @ A @ B )
% 4.98/5.20 = ( product_Pair_num_num @ A2 @ B2 ) )
% 4.98/5.20 = ( ( A = A2 )
% 4.98/5.20 & ( B = B2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % old.prod.inject
% 4.98/5.20 thf(fact_35_old_Oprod_Oinject,axiom,
% 4.98/5.20 ! [A: nat,B: num,A2: nat,B2: num] :
% 4.98/5.20 ( ( ( product_Pair_nat_num @ A @ B )
% 4.98/5.20 = ( product_Pair_nat_num @ A2 @ B2 ) )
% 4.98/5.20 = ( ( A = A2 )
% 4.98/5.20 & ( B = B2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % old.prod.inject
% 4.98/5.20 thf(fact_36_old_Oprod_Oinject,axiom,
% 4.98/5.20 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 4.98/5.20 ( ( ( product_Pair_nat_nat @ A @ B )
% 4.98/5.20 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 4.98/5.20 = ( ( A = A2 )
% 4.98/5.20 & ( B = B2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % old.prod.inject
% 4.98/5.20 thf(fact_37_old_Oprod_Oinject,axiom,
% 4.98/5.20 ! [A: int,B: int,A2: int,B2: int] :
% 4.98/5.20 ( ( ( product_Pair_int_int @ A @ B )
% 4.98/5.20 = ( product_Pair_int_int @ A2 @ B2 ) )
% 4.98/5.20 = ( ( A = A2 )
% 4.98/5.20 & ( B = B2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % old.prod.inject
% 4.98/5.20 thf(fact_38__C5_Ohyps_C_I2_J,axiom,
% 4.98/5.20 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 4.98/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(2)
% 4.98/5.20 thf(fact_39_member__valid__both__member__options,axiom,
% 4.98/5.20 ! [Tree: vEBT_VEBT,N2: nat,X2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ Tree @ N2 )
% 4.98/5.20 => ( ( vEBT_vebt_member @ Tree @ X2 )
% 4.98/5.20 => ( ( vEBT_V5719532721284313246member @ Tree @ X2 )
% 4.98/5.20 | ( vEBT_VEBT_membermima @ Tree @ X2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % member_valid_both_member_options
% 4.98/5.20 thf(fact_40_min__Null__member,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT,X2: nat] :
% 4.98/5.20 ( ( vEBT_VEBT_minNull @ T2 )
% 4.98/5.20 => ~ ( vEBT_vebt_member @ T2 @ X2 ) ) ).
% 4.98/5.20
% 4.98/5.20 % min_Null_member
% 4.98/5.20 thf(fact_41_deg__not__0,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT,N2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 4.98/5.20 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 4.98/5.20
% 4.98/5.20 % deg_not_0
% 4.98/5.20 thf(fact_42_inthall,axiom,
% 4.98/5.20 ! [Xs: list_complex,P: complex > $o,N2: nat] :
% 4.98/5.20 ( ! [X5: complex] :
% 4.98/5.20 ( ( member_complex @ X5 @ ( set_complex2 @ Xs ) )
% 4.98/5.20 => ( P @ X5 ) )
% 4.98/5.20 => ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.98/5.20 => ( P @ ( nth_complex @ Xs @ N2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % inthall
% 4.98/5.20 thf(fact_43_inthall,axiom,
% 4.98/5.20 ! [Xs: list_real,P: real > $o,N2: nat] :
% 4.98/5.20 ( ! [X5: real] :
% 4.98/5.20 ( ( member_real @ X5 @ ( set_real2 @ Xs ) )
% 4.98/5.20 => ( P @ X5 ) )
% 4.98/5.20 => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 4.98/5.20 => ( P @ ( nth_real @ Xs @ N2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % inthall
% 4.98/5.20 thf(fact_44_inthall,axiom,
% 4.98/5.20 ! [Xs: list_set_nat,P: set_nat > $o,N2: nat] :
% 4.98/5.20 ( ! [X5: set_nat] :
% 4.98/5.20 ( ( member_set_nat @ X5 @ ( set_set_nat2 @ Xs ) )
% 4.98/5.20 => ( P @ X5 ) )
% 4.98/5.20 => ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.98/5.20 => ( P @ ( nth_set_nat @ Xs @ N2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % inthall
% 4.98/5.20 thf(fact_45_inthall,axiom,
% 4.98/5.20 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 4.98/5.20 ( ! [X5: vEBT_VEBT] :
% 4.98/5.20 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.98/5.20 => ( P @ X5 ) )
% 4.98/5.20 => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.20 => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % inthall
% 4.98/5.20 thf(fact_46_inthall,axiom,
% 4.98/5.20 ! [Xs: list_o,P: $o > $o,N2: nat] :
% 4.98/5.20 ( ! [X5: $o] :
% 4.98/5.20 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 4.98/5.20 => ( P @ X5 ) )
% 4.98/5.20 => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 4.98/5.20 => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % inthall
% 4.98/5.20 thf(fact_47_inthall,axiom,
% 4.98/5.20 ! [Xs: list_nat,P: nat > $o,N2: nat] :
% 4.98/5.20 ( ! [X5: nat] :
% 4.98/5.20 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 4.98/5.20 => ( P @ X5 ) )
% 4.98/5.20 => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.20 => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % inthall
% 4.98/5.20 thf(fact_48_inthall,axiom,
% 4.98/5.20 ! [Xs: list_int,P: int > $o,N2: nat] :
% 4.98/5.20 ( ! [X5: int] :
% 4.98/5.20 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 4.98/5.20 => ( P @ X5 ) )
% 4.98/5.20 => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 4.98/5.20 => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % inthall
% 4.98/5.20 thf(fact_49_bit__split__inv,axiom,
% 4.98/5.20 ! [X2: nat,D: nat] :
% 4.98/5.20 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X2 @ D ) @ ( vEBT_VEBT_low @ X2 @ D ) @ D )
% 4.98/5.20 = X2 ) ).
% 4.98/5.20
% 4.98/5.20 % bit_split_inv
% 4.98/5.20 thf(fact_50_xyprop,axiom,
% 4.98/5.20 ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.98/5.20 & ( ord_less_nat @ ( vEBT_VEBT_high @ ya @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % xyprop
% 4.98/5.20 thf(fact_51_member__correct,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT,N2: nat,X2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 4.98/5.20 => ( ( vEBT_vebt_member @ T2 @ X2 )
% 4.98/5.20 = ( member_nat @ X2 @ ( vEBT_set_vebt @ T2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % member_correct
% 4.98/5.20 thf(fact_52__C5_OIH_C_I1_J,axiom,
% 4.98/5.20 ! [X3: vEBT_VEBT] :
% 4.98/5.20 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ treeList ) )
% 4.98/5.20 => ( ( vEBT_invar_vebt @ X3 @ na )
% 4.98/5.20 & ! [Xa: nat] :
% 4.98/5.20 ( ( ord_less_nat @ Xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 4.98/5.20 => ! [Xb: nat] :
% 4.98/5.20 ( ( ord_less_nat @ Xb @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 4.98/5.20 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ X3 @ Xa ) @ Xb )
% 4.98/5.20 => ( ( vEBT_vebt_member @ X3 @ Xb )
% 4.98/5.20 | ( Xa = Xb ) ) ) ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % "5.IH"(1)
% 4.98/5.20 thf(fact_53__C00_C,axiom,
% 4.98/5.20 ( ( deg
% 4.98/5.20 = ( plus_plus_nat @ na @ m ) )
% 4.98/5.20 & ( ord_less_eq_nat @ zero_zero_nat @ na )
% 4.98/5.20 & ( ( suc @ na )
% 4.98/5.20 = m )
% 4.98/5.20 & ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
% 4.98/5.20 & ( ( size_s6755466524823107622T_VEBT @ treeList )
% 4.98/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.98/5.20 & ( ord_less_eq_nat @ one_one_nat @ na ) ) ).
% 4.98/5.20
% 4.98/5.20 % "00"
% 4.98/5.20 thf(fact_54_high__bound__aux,axiom,
% 4.98/5.20 ! [Ma: nat,N2: nat,M: nat] :
% 4.98/5.20 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 4.98/5.20 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % high_bound_aux
% 4.98/5.20 thf(fact_55_member__bound,axiom,
% 4.98/5.20 ! [Tree: vEBT_VEBT,X2: nat,N2: nat] :
% 4.98/5.20 ( ( vEBT_vebt_member @ Tree @ X2 )
% 4.98/5.20 => ( ( vEBT_invar_vebt @ Tree @ N2 )
% 4.98/5.20 => ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % member_bound
% 4.98/5.20 thf(fact_56_insert__simp__mima,axiom,
% 4.98/5.20 ! [X2: nat,Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 4.98/5.20 ( ( ( X2 = Mi )
% 4.98/5.20 | ( X2 = Ma ) )
% 4.98/5.20 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.98/5.20 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 4.98/5.20 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % insert_simp_mima
% 4.98/5.20 thf(fact_57_valid__insert__both__member__options__pres,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT,N2: nat,X2: nat,Y: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 4.98/5.20 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.20 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.20 => ( ( vEBT_V8194947554948674370ptions @ T2 @ X2 )
% 4.98/5.20 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T2 @ Y ) @ X2 ) ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % valid_insert_both_member_options_pres
% 4.98/5.20 thf(fact_58_valid__insert__both__member__options__add,axiom,
% 4.98/5.20 ! [T2: vEBT_VEBT,N2: nat,X2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 4.98/5.20 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.20 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T2 @ X2 ) @ X2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % valid_insert_both_member_options_add
% 4.98/5.20 thf(fact_59__C5_Ohyps_C_I9_J,axiom,
% 4.98/5.20 ( ( mi != ma )
% 4.98/5.20 => ! [I: nat] :
% 4.98/5.20 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.98/5.20 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 4.98/5.20 = I )
% 4.98/5.20 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 4.98/5.20 & ! [X3: nat] :
% 4.98/5.20 ( ( ( ( vEBT_VEBT_high @ X3 @ na )
% 4.98/5.20 = I )
% 4.98/5.20 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X3 @ na ) ) )
% 4.98/5.20 => ( ( ord_less_nat @ mi @ X3 )
% 4.98/5.20 & ( ord_less_eq_nat @ X3 @ ma ) ) ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % "5.hyps"(9)
% 4.98/5.20 thf(fact_60_mem__Collect__eq,axiom,
% 4.98/5.20 ! [A: complex,P: complex > $o] :
% 4.98/5.20 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 4.98/5.20 = ( P @ A ) ) ).
% 4.98/5.20
% 4.98/5.20 % mem_Collect_eq
% 4.98/5.20 thf(fact_61_mem__Collect__eq,axiom,
% 4.98/5.20 ! [A: real,P: real > $o] :
% 4.98/5.20 ( ( member_real @ A @ ( collect_real @ P ) )
% 4.98/5.20 = ( P @ A ) ) ).
% 4.98/5.20
% 4.98/5.20 % mem_Collect_eq
% 4.98/5.20 thf(fact_62_mem__Collect__eq,axiom,
% 4.98/5.20 ! [A: list_nat,P: list_nat > $o] :
% 4.98/5.20 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 4.98/5.20 = ( P @ A ) ) ).
% 4.98/5.20
% 4.98/5.20 % mem_Collect_eq
% 4.98/5.20 thf(fact_63_mem__Collect__eq,axiom,
% 4.98/5.20 ! [A: set_nat,P: set_nat > $o] :
% 4.98/5.20 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 4.98/5.20 = ( P @ A ) ) ).
% 4.98/5.20
% 4.98/5.20 % mem_Collect_eq
% 4.98/5.20 thf(fact_64_mem__Collect__eq,axiom,
% 4.98/5.20 ! [A: nat,P: nat > $o] :
% 4.98/5.20 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 4.98/5.20 = ( P @ A ) ) ).
% 4.98/5.20
% 4.98/5.20 % mem_Collect_eq
% 4.98/5.20 thf(fact_65_mem__Collect__eq,axiom,
% 4.98/5.20 ! [A: int,P: int > $o] :
% 4.98/5.20 ( ( member_int @ A @ ( collect_int @ P ) )
% 4.98/5.20 = ( P @ A ) ) ).
% 4.98/5.20
% 4.98/5.20 % mem_Collect_eq
% 4.98/5.20 thf(fact_66_Collect__mem__eq,axiom,
% 4.98/5.20 ! [A3: set_complex] :
% 4.98/5.20 ( ( collect_complex
% 4.98/5.20 @ ^ [X: complex] : ( member_complex @ X @ A3 ) )
% 4.98/5.20 = A3 ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_mem_eq
% 4.98/5.20 thf(fact_67_Collect__mem__eq,axiom,
% 4.98/5.20 ! [A3: set_real] :
% 4.98/5.20 ( ( collect_real
% 4.98/5.20 @ ^ [X: real] : ( member_real @ X @ A3 ) )
% 4.98/5.20 = A3 ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_mem_eq
% 4.98/5.20 thf(fact_68_Collect__mem__eq,axiom,
% 4.98/5.20 ! [A3: set_list_nat] :
% 4.98/5.20 ( ( collect_list_nat
% 4.98/5.20 @ ^ [X: list_nat] : ( member_list_nat @ X @ A3 ) )
% 4.98/5.20 = A3 ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_mem_eq
% 4.98/5.20 thf(fact_69_Collect__mem__eq,axiom,
% 4.98/5.20 ! [A3: set_set_nat] :
% 4.98/5.20 ( ( collect_set_nat
% 4.98/5.20 @ ^ [X: set_nat] : ( member_set_nat @ X @ A3 ) )
% 4.98/5.20 = A3 ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_mem_eq
% 4.98/5.20 thf(fact_70_Collect__mem__eq,axiom,
% 4.98/5.20 ! [A3: set_nat] :
% 4.98/5.20 ( ( collect_nat
% 4.98/5.20 @ ^ [X: nat] : ( member_nat @ X @ A3 ) )
% 4.98/5.20 = A3 ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_mem_eq
% 4.98/5.20 thf(fact_71_Collect__mem__eq,axiom,
% 4.98/5.20 ! [A3: set_int] :
% 4.98/5.20 ( ( collect_int
% 4.98/5.20 @ ^ [X: int] : ( member_int @ X @ A3 ) )
% 4.98/5.20 = A3 ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_mem_eq
% 4.98/5.20 thf(fact_72_Collect__cong,axiom,
% 4.98/5.20 ! [P: real > $o,Q: real > $o] :
% 4.98/5.20 ( ! [X5: real] :
% 4.98/5.20 ( ( P @ X5 )
% 4.98/5.20 = ( Q @ X5 ) )
% 4.98/5.20 => ( ( collect_real @ P )
% 4.98/5.20 = ( collect_real @ Q ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_cong
% 4.98/5.20 thf(fact_73_Collect__cong,axiom,
% 4.98/5.20 ! [P: list_nat > $o,Q: list_nat > $o] :
% 4.98/5.20 ( ! [X5: list_nat] :
% 4.98/5.20 ( ( P @ X5 )
% 4.98/5.20 = ( Q @ X5 ) )
% 4.98/5.20 => ( ( collect_list_nat @ P )
% 4.98/5.20 = ( collect_list_nat @ Q ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_cong
% 4.98/5.20 thf(fact_74_Collect__cong,axiom,
% 4.98/5.20 ! [P: set_nat > $o,Q: set_nat > $o] :
% 4.98/5.20 ( ! [X5: set_nat] :
% 4.98/5.20 ( ( P @ X5 )
% 4.98/5.20 = ( Q @ X5 ) )
% 4.98/5.20 => ( ( collect_set_nat @ P )
% 4.98/5.20 = ( collect_set_nat @ Q ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_cong
% 4.98/5.20 thf(fact_75_Collect__cong,axiom,
% 4.98/5.20 ! [P: nat > $o,Q: nat > $o] :
% 4.98/5.20 ( ! [X5: nat] :
% 4.98/5.20 ( ( P @ X5 )
% 4.98/5.20 = ( Q @ X5 ) )
% 4.98/5.20 => ( ( collect_nat @ P )
% 4.98/5.20 = ( collect_nat @ Q ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_cong
% 4.98/5.20 thf(fact_76_Collect__cong,axiom,
% 4.98/5.20 ! [P: int > $o,Q: int > $o] :
% 4.98/5.20 ( ! [X5: int] :
% 4.98/5.20 ( ( P @ X5 )
% 4.98/5.20 = ( Q @ X5 ) )
% 4.98/5.20 => ( ( collect_int @ P )
% 4.98/5.20 = ( collect_int @ Q ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % Collect_cong
% 4.98/5.20 thf(fact_77_mi__ma__2__deg,axiom,
% 4.98/5.20 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 4.98/5.20 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ N2 )
% 4.98/5.20 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.98/5.20 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % mi_ma_2_deg
% 4.98/5.20 thf(fact_78__C5_OIH_C_I2_J,axiom,
% 4.98/5.20 ! [X2: nat,Y: nat] :
% 4.98/5.20 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.98/5.20 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.98/5.20 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ summary @ X2 ) @ Y )
% 4.98/5.20 => ( ( vEBT_vebt_member @ summary @ Y )
% 4.98/5.20 | ( X2 = Y ) ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % "5.IH"(2)
% 4.98/5.20 thf(fact_79__092_060open_062low_Ax_An_A_060_A2_A_094_An_A_092_060and_062_Alow_Ay_An_A_060_A2_A_094_An_092_060close_062,axiom,
% 4.98/5.20 ( ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 4.98/5.20 & ( ord_less_nat @ ( vEBT_VEBT_low @ ya @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % \<open>low x n < 2 ^ n \<and> low y n < 2 ^ n\<close>
% 4.98/5.20 thf(fact_80_set__n__deg__not__0,axiom,
% 4.98/5.20 ! [TreeList: list_VEBT_VEBT,N2: nat,M: nat] :
% 4.98/5.20 ( ! [X5: vEBT_VEBT] :
% 4.98/5.20 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.20 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 4.98/5.20 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.98/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.20 => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % set_n_deg_not_0
% 4.98/5.20 thf(fact_81_mimaxyprop,axiom,
% 4.98/5.20 ( ~ ( ( xa = mi )
% 4.98/5.20 | ( xa = ma ) )
% 4.98/5.20 & ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.98/5.20 & ( ord_less_nat @ ( vEBT_VEBT_high @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 4.98/5.20 & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 4.98/5.20 & ( ord_less_nat @ ( vEBT_VEBT_low @ mi @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) )
% 4.98/5.20 & ( ( size_s6755466524823107622T_VEBT @ treeList )
% 4.98/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % mimaxyprop
% 4.98/5.20 thf(fact_82_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 4.98/5.20 ! [X2: nat,N2: nat,M: nat] :
% 4.98/5.20 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 4.98/5.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.20 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.98/5.20 => ( ord_less_nat @ ( vEBT_VEBT_low @ X2 @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % VEBT_internal.exp_split_high_low(2)
% 4.98/5.20 thf(fact_83_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 4.98/5.20 ! [X2: nat,N2: nat,M: nat] :
% 4.98/5.20 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 4.98/5.20 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.20 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.98/5.20 => ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % VEBT_internal.exp_split_high_low(1)
% 4.98/5.20 thf(fact_84_vebt__buildup_Ocases,axiom,
% 4.98/5.20 ! [X2: nat] :
% 4.98/5.20 ( ( X2 != zero_zero_nat )
% 4.98/5.20 => ( ( X2
% 4.98/5.20 != ( suc @ zero_zero_nat ) )
% 4.98/5.20 => ~ ! [Va: nat] :
% 4.98/5.20 ( X2
% 4.98/5.20 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 4.98/5.20
% 4.98/5.20 % vebt_buildup.cases
% 4.98/5.20 thf(fact_85_vebt__insert_Osimps_I3_J,axiom,
% 4.98/5.20 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 4.98/5.20 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) @ X2 )
% 4.98/5.20 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S2 ) ) ).
% 4.98/5.20
% 4.98/5.20 % vebt_insert.simps(3)
% 4.98/5.20 thf(fact_86_invar__vebt_Ointros_I5_J,axiom,
% 4.98/5.20 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 4.98/5.20 ( ! [X5: vEBT_VEBT] :
% 4.98/5.20 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.20 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 4.98/5.20 => ( ( vEBT_invar_vebt @ Summary @ M )
% 4.98/5.20 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.98/5.20 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.20 => ( ( M
% 4.98/5.20 = ( suc @ N2 ) )
% 4.98/5.20 => ( ( Deg
% 4.98/5.20 = ( plus_plus_nat @ N2 @ M ) )
% 4.98/5.20 => ( ! [I2: nat] :
% 4.98/5.20 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.20 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X4 ) )
% 4.98/5.20 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 4.98/5.21 => ( ( ( Mi = Ma )
% 4.98/5.21 => ! [X5: vEBT_VEBT] :
% 4.98/5.21 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.21 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.98/5.21 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.98/5.21 => ( ( ( Mi != Ma )
% 4.98/5.21 => ! [I2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.21 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 4.98/5.21 = I2 )
% 4.98/5.21 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 4.98/5.21 & ! [X5: nat] :
% 4.98/5.21 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 4.98/5.21 = I2 )
% 4.98/5.21 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_nat @ Mi @ X5 )
% 4.98/5.21 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 4.98/5.21 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % invar_vebt.intros(5)
% 4.98/5.21 thf(fact_87_invar__vebt_Ointros_I4_J,axiom,
% 4.98/5.21 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 4.98/5.21 ( ! [X5: vEBT_VEBT] :
% 4.98/5.21 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.21 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 4.98/5.21 => ( ( vEBT_invar_vebt @ Summary @ M )
% 4.98/5.21 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.98/5.21 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.21 => ( ( M = N2 )
% 4.98/5.21 => ( ( Deg
% 4.98/5.21 = ( plus_plus_nat @ N2 @ M ) )
% 4.98/5.21 => ( ! [I2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.21 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ X4 ) )
% 4.98/5.21 = ( vEBT_V8194947554948674370ptions @ Summary @ I2 ) ) )
% 4.98/5.21 => ( ( ( Mi = Ma )
% 4.98/5.21 => ! [X5: vEBT_VEBT] :
% 4.98/5.21 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.21 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 4.98/5.21 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.98/5.21 => ( ( ( Mi != Ma )
% 4.98/5.21 => ! [I2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.21 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 4.98/5.21 = I2 )
% 4.98/5.21 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 4.98/5.21 & ! [X5: nat] :
% 4.98/5.21 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 4.98/5.21 = I2 )
% 4.98/5.21 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I2 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_nat @ Mi @ X5 )
% 4.98/5.21 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 4.98/5.21 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % invar_vebt.intros(4)
% 4.98/5.21 thf(fact_88_vebt__insert_Osimps_I2_J,axiom,
% 4.98/5.21 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 4.98/5.21 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S2 ) @ X2 )
% 4.98/5.21 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % vebt_insert.simps(2)
% 4.98/5.21 thf(fact_89_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 4.98/5.21 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 4.98/5.21 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 4.98/5.21
% 4.98/5.21 % VEBT_internal.naive_member.simps(2)
% 4.98/5.21 thf(fact_90_Pair__inject,axiom,
% 4.98/5.21 ! [A: code_integer,B: $o,A2: code_integer,B2: $o] :
% 4.98/5.21 ( ( ( produc6677183202524767010eger_o @ A @ B )
% 4.98/5.21 = ( produc6677183202524767010eger_o @ A2 @ B2 ) )
% 4.98/5.21 => ~ ( ( A = A2 )
% 4.98/5.21 => ( B = ~ B2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % Pair_inject
% 4.98/5.21 thf(fact_91_Pair__inject,axiom,
% 4.98/5.21 ! [A: num,B: num,A2: num,B2: num] :
% 4.98/5.21 ( ( ( product_Pair_num_num @ A @ B )
% 4.98/5.21 = ( product_Pair_num_num @ A2 @ B2 ) )
% 4.98/5.21 => ~ ( ( A = A2 )
% 4.98/5.21 => ( B != B2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % Pair_inject
% 4.98/5.21 thf(fact_92_Pair__inject,axiom,
% 4.98/5.21 ! [A: nat,B: num,A2: nat,B2: num] :
% 4.98/5.21 ( ( ( product_Pair_nat_num @ A @ B )
% 4.98/5.21 = ( product_Pair_nat_num @ A2 @ B2 ) )
% 4.98/5.21 => ~ ( ( A = A2 )
% 4.98/5.21 => ( B != B2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % Pair_inject
% 4.98/5.21 thf(fact_93_Pair__inject,axiom,
% 4.98/5.21 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 4.98/5.21 ( ( ( product_Pair_nat_nat @ A @ B )
% 4.98/5.21 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 4.98/5.21 => ~ ( ( A = A2 )
% 4.98/5.21 => ( B != B2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % Pair_inject
% 4.98/5.21 thf(fact_94_Pair__inject,axiom,
% 4.98/5.21 ! [A: int,B: int,A2: int,B2: int] :
% 4.98/5.21 ( ( ( product_Pair_int_int @ A @ B )
% 4.98/5.21 = ( product_Pair_int_int @ A2 @ B2 ) )
% 4.98/5.21 => ~ ( ( A = A2 )
% 4.98/5.21 => ( B != B2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % Pair_inject
% 4.98/5.21 thf(fact_95_prod__cases,axiom,
% 4.98/5.21 ! [P: produc6271795597528267376eger_o > $o,P2: produc6271795597528267376eger_o] :
% 4.98/5.21 ( ! [A4: code_integer,B3: $o] : ( P @ ( produc6677183202524767010eger_o @ A4 @ B3 ) )
% 4.98/5.21 => ( P @ P2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % prod_cases
% 4.98/5.21 thf(fact_96_prod__cases,axiom,
% 4.98/5.21 ! [P: product_prod_num_num > $o,P2: product_prod_num_num] :
% 4.98/5.21 ( ! [A4: num,B3: num] : ( P @ ( product_Pair_num_num @ A4 @ B3 ) )
% 4.98/5.21 => ( P @ P2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % prod_cases
% 4.98/5.21 thf(fact_97_prod__cases,axiom,
% 4.98/5.21 ! [P: product_prod_nat_num > $o,P2: product_prod_nat_num] :
% 4.98/5.21 ( ! [A4: nat,B3: num] : ( P @ ( product_Pair_nat_num @ A4 @ B3 ) )
% 4.98/5.21 => ( P @ P2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % prod_cases
% 4.98/5.21 thf(fact_98_prod__cases,axiom,
% 4.98/5.21 ! [P: product_prod_nat_nat > $o,P2: product_prod_nat_nat] :
% 4.98/5.21 ( ! [A4: nat,B3: nat] : ( P @ ( product_Pair_nat_nat @ A4 @ B3 ) )
% 4.98/5.21 => ( P @ P2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % prod_cases
% 4.98/5.21 thf(fact_99_prod__cases,axiom,
% 4.98/5.21 ! [P: product_prod_int_int > $o,P2: product_prod_int_int] :
% 4.98/5.21 ( ! [A4: int,B3: int] : ( P @ ( product_Pair_int_int @ A4 @ B3 ) )
% 4.98/5.21 => ( P @ P2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % prod_cases
% 4.98/5.21 thf(fact_100_surj__pair,axiom,
% 4.98/5.21 ! [P2: produc6271795597528267376eger_o] :
% 4.98/5.21 ? [X5: code_integer,Y3: $o] :
% 4.98/5.21 ( P2
% 4.98/5.21 = ( produc6677183202524767010eger_o @ X5 @ Y3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % surj_pair
% 4.98/5.21 thf(fact_101_surj__pair,axiom,
% 4.98/5.21 ! [P2: product_prod_num_num] :
% 4.98/5.21 ? [X5: num,Y3: num] :
% 4.98/5.21 ( P2
% 4.98/5.21 = ( product_Pair_num_num @ X5 @ Y3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % surj_pair
% 4.98/5.21 thf(fact_102_surj__pair,axiom,
% 4.98/5.21 ! [P2: product_prod_nat_num] :
% 4.98/5.21 ? [X5: nat,Y3: num] :
% 4.98/5.21 ( P2
% 4.98/5.21 = ( product_Pair_nat_num @ X5 @ Y3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % surj_pair
% 4.98/5.21 thf(fact_103_surj__pair,axiom,
% 4.98/5.21 ! [P2: product_prod_nat_nat] :
% 4.98/5.21 ? [X5: nat,Y3: nat] :
% 4.98/5.21 ( P2
% 4.98/5.21 = ( product_Pair_nat_nat @ X5 @ Y3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % surj_pair
% 4.98/5.21 thf(fact_104_surj__pair,axiom,
% 4.98/5.21 ! [P2: product_prod_int_int] :
% 4.98/5.21 ? [X5: int,Y3: int] :
% 4.98/5.21 ( P2
% 4.98/5.21 = ( product_Pair_int_int @ X5 @ Y3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % surj_pair
% 4.98/5.21 thf(fact_105_old_Oprod_Oexhaust,axiom,
% 4.98/5.21 ! [Y: produc6271795597528267376eger_o] :
% 4.98/5.21 ~ ! [A4: code_integer,B3: $o] :
% 4.98/5.21 ( Y
% 4.98/5.21 != ( produc6677183202524767010eger_o @ A4 @ B3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % old.prod.exhaust
% 4.98/5.21 thf(fact_106_old_Oprod_Oexhaust,axiom,
% 4.98/5.21 ! [Y: product_prod_num_num] :
% 4.98/5.21 ~ ! [A4: num,B3: num] :
% 4.98/5.21 ( Y
% 4.98/5.21 != ( product_Pair_num_num @ A4 @ B3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % old.prod.exhaust
% 4.98/5.21 thf(fact_107_old_Oprod_Oexhaust,axiom,
% 4.98/5.21 ! [Y: product_prod_nat_num] :
% 4.98/5.21 ~ ! [A4: nat,B3: num] :
% 4.98/5.21 ( Y
% 4.98/5.21 != ( product_Pair_nat_num @ A4 @ B3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % old.prod.exhaust
% 4.98/5.21 thf(fact_108_old_Oprod_Oexhaust,axiom,
% 4.98/5.21 ! [Y: product_prod_nat_nat] :
% 4.98/5.21 ~ ! [A4: nat,B3: nat] :
% 4.98/5.21 ( Y
% 4.98/5.21 != ( product_Pair_nat_nat @ A4 @ B3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % old.prod.exhaust
% 4.98/5.21 thf(fact_109_old_Oprod_Oexhaust,axiom,
% 4.98/5.21 ! [Y: product_prod_int_int] :
% 4.98/5.21 ~ ! [A4: int,B3: int] :
% 4.98/5.21 ( Y
% 4.98/5.21 != ( product_Pair_int_int @ A4 @ B3 ) ) ).
% 4.98/5.21
% 4.98/5.21 % old.prod.exhaust
% 4.98/5.21 thf(fact_110_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 4.98/5.21 ! [Mi: nat,Ma: nat,Va2: list_VEBT_VEBT,Vb: vEBT_VEBT,X2: nat] :
% 4.98/5.21 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va2 @ Vb ) @ X2 )
% 4.98/5.21 = ( ( X2 = Mi )
% 4.98/5.21 | ( X2 = Ma ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % VEBT_internal.membermima.simps(3)
% 4.98/5.21 thf(fact_111_in__children__def,axiom,
% 4.98/5.21 ( vEBT_V5917875025757280293ildren
% 4.98/5.21 = ( ^ [N3: nat,TreeList3: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ X @ N3 ) ) @ ( vEBT_VEBT_low @ X @ N3 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % in_children_def
% 4.98/5.21 thf(fact_112_sum__power2__eq__zero__iff,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] :
% 4.98/5.21 ( ( ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = zero_zero_rat )
% 4.98/5.21 = ( ( X2 = zero_zero_rat )
% 4.98/5.21 & ( Y = zero_zero_rat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_eq_zero_iff
% 4.98/5.21 thf(fact_113_sum__power2__eq__zero__iff,axiom,
% 4.98/5.21 ! [X2: int,Y: int] :
% 4.98/5.21 ( ( ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = zero_zero_int )
% 4.98/5.21 = ( ( X2 = zero_zero_int )
% 4.98/5.21 & ( Y = zero_zero_int ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_eq_zero_iff
% 4.98/5.21 thf(fact_114_sum__power2__eq__zero__iff,axiom,
% 4.98/5.21 ! [X2: real,Y: real] :
% 4.98/5.21 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = zero_zero_real )
% 4.98/5.21 = ( ( X2 = zero_zero_real )
% 4.98/5.21 & ( Y = zero_zero_real ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_eq_zero_iff
% 4.98/5.21 thf(fact_115_zero__less__power2,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( A != zero_zero_real ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_power2
% 4.98/5.21 thf(fact_116_zero__less__power2,axiom,
% 4.98/5.21 ! [A: rat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( A != zero_zero_rat ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_power2
% 4.98/5.21 thf(fact_117_zero__less__power2,axiom,
% 4.98/5.21 ! [A: int] :
% 4.98/5.21 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( A != zero_zero_int ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_power2
% 4.98/5.21 thf(fact_118_power2__less__eq__zero__iff,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 4.98/5.21 = ( A = zero_zero_real ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_eq_zero_iff
% 4.98/5.21 thf(fact_119_power2__less__eq__zero__iff,axiom,
% 4.98/5.21 ! [A: rat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 4.98/5.21 = ( A = zero_zero_rat ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_eq_zero_iff
% 4.98/5.21 thf(fact_120_power2__less__eq__zero__iff,axiom,
% 4.98/5.21 ! [A: int] :
% 4.98/5.21 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 4.98/5.21 = ( A = zero_zero_int ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_eq_zero_iff
% 4.98/5.21 thf(fact_121_power2__eq__iff__nonneg,axiom,
% 4.98/5.21 ! [X2: real,Y: real] :
% 4.98/5.21 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.21 => ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( X2 = Y ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_eq_iff_nonneg
% 4.98/5.21 thf(fact_122_power2__eq__iff__nonneg,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.21 => ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( X2 = Y ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_eq_iff_nonneg
% 4.98/5.21 thf(fact_123_power2__eq__iff__nonneg,axiom,
% 4.98/5.21 ! [X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.98/5.21 => ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( X2 = Y ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_eq_iff_nonneg
% 4.98/5.21 thf(fact_124_power2__eq__iff__nonneg,axiom,
% 4.98/5.21 ! [X2: int,Y: int] :
% 4.98/5.21 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.98/5.21 => ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( X2 = Y ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_eq_iff_nonneg
% 4.98/5.21 thf(fact_125_add__2__eq__Suc,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.98/5.21 = ( suc @ ( suc @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % add_2_eq_Suc
% 4.98/5.21 thf(fact_126_add__2__eq__Suc_H,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( suc @ ( suc @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % add_2_eq_Suc'
% 4.98/5.21 thf(fact_127_zero__eq__power2,axiom,
% 4.98/5.21 ! [A: rat] :
% 4.98/5.21 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_rat )
% 4.98/5.21 = ( A = zero_zero_rat ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_eq_power2
% 4.98/5.21 thf(fact_128_zero__eq__power2,axiom,
% 4.98/5.21 ! [A: nat] :
% 4.98/5.21 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_nat )
% 4.98/5.21 = ( A = zero_zero_nat ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_eq_power2
% 4.98/5.21 thf(fact_129_zero__eq__power2,axiom,
% 4.98/5.21 ! [A: int] :
% 4.98/5.21 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_int )
% 4.98/5.21 = ( A = zero_zero_int ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_eq_power2
% 4.98/5.21 thf(fact_130_zero__eq__power2,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_real )
% 4.98/5.21 = ( A = zero_zero_real ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_eq_power2
% 4.98/5.21 thf(fact_131_zero__eq__power2,axiom,
% 4.98/5.21 ! [A: complex] :
% 4.98/5.21 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_complex )
% 4.98/5.21 = ( A = zero_zero_complex ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_eq_power2
% 4.98/5.21 thf(fact_132_power__mono__iff,axiom,
% 4.98/5.21 ! [A: real,B: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_mono_iff
% 4.98/5.21 thf(fact_133_power__mono__iff,axiom,
% 4.98/5.21 ! [A: rat,B: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_mono_iff
% 4.98/5.21 thf(fact_134_power__mono__iff,axiom,
% 4.98/5.21 ! [A: nat,B: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_mono_iff
% 4.98/5.21 thf(fact_135_power__mono__iff,axiom,
% 4.98/5.21 ! [A: int,B: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_mono_iff
% 4.98/5.21 thf(fact_136_member__inv,axiom,
% 4.98/5.21 ! [Mi: nat,Ma: nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 4.98/5.21 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.98/5.21 & ( ( X2 = Mi )
% 4.98/5.21 | ( X2 = Ma )
% 4.98/5.21 | ( ( ord_less_nat @ X2 @ Ma )
% 4.98/5.21 & ( ord_less_nat @ Mi @ X2 )
% 4.98/5.21 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.98/5.21 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % member_inv
% 4.98/5.21 thf(fact_137_power__eq__0__iff,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ( power_power_rat @ A @ N2 )
% 4.98/5.21 = zero_zero_rat )
% 4.98/5.21 = ( ( A = zero_zero_rat )
% 4.98/5.21 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_0_iff
% 4.98/5.21 thf(fact_138_power__eq__0__iff,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ( power_power_nat @ A @ N2 )
% 4.98/5.21 = zero_zero_nat )
% 4.98/5.21 = ( ( A = zero_zero_nat )
% 4.98/5.21 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_0_iff
% 4.98/5.21 thf(fact_139_power__eq__0__iff,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ( power_power_int @ A @ N2 )
% 4.98/5.21 = zero_zero_int )
% 4.98/5.21 = ( ( A = zero_zero_int )
% 4.98/5.21 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_0_iff
% 4.98/5.21 thf(fact_140_power__eq__0__iff,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ( power_power_real @ A @ N2 )
% 4.98/5.21 = zero_zero_real )
% 4.98/5.21 = ( ( A = zero_zero_real )
% 4.98/5.21 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_0_iff
% 4.98/5.21 thf(fact_141_power__eq__0__iff,axiom,
% 4.98/5.21 ! [A: complex,N2: nat] :
% 4.98/5.21 ( ( ( power_power_complex @ A @ N2 )
% 4.98/5.21 = zero_zero_complex )
% 4.98/5.21 = ( ( A = zero_zero_complex )
% 4.98/5.21 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_0_iff
% 4.98/5.21 thf(fact_142__092_060open_062vebt__member_A_ItreeList_091high_Ami_An_A_058_061_Avebt__insert_A_ItreeList_A_B_Ahigh_Ami_An_J_A_Ilow_Ami_An_J_093_A_B_Ahigh_Ay_An_J_A_Ilow_Ay_An_J_092_060close_062,axiom,
% 4.98/5.21 vEBT_vebt_member @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) @ ( vEBT_VEBT_high @ ya @ na ) ) @ ( vEBT_VEBT_low @ ya @ na ) ).
% 4.98/5.21
% 4.98/5.21 % \<open>vebt_member (treeList[high mi n := vebt_insert (treeList ! high mi n) (low mi n)] ! high y n) (low y n)\<close>
% 4.98/5.21 thf(fact_143_numeral__eq__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ( numera6690914467698888265omplex @ M )
% 4.98/5.21 = ( numera6690914467698888265omplex @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_iff
% 4.98/5.21 thf(fact_144_numeral__eq__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ( numeral_numeral_real @ M )
% 4.98/5.21 = ( numeral_numeral_real @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_iff
% 4.98/5.21 thf(fact_145_numeral__eq__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ( numeral_numeral_rat @ M )
% 4.98/5.21 = ( numeral_numeral_rat @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_iff
% 4.98/5.21 thf(fact_146_numeral__eq__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ( numeral_numeral_nat @ M )
% 4.98/5.21 = ( numeral_numeral_nat @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_iff
% 4.98/5.21 thf(fact_147_numeral__eq__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ( numeral_numeral_int @ M )
% 4.98/5.21 = ( numeral_numeral_int @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_iff
% 4.98/5.21 thf(fact_148_pow__sum,axiom,
% 4.98/5.21 ! [A: nat,B: nat] :
% 4.98/5.21 ( ( 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 ) )
% 4.98/5.21 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 4.98/5.21
% 4.98/5.21 % pow_sum
% 4.98/5.21 thf(fact_149_high__def,axiom,
% 4.98/5.21 ( vEBT_VEBT_high
% 4.98/5.21 = ( ^ [X: nat,N3: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % high_def
% 4.98/5.21 thf(fact_150_numeral__le__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_le_iff
% 4.98/5.21 thf(fact_151_numeral__le__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_le_iff
% 4.98/5.21 thf(fact_152_numeral__le__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_le_iff
% 4.98/5.21 thf(fact_153_numeral__le__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_le_iff
% 4.98/5.21 thf(fact_154_numeral__less__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 4.98/5.21 = ( ord_less_num @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_less_iff
% 4.98/5.21 thf(fact_155_numeral__less__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 4.98/5.21 = ( ord_less_num @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_less_iff
% 4.98/5.21 thf(fact_156_numeral__less__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.21 = ( ord_less_num @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_less_iff
% 4.98/5.21 thf(fact_157_numeral__less__iff,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 4.98/5.21 = ( ord_less_num @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_less_iff
% 4.98/5.21 thf(fact_158_add__numeral__left,axiom,
% 4.98/5.21 ! [V: num,W: num,Z: complex] :
% 4.98/5.21 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 4.98/5.21 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.21
% 4.98/5.21 % add_numeral_left
% 4.98/5.21 thf(fact_159_add__numeral__left,axiom,
% 4.98/5.21 ! [V: num,W: num,Z: real] :
% 4.98/5.21 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 4.98/5.21 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.21
% 4.98/5.21 % add_numeral_left
% 4.98/5.21 thf(fact_160_add__numeral__left,axiom,
% 4.98/5.21 ! [V: num,W: num,Z: rat] :
% 4.98/5.21 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 4.98/5.21 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.21
% 4.98/5.21 % add_numeral_left
% 4.98/5.21 thf(fact_161_add__numeral__left,axiom,
% 4.98/5.21 ! [V: num,W: num,Z: nat] :
% 4.98/5.21 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 4.98/5.21 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.21
% 4.98/5.21 % add_numeral_left
% 4.98/5.21 thf(fact_162_add__numeral__left,axiom,
% 4.98/5.21 ! [V: num,W: num,Z: int] :
% 4.98/5.21 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 4.98/5.21 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.21
% 4.98/5.21 % add_numeral_left
% 4.98/5.21 thf(fact_163_numeral__plus__numeral,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 4.98/5.21 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_numeral
% 4.98/5.21 thf(fact_164_numeral__plus__numeral,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_numeral
% 4.98/5.21 thf(fact_165_numeral__plus__numeral,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_numeral
% 4.98/5.21 thf(fact_166_numeral__plus__numeral,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_numeral
% 4.98/5.21 thf(fact_167_numeral__plus__numeral,axiom,
% 4.98/5.21 ! [M: num,N2: num] :
% 4.98/5.21 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_numeral
% 4.98/5.21 thf(fact_168_power__one,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_rat @ one_one_rat @ N2 )
% 4.98/5.21 = one_one_rat ) ).
% 4.98/5.21
% 4.98/5.21 % power_one
% 4.98/5.21 thf(fact_169_power__one,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_nat @ one_one_nat @ N2 )
% 4.98/5.21 = one_one_nat ) ).
% 4.98/5.21
% 4.98/5.21 % power_one
% 4.98/5.21 thf(fact_170_power__one,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_int @ one_one_int @ N2 )
% 4.98/5.21 = one_one_int ) ).
% 4.98/5.21
% 4.98/5.21 % power_one
% 4.98/5.21 thf(fact_171_power__one,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_real @ one_one_real @ N2 )
% 4.98/5.21 = one_one_real ) ).
% 4.98/5.21
% 4.98/5.21 % power_one
% 4.98/5.21 thf(fact_172_power__one,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_complex @ one_one_complex @ N2 )
% 4.98/5.21 = one_one_complex ) ).
% 4.98/5.21
% 4.98/5.21 % power_one
% 4.98/5.21 thf(fact_173_power__one__right,axiom,
% 4.98/5.21 ! [A: nat] :
% 4.98/5.21 ( ( power_power_nat @ A @ one_one_nat )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % power_one_right
% 4.98/5.21 thf(fact_174_power__one__right,axiom,
% 4.98/5.21 ! [A: int] :
% 4.98/5.21 ( ( power_power_int @ A @ one_one_nat )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % power_one_right
% 4.98/5.21 thf(fact_175_power__one__right,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( power_power_real @ A @ one_one_nat )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % power_one_right
% 4.98/5.21 thf(fact_176_power__one__right,axiom,
% 4.98/5.21 ! [A: complex] :
% 4.98/5.21 ( ( power_power_complex @ A @ one_one_nat )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % power_one_right
% 4.98/5.21 thf(fact_177_set__vebt__set__vebt_H__valid,axiom,
% 4.98/5.21 ! [T2: vEBT_VEBT,N2: nat] :
% 4.98/5.21 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 4.98/5.21 => ( ( vEBT_set_vebt @ T2 )
% 4.98/5.21 = ( vEBT_VEBT_set_vebt @ T2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % set_vebt_set_vebt'_valid
% 4.98/5.21 thf(fact_178_one__eq__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( one_one_complex
% 4.98/5.21 = ( numera6690914467698888265omplex @ N2 ) )
% 4.98/5.21 = ( one = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_eq_numeral_iff
% 4.98/5.21 thf(fact_179_one__eq__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( one_one_real
% 4.98/5.21 = ( numeral_numeral_real @ N2 ) )
% 4.98/5.21 = ( one = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_eq_numeral_iff
% 4.98/5.21 thf(fact_180_one__eq__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( one_one_rat
% 4.98/5.21 = ( numeral_numeral_rat @ N2 ) )
% 4.98/5.21 = ( one = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_eq_numeral_iff
% 4.98/5.21 thf(fact_181_one__eq__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( one_one_nat
% 4.98/5.21 = ( numeral_numeral_nat @ N2 ) )
% 4.98/5.21 = ( one = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_eq_numeral_iff
% 4.98/5.21 thf(fact_182_one__eq__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( one_one_int
% 4.98/5.21 = ( numeral_numeral_int @ N2 ) )
% 4.98/5.21 = ( one = N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_eq_numeral_iff
% 4.98/5.21 thf(fact_183_numeral__eq__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ( numera6690914467698888265omplex @ N2 )
% 4.98/5.21 = one_one_complex )
% 4.98/5.21 = ( N2 = one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_one_iff
% 4.98/5.21 thf(fact_184_numeral__eq__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ( numeral_numeral_real @ N2 )
% 4.98/5.21 = one_one_real )
% 4.98/5.21 = ( N2 = one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_one_iff
% 4.98/5.21 thf(fact_185_numeral__eq__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ( numeral_numeral_rat @ N2 )
% 4.98/5.21 = one_one_rat )
% 4.98/5.21 = ( N2 = one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_one_iff
% 4.98/5.21 thf(fact_186_numeral__eq__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ( numeral_numeral_nat @ N2 )
% 4.98/5.21 = one_one_nat )
% 4.98/5.21 = ( N2 = one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_one_iff
% 4.98/5.21 thf(fact_187_numeral__eq__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ( numeral_numeral_int @ N2 )
% 4.98/5.21 = one_one_int )
% 4.98/5.21 = ( N2 = one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_eq_one_iff
% 4.98/5.21 thf(fact_188_power__inject__exp,axiom,
% 4.98/5.21 ! [A: real,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ one_one_real @ A )
% 4.98/5.21 => ( ( ( power_power_real @ A @ M )
% 4.98/5.21 = ( power_power_real @ A @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_inject_exp
% 4.98/5.21 thf(fact_189_power__inject__exp,axiom,
% 4.98/5.21 ! [A: rat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ( ( power_power_rat @ A @ M )
% 4.98/5.21 = ( power_power_rat @ A @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_inject_exp
% 4.98/5.21 thf(fact_190_power__inject__exp,axiom,
% 4.98/5.21 ! [A: nat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ( ( power_power_nat @ A @ M )
% 4.98/5.21 = ( power_power_nat @ A @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_inject_exp
% 4.98/5.21 thf(fact_191_power__inject__exp,axiom,
% 4.98/5.21 ! [A: int,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ one_one_int @ A )
% 4.98/5.21 => ( ( ( power_power_int @ A @ M )
% 4.98/5.21 = ( power_power_int @ A @ N2 ) )
% 4.98/5.21 = ( M = N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_inject_exp
% 4.98/5.21 thf(fact_192_power__0__Suc,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N2 ) )
% 4.98/5.21 = zero_zero_rat ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_Suc
% 4.98/5.21 thf(fact_193_power__0__Suc,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 4.98/5.21 = zero_zero_nat ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_Suc
% 4.98/5.21 thf(fact_194_power__0__Suc,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 4.98/5.21 = zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_Suc
% 4.98/5.21 thf(fact_195_power__0__Suc,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 4.98/5.21 = zero_zero_real ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_Suc
% 4.98/5.21 thf(fact_196_power__0__Suc,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 4.98/5.21 = zero_zero_complex ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_Suc
% 4.98/5.21 thf(fact_197_power__zero__numeral,axiom,
% 4.98/5.21 ! [K: num] :
% 4.98/5.21 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 4.98/5.21 = zero_zero_rat ) ).
% 4.98/5.21
% 4.98/5.21 % power_zero_numeral
% 4.98/5.21 thf(fact_198_power__zero__numeral,axiom,
% 4.98/5.21 ! [K: num] :
% 4.98/5.21 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 4.98/5.21 = zero_zero_nat ) ).
% 4.98/5.21
% 4.98/5.21 % power_zero_numeral
% 4.98/5.21 thf(fact_199_power__zero__numeral,axiom,
% 4.98/5.21 ! [K: num] :
% 4.98/5.21 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 4.98/5.21 = zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % power_zero_numeral
% 4.98/5.21 thf(fact_200_power__zero__numeral,axiom,
% 4.98/5.21 ! [K: num] :
% 4.98/5.21 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 4.98/5.21 = zero_zero_real ) ).
% 4.98/5.21
% 4.98/5.21 % power_zero_numeral
% 4.98/5.21 thf(fact_201_power__zero__numeral,axiom,
% 4.98/5.21 ! [K: num] :
% 4.98/5.21 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 4.98/5.21 = zero_zero_complex ) ).
% 4.98/5.21
% 4.98/5.21 % power_zero_numeral
% 4.98/5.21 thf(fact_202_Suc__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % Suc_numeral
% 4.98/5.21 thf(fact_203_power__Suc0__right,axiom,
% 4.98/5.21 ! [A: nat] :
% 4.98/5.21 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc0_right
% 4.98/5.21 thf(fact_204_power__Suc0__right,axiom,
% 4.98/5.21 ! [A: int] :
% 4.98/5.21 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc0_right
% 4.98/5.21 thf(fact_205_power__Suc0__right,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc0_right
% 4.98/5.21 thf(fact_206_power__Suc0__right,axiom,
% 4.98/5.21 ! [A: complex] :
% 4.98/5.21 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc0_right
% 4.98/5.21 thf(fact_207_nat__power__eq__Suc__0__iff,axiom,
% 4.98/5.21 ! [X2: nat,M: nat] :
% 4.98/5.21 ( ( ( power_power_nat @ X2 @ M )
% 4.98/5.21 = ( suc @ zero_zero_nat ) )
% 4.98/5.21 = ( ( M = zero_zero_nat )
% 4.98/5.21 | ( X2
% 4.98/5.21 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % nat_power_eq_Suc_0_iff
% 4.98/5.21 thf(fact_208_power__Suc__0,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 4.98/5.21 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_0
% 4.98/5.21 thf(fact_209_nat__zero__less__power__iff,axiom,
% 4.98/5.21 ! [X2: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X2 @ N2 ) )
% 4.98/5.21 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 4.98/5.21 | ( N2 = zero_zero_nat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % nat_zero_less_power_iff
% 4.98/5.21 thf(fact_210_both__member__options__ding,axiom,
% 4.98/5.21 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat,X2: nat] :
% 4.98/5.21 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ N2 )
% 4.98/5.21 => ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 4.98/5.21 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.98/5.21 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % both_member_options_ding
% 4.98/5.21 thf(fact_211_both__member__options__from__complete__tree__to__child,axiom,
% 4.98/5.21 ! [Deg: nat,Mi: nat,Ma: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 4.98/5.21 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 4.98/5.21 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.98/5.21 | ( X2 = Mi )
% 4.98/5.21 | ( X2 = Ma ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % both_member_options_from_complete_tree_to_child
% 4.98/5.21 thf(fact_212_numeral__le__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 4.98/5.21 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_le_one_iff
% 4.98/5.21 thf(fact_213_numeral__le__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 4.98/5.21 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_le_one_iff
% 4.98/5.21 thf(fact_214_numeral__le__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 4.98/5.21 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_le_one_iff
% 4.98/5.21 thf(fact_215_numeral__le__one__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 4.98/5.21 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_le_one_iff
% 4.98/5.21 thf(fact_216_one__less__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 4.98/5.21 = ( ord_less_num @ one @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_less_numeral_iff
% 4.98/5.21 thf(fact_217_one__less__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 4.98/5.21 = ( ord_less_num @ one @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_less_numeral_iff
% 4.98/5.21 thf(fact_218_one__less__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.21 = ( ord_less_num @ one @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_less_numeral_iff
% 4.98/5.21 thf(fact_219_one__less__numeral__iff,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 4.98/5.21 = ( ord_less_num @ one @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_less_numeral_iff
% 4.98/5.21 thf(fact_220_one__plus__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 4.98/5.21 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral
% 4.98/5.21 thf(fact_221_one__plus__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral
% 4.98/5.21 thf(fact_222_one__plus__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral
% 4.98/5.21 thf(fact_223_one__plus__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral
% 4.98/5.21 thf(fact_224_one__plus__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 4.98/5.21 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral
% 4.98/5.21 thf(fact_225_numeral__plus__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 4.98/5.21 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_one
% 4.98/5.21 thf(fact_226_numeral__plus__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 4.98/5.21 = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_one
% 4.98/5.21 thf(fact_227_numeral__plus__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 4.98/5.21 = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_one
% 4.98/5.21 thf(fact_228_numeral__plus__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 4.98/5.21 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_one
% 4.98/5.21 thf(fact_229_numeral__plus__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 4.98/5.21 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_plus_one
% 4.98/5.21 thf(fact_230_power__strict__increasing__iff,axiom,
% 4.98/5.21 ! [B: real,X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_real @ one_one_real @ B )
% 4.98/5.21 => ( ( ord_less_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y ) )
% 4.98/5.21 = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_increasing_iff
% 4.98/5.21 thf(fact_231_power__strict__increasing__iff,axiom,
% 4.98/5.21 ! [B: rat,X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_rat @ one_one_rat @ B )
% 4.98/5.21 => ( ( ord_less_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y ) )
% 4.98/5.21 = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_increasing_iff
% 4.98/5.21 thf(fact_232_power__strict__increasing__iff,axiom,
% 4.98/5.21 ! [B: nat,X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_nat @ one_one_nat @ B )
% 4.98/5.21 => ( ( ord_less_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y ) )
% 4.98/5.21 = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_increasing_iff
% 4.98/5.21 thf(fact_233_power__strict__increasing__iff,axiom,
% 4.98/5.21 ! [B: int,X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_int @ one_one_int @ B )
% 4.98/5.21 => ( ( ord_less_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y ) )
% 4.98/5.21 = ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_increasing_iff
% 4.98/5.21 thf(fact_234_both__member__options__from__chilf__to__complete__tree,axiom,
% 4.98/5.21 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 4.98/5.21 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 4.98/5.21 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.98/5.21 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % both_member_options_from_chilf_to_complete_tree
% 4.98/5.21 thf(fact_235_one__add__one,axiom,
% 4.98/5.21 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 4.98/5.21 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_add_one
% 4.98/5.21 thf(fact_236_one__add__one,axiom,
% 4.98/5.21 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 4.98/5.21 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_add_one
% 4.98/5.21 thf(fact_237_one__add__one,axiom,
% 4.98/5.21 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 4.98/5.21 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_add_one
% 4.98/5.21 thf(fact_238_one__add__one,axiom,
% 4.98/5.21 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 4.98/5.21 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_add_one
% 4.98/5.21 thf(fact_239_one__add__one,axiom,
% 4.98/5.21 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 4.98/5.21 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_add_one
% 4.98/5.21 thf(fact_240_power__strict__decreasing__iff,axiom,
% 4.98/5.21 ! [B: real,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ B )
% 4.98/5.21 => ( ( ord_less_real @ B @ one_one_real )
% 4.98/5.21 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_decreasing_iff
% 4.98/5.21 thf(fact_241_power__strict__decreasing__iff,axiom,
% 4.98/5.21 ! [B: rat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.98/5.21 => ( ( ord_less_rat @ B @ one_one_rat )
% 4.98/5.21 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_decreasing_iff
% 4.98/5.21 thf(fact_242_power__strict__decreasing__iff,axiom,
% 4.98/5.21 ! [B: nat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.21 => ( ( ord_less_nat @ B @ one_one_nat )
% 4.98/5.21 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_decreasing_iff
% 4.98/5.21 thf(fact_243_power__strict__decreasing__iff,axiom,
% 4.98/5.21 ! [B: int,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.21 => ( ( ord_less_int @ B @ one_one_int )
% 4.98/5.21 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_decreasing_iff
% 4.98/5.21 thf(fact_244_power__increasing__iff,axiom,
% 4.98/5.21 ! [B: real,X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_real @ one_one_real @ B )
% 4.98/5.21 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X2 ) @ ( power_power_real @ B @ Y ) )
% 4.98/5.21 = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_increasing_iff
% 4.98/5.21 thf(fact_245_power__increasing__iff,axiom,
% 4.98/5.21 ! [B: rat,X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_rat @ one_one_rat @ B )
% 4.98/5.21 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X2 ) @ ( power_power_rat @ B @ Y ) )
% 4.98/5.21 = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_increasing_iff
% 4.98/5.21 thf(fact_246_power__increasing__iff,axiom,
% 4.98/5.21 ! [B: nat,X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_nat @ one_one_nat @ B )
% 4.98/5.21 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X2 ) @ ( power_power_nat @ B @ Y ) )
% 4.98/5.21 = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_increasing_iff
% 4.98/5.21 thf(fact_247_power__increasing__iff,axiom,
% 4.98/5.21 ! [B: int,X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_int @ one_one_int @ B )
% 4.98/5.21 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X2 ) @ ( power_power_int @ B @ Y ) )
% 4.98/5.21 = ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_increasing_iff
% 4.98/5.21 thf(fact_248_Suc__1,axiom,
% 4.98/5.21 ( ( suc @ one_one_nat )
% 4.98/5.21 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % Suc_1
% 4.98/5.21 thf(fact_249_power__decreasing__iff,axiom,
% 4.98/5.21 ! [B: real,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ B )
% 4.98/5.21 => ( ( ord_less_real @ B @ one_one_real )
% 4.98/5.21 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_decreasing_iff
% 4.98/5.21 thf(fact_250_power__decreasing__iff,axiom,
% 4.98/5.21 ! [B: rat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.98/5.21 => ( ( ord_less_rat @ B @ one_one_rat )
% 4.98/5.21 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_decreasing_iff
% 4.98/5.21 thf(fact_251_power__decreasing__iff,axiom,
% 4.98/5.21 ! [B: nat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.21 => ( ( ord_less_nat @ B @ one_one_nat )
% 4.98/5.21 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_decreasing_iff
% 4.98/5.21 thf(fact_252_power__decreasing__iff,axiom,
% 4.98/5.21 ! [B: int,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.21 => ( ( ord_less_int @ B @ one_one_int )
% 4.98/5.21 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 4.98/5.21 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_decreasing_iff
% 4.98/5.21 thf(fact_253_power__one__over,axiom,
% 4.98/5.21 ! [A: complex,N2: nat] :
% 4.98/5.21 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N2 )
% 4.98/5.21 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_one_over
% 4.98/5.21 thf(fact_254_power__one__over,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N2 )
% 4.98/5.21 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_one_over
% 4.98/5.21 thf(fact_255_power__one__over,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N2 )
% 4.98/5.21 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_one_over
% 4.98/5.21 thf(fact_256_add__One__commute,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( plus_plus_num @ one @ N2 )
% 4.98/5.21 = ( plus_plus_num @ N2 @ one ) ) ).
% 4.98/5.21
% 4.98/5.21 % add_One_commute
% 4.98/5.21 thf(fact_257_power__divide,axiom,
% 4.98/5.21 ! [A: complex,B: complex,N2: nat] :
% 4.98/5.21 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N2 )
% 4.98/5.21 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_divide
% 4.98/5.21 thf(fact_258_power__divide,axiom,
% 4.98/5.21 ! [A: real,B: real,N2: nat] :
% 4.98/5.21 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N2 )
% 4.98/5.21 = ( divide_divide_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_divide
% 4.98/5.21 thf(fact_259_power__divide,axiom,
% 4.98/5.21 ! [A: rat,B: rat,N2: nat] :
% 4.98/5.21 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N2 )
% 4.98/5.21 = ( divide_divide_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_divide
% 4.98/5.21 thf(fact_260_le__num__One__iff,axiom,
% 4.98/5.21 ! [X2: num] :
% 4.98/5.21 ( ( ord_less_eq_num @ X2 @ one )
% 4.98/5.21 = ( X2 = one ) ) ).
% 4.98/5.21
% 4.98/5.21 % le_num_One_iff
% 4.98/5.21 thf(fact_261_divide__numeral__1,axiom,
% 4.98/5.21 ! [A: complex] :
% 4.98/5.21 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % divide_numeral_1
% 4.98/5.21 thf(fact_262_divide__numeral__1,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % divide_numeral_1
% 4.98/5.21 thf(fact_263_divide__numeral__1,axiom,
% 4.98/5.21 ! [A: rat] :
% 4.98/5.21 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 4.98/5.21 = A ) ).
% 4.98/5.21
% 4.98/5.21 % divide_numeral_1
% 4.98/5.21 thf(fact_264_le__numeral__extra_I4_J,axiom,
% 4.98/5.21 ord_less_eq_real @ one_one_real @ one_one_real ).
% 4.98/5.21
% 4.98/5.21 % le_numeral_extra(4)
% 4.98/5.21 thf(fact_265_le__numeral__extra_I4_J,axiom,
% 4.98/5.21 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 4.98/5.21
% 4.98/5.21 % le_numeral_extra(4)
% 4.98/5.21 thf(fact_266_le__numeral__extra_I4_J,axiom,
% 4.98/5.21 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 4.98/5.21
% 4.98/5.21 % le_numeral_extra(4)
% 4.98/5.21 thf(fact_267_le__numeral__extra_I4_J,axiom,
% 4.98/5.21 ord_less_eq_int @ one_one_int @ one_one_int ).
% 4.98/5.21
% 4.98/5.21 % le_numeral_extra(4)
% 4.98/5.21 thf(fact_268_less__numeral__extra_I4_J,axiom,
% 4.98/5.21 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(4)
% 4.98/5.21 thf(fact_269_less__numeral__extra_I4_J,axiom,
% 4.98/5.21 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(4)
% 4.98/5.21 thf(fact_270_less__numeral__extra_I4_J,axiom,
% 4.98/5.21 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(4)
% 4.98/5.21 thf(fact_271_less__numeral__extra_I4_J,axiom,
% 4.98/5.21 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(4)
% 4.98/5.21 thf(fact_272_Suc__nat__number__of__add,axiom,
% 4.98/5.21 ! [V: num,N2: nat] :
% 4.98/5.21 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 4.98/5.21 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % Suc_nat_number_of_add
% 4.98/5.21 thf(fact_273_is__num__normalize_I1_J,axiom,
% 4.98/5.21 ! [A: real,B: real,C: real] :
% 4.98/5.21 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.98/5.21 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % is_num_normalize(1)
% 4.98/5.21 thf(fact_274_is__num__normalize_I1_J,axiom,
% 4.98/5.21 ! [A: rat,B: rat,C: rat] :
% 4.98/5.21 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.98/5.21 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % is_num_normalize(1)
% 4.98/5.21 thf(fact_275_is__num__normalize_I1_J,axiom,
% 4.98/5.21 ! [A: int,B: int,C: int] :
% 4.98/5.21 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.21 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % is_num_normalize(1)
% 4.98/5.21 thf(fact_276_less__numeral__extra_I1_J,axiom,
% 4.98/5.21 ord_less_real @ zero_zero_real @ one_one_real ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(1)
% 4.98/5.21 thf(fact_277_less__numeral__extra_I1_J,axiom,
% 4.98/5.21 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(1)
% 4.98/5.21 thf(fact_278_less__numeral__extra_I1_J,axiom,
% 4.98/5.21 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(1)
% 4.98/5.21 thf(fact_279_less__numeral__extra_I1_J,axiom,
% 4.98/5.21 ord_less_int @ zero_zero_int @ one_one_int ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(1)
% 4.98/5.21 thf(fact_280_one__le__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_le_numeral
% 4.98/5.21 thf(fact_281_one__le__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_le_numeral
% 4.98/5.21 thf(fact_282_one__le__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_le_numeral
% 4.98/5.21 thf(fact_283_one__le__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_le_numeral
% 4.98/5.21 thf(fact_284_not__numeral__less__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_less_one
% 4.98/5.21 thf(fact_285_not__numeral__less__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_less_one
% 4.98/5.21 thf(fact_286_not__numeral__less__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_less_one
% 4.98/5.21 thf(fact_287_not__numeral__less__one,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_less_one
% 4.98/5.21 thf(fact_288_half__gt__zero__iff,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.98/5.21
% 4.98/5.21 % half_gt_zero_iff
% 4.98/5.21 thf(fact_289_half__gt__zero__iff,axiom,
% 4.98/5.21 ! [A: rat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.98/5.21
% 4.98/5.21 % half_gt_zero_iff
% 4.98/5.21 thf(fact_290_half__gt__zero,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % half_gt_zero
% 4.98/5.21 thf(fact_291_half__gt__zero,axiom,
% 4.98/5.21 ! [A: rat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % half_gt_zero
% 4.98/5.21 thf(fact_292_one__plus__numeral__commute,axiom,
% 4.98/5.21 ! [X2: num] :
% 4.98/5.21 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X2 ) )
% 4.98/5.21 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral_commute
% 4.98/5.21 thf(fact_293_one__plus__numeral__commute,axiom,
% 4.98/5.21 ! [X2: num] :
% 4.98/5.21 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 4.98/5.21 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral_commute
% 4.98/5.21 thf(fact_294_one__plus__numeral__commute,axiom,
% 4.98/5.21 ! [X2: num] :
% 4.98/5.21 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 4.98/5.21 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral_commute
% 4.98/5.21 thf(fact_295_one__plus__numeral__commute,axiom,
% 4.98/5.21 ! [X2: num] :
% 4.98/5.21 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 4.98/5.21 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral_commute
% 4.98/5.21 thf(fact_296_one__plus__numeral__commute,axiom,
% 4.98/5.21 ! [X2: num] :
% 4.98/5.21 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 4.98/5.21 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_plus_numeral_commute
% 4.98/5.21 thf(fact_297_numeral__One,axiom,
% 4.98/5.21 ( ( numera6690914467698888265omplex @ one )
% 4.98/5.21 = one_one_complex ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_One
% 4.98/5.21 thf(fact_298_numeral__One,axiom,
% 4.98/5.21 ( ( numeral_numeral_real @ one )
% 4.98/5.21 = one_one_real ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_One
% 4.98/5.21 thf(fact_299_numeral__One,axiom,
% 4.98/5.21 ( ( numeral_numeral_rat @ one )
% 4.98/5.21 = one_one_rat ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_One
% 4.98/5.21 thf(fact_300_numeral__One,axiom,
% 4.98/5.21 ( ( numeral_numeral_nat @ one )
% 4.98/5.21 = one_one_nat ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_One
% 4.98/5.21 thf(fact_301_numeral__One,axiom,
% 4.98/5.21 ( ( numeral_numeral_int @ one )
% 4.98/5.21 = one_one_int ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_One
% 4.98/5.21 thf(fact_302_one__le__power,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_real @ one_one_real @ A )
% 4.98/5.21 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_le_power
% 4.98/5.21 thf(fact_303_one__le__power,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_le_power
% 4.98/5.21 thf(fact_304_one__le__power,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_le_power
% 4.98/5.21 thf(fact_305_one__le__power,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_int @ one_one_int @ A )
% 4.98/5.21 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_le_power
% 4.98/5.21 thf(fact_306_numerals_I1_J,axiom,
% 4.98/5.21 ( ( numeral_numeral_nat @ one )
% 4.98/5.21 = one_one_nat ) ).
% 4.98/5.21
% 4.98/5.21 % numerals(1)
% 4.98/5.21 thf(fact_307_power__0,axiom,
% 4.98/5.21 ! [A: rat] :
% 4.98/5.21 ( ( power_power_rat @ A @ zero_zero_nat )
% 4.98/5.21 = one_one_rat ) ).
% 4.98/5.21
% 4.98/5.21 % power_0
% 4.98/5.21 thf(fact_308_power__0,axiom,
% 4.98/5.21 ! [A: nat] :
% 4.98/5.21 ( ( power_power_nat @ A @ zero_zero_nat )
% 4.98/5.21 = one_one_nat ) ).
% 4.98/5.21
% 4.98/5.21 % power_0
% 4.98/5.21 thf(fact_309_power__0,axiom,
% 4.98/5.21 ! [A: int] :
% 4.98/5.21 ( ( power_power_int @ A @ zero_zero_nat )
% 4.98/5.21 = one_one_int ) ).
% 4.98/5.21
% 4.98/5.21 % power_0
% 4.98/5.21 thf(fact_310_power__0,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ( ( power_power_real @ A @ zero_zero_nat )
% 4.98/5.21 = one_one_real ) ).
% 4.98/5.21
% 4.98/5.21 % power_0
% 4.98/5.21 thf(fact_311_power__0,axiom,
% 4.98/5.21 ! [A: complex] :
% 4.98/5.21 ( ( power_power_complex @ A @ zero_zero_nat )
% 4.98/5.21 = one_one_complex ) ).
% 4.98/5.21
% 4.98/5.21 % power_0
% 4.98/5.21 thf(fact_312_power__le__one,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ A @ one_one_real )
% 4.98/5.21 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ one_one_real ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_one
% 4.98/5.21 thf(fact_313_power__le__one,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.98/5.21 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_one
% 4.98/5.21 thf(fact_314_power__le__one,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 4.98/5.21 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_one
% 4.98/5.21 thf(fact_315_power__le__one,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_eq_int @ A @ one_one_int )
% 4.98/5.21 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_one
% 4.98/5.21 thf(fact_316_power__0__left,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ( N2 = zero_zero_nat )
% 4.98/5.21 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 4.98/5.21 = one_one_rat ) )
% 4.98/5.21 & ( ( N2 != zero_zero_nat )
% 4.98/5.21 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 4.98/5.21 = zero_zero_rat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_left
% 4.98/5.21 thf(fact_317_power__0__left,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ( N2 = zero_zero_nat )
% 4.98/5.21 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 = one_one_nat ) )
% 4.98/5.21 & ( ( N2 != zero_zero_nat )
% 4.98/5.21 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 = zero_zero_nat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_left
% 4.98/5.21 thf(fact_318_power__0__left,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ( N2 = zero_zero_nat )
% 4.98/5.21 => ( ( power_power_int @ zero_zero_int @ N2 )
% 4.98/5.21 = one_one_int ) )
% 4.98/5.21 & ( ( N2 != zero_zero_nat )
% 4.98/5.21 => ( ( power_power_int @ zero_zero_int @ N2 )
% 4.98/5.21 = zero_zero_int ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_left
% 4.98/5.21 thf(fact_319_power__0__left,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ( N2 = zero_zero_nat )
% 4.98/5.21 => ( ( power_power_real @ zero_zero_real @ N2 )
% 4.98/5.21 = one_one_real ) )
% 4.98/5.21 & ( ( N2 != zero_zero_nat )
% 4.98/5.21 => ( ( power_power_real @ zero_zero_real @ N2 )
% 4.98/5.21 = zero_zero_real ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_left
% 4.98/5.21 thf(fact_320_power__0__left,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ( N2 = zero_zero_nat )
% 4.98/5.21 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 4.98/5.21 = one_one_complex ) )
% 4.98/5.21 & ( ( N2 != zero_zero_nat )
% 4.98/5.21 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 4.98/5.21 = zero_zero_complex ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_0_left
% 4.98/5.21 thf(fact_321_power__gt1,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ one_one_real @ A )
% 4.98/5.21 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_gt1
% 4.98/5.21 thf(fact_322_power__gt1,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_gt1
% 4.98/5.21 thf(fact_323_power__gt1,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_gt1
% 4.98/5.21 thf(fact_324_power__gt1,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ one_one_int @ A )
% 4.98/5.21 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_gt1
% 4.98/5.21 thf(fact_325_power__strict__increasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: real] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_real @ one_one_real @ A )
% 4.98/5.21 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_increasing
% 4.98/5.21 thf(fact_326_power__strict__increasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: rat] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_increasing
% 4.98/5.21 thf(fact_327_power__strict__increasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: nat] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_increasing
% 4.98/5.21 thf(fact_328_power__strict__increasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: int] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_int @ one_one_int @ A )
% 4.98/5.21 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_increasing
% 4.98/5.21 thf(fact_329_power__less__imp__less__exp,axiom,
% 4.98/5.21 ! [A: real,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ one_one_real @ A )
% 4.98/5.21 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 4.98/5.21 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_less_imp_less_exp
% 4.98/5.21 thf(fact_330_power__less__imp__less__exp,axiom,
% 4.98/5.21 ! [A: rat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 4.98/5.21 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_less_imp_less_exp
% 4.98/5.21 thf(fact_331_power__less__imp__less__exp,axiom,
% 4.98/5.21 ! [A: nat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 4.98/5.21 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_less_imp_less_exp
% 4.98/5.21 thf(fact_332_power__less__imp__less__exp,axiom,
% 4.98/5.21 ! [A: int,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ one_one_int @ A )
% 4.98/5.21 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 4.98/5.21 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_less_imp_less_exp
% 4.98/5.21 thf(fact_333_power__increasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: real] :
% 4.98/5.21 ( ( ord_less_eq_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_eq_real @ one_one_real @ A )
% 4.98/5.21 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_increasing
% 4.98/5.21 thf(fact_334_power__increasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: rat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_increasing
% 4.98/5.21 thf(fact_335_power__increasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_increasing
% 4.98/5.21 thf(fact_336_power__increasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: int] :
% 4.98/5.21 ( ( ord_less_eq_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_eq_int @ one_one_int @ A )
% 4.98/5.21 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_increasing
% 4.98/5.21 thf(fact_337_le__numeral__extra_I3_J,axiom,
% 4.98/5.21 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 4.98/5.21
% 4.98/5.21 % le_numeral_extra(3)
% 4.98/5.21 thf(fact_338_le__numeral__extra_I3_J,axiom,
% 4.98/5.21 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 4.98/5.21
% 4.98/5.21 % le_numeral_extra(3)
% 4.98/5.21 thf(fact_339_le__numeral__extra_I3_J,axiom,
% 4.98/5.21 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 4.98/5.21
% 4.98/5.21 % le_numeral_extra(3)
% 4.98/5.21 thf(fact_340_le__numeral__extra_I3_J,axiom,
% 4.98/5.21 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 4.98/5.21
% 4.98/5.21 % le_numeral_extra(3)
% 4.98/5.21 thf(fact_341_less__numeral__extra_I3_J,axiom,
% 4.98/5.21 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(3)
% 4.98/5.21 thf(fact_342_less__numeral__extra_I3_J,axiom,
% 4.98/5.21 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(3)
% 4.98/5.21 thf(fact_343_less__numeral__extra_I3_J,axiom,
% 4.98/5.21 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(3)
% 4.98/5.21 thf(fact_344_less__numeral__extra_I3_J,axiom,
% 4.98/5.21 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % less_numeral_extra(3)
% 4.98/5.21 thf(fact_345_zero__neq__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( zero_zero_complex
% 4.98/5.21 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_neq_numeral
% 4.98/5.21 thf(fact_346_zero__neq__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( zero_zero_real
% 4.98/5.21 != ( numeral_numeral_real @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_neq_numeral
% 4.98/5.21 thf(fact_347_zero__neq__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( zero_zero_rat
% 4.98/5.21 != ( numeral_numeral_rat @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_neq_numeral
% 4.98/5.21 thf(fact_348_zero__neq__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( zero_zero_nat
% 4.98/5.21 != ( numeral_numeral_nat @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_neq_numeral
% 4.98/5.21 thf(fact_349_zero__neq__numeral,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( zero_zero_int
% 4.98/5.21 != ( numeral_numeral_int @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_neq_numeral
% 4.98/5.21 thf(fact_350_power__not__zero,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( A != zero_zero_rat )
% 4.98/5.21 => ( ( power_power_rat @ A @ N2 )
% 4.98/5.21 != zero_zero_rat ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_not_zero
% 4.98/5.21 thf(fact_351_power__not__zero,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( A != zero_zero_nat )
% 4.98/5.21 => ( ( power_power_nat @ A @ N2 )
% 4.98/5.21 != zero_zero_nat ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_not_zero
% 4.98/5.21 thf(fact_352_power__not__zero,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( A != zero_zero_int )
% 4.98/5.21 => ( ( power_power_int @ A @ N2 )
% 4.98/5.21 != zero_zero_int ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_not_zero
% 4.98/5.21 thf(fact_353_power__not__zero,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( A != zero_zero_real )
% 4.98/5.21 => ( ( power_power_real @ A @ N2 )
% 4.98/5.21 != zero_zero_real ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_not_zero
% 4.98/5.21 thf(fact_354_power__not__zero,axiom,
% 4.98/5.21 ! [A: complex,N2: nat] :
% 4.98/5.21 ( ( A != zero_zero_complex )
% 4.98/5.21 => ( ( power_power_complex @ A @ N2 )
% 4.98/5.21 != zero_zero_complex ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_not_zero
% 4.98/5.21 thf(fact_355_power__Suc__le__self,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ A @ one_one_real )
% 4.98/5.21 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_le_self
% 4.98/5.21 thf(fact_356_power__Suc__le__self,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.98/5.21 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_le_self
% 4.98/5.21 thf(fact_357_power__Suc__le__self,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 4.98/5.21 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_le_self
% 4.98/5.21 thf(fact_358_power__Suc__le__self,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_eq_int @ A @ one_one_int )
% 4.98/5.21 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_le_self
% 4.98/5.21 thf(fact_359_power__Suc__less__one,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_real @ A @ one_one_real )
% 4.98/5.21 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ one_one_real ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_less_one
% 4.98/5.21 thf(fact_360_power__Suc__less__one,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_rat @ A @ one_one_rat )
% 4.98/5.21 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_less_one
% 4.98/5.21 thf(fact_361_power__Suc__less__one,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ A @ one_one_nat )
% 4.98/5.21 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_less_one
% 4.98/5.21 thf(fact_362_power__Suc__less__one,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_int @ A @ one_one_int )
% 4.98/5.21 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_Suc_less_one
% 4.98/5.21 thf(fact_363_power__strict__decreasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: real] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_real @ A @ one_one_real )
% 4.98/5.21 => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_decreasing
% 4.98/5.21 thf(fact_364_power__strict__decreasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: rat] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_rat @ A @ one_one_rat )
% 4.98/5.21 => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_decreasing
% 4.98/5.21 thf(fact_365_power__strict__decreasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: nat] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ A @ one_one_nat )
% 4.98/5.21 => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_decreasing
% 4.98/5.21 thf(fact_366_power__strict__decreasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: int] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_int @ A @ one_one_int )
% 4.98/5.21 => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_decreasing
% 4.98/5.21 thf(fact_367_power__decreasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: real] :
% 4.98/5.21 ( ( ord_less_eq_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ A @ one_one_real )
% 4.98/5.21 => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_decreasing
% 4.98/5.21 thf(fact_368_power__decreasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: rat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.98/5.21 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_decreasing
% 4.98/5.21 thf(fact_369_power__decreasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 4.98/5.21 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_decreasing
% 4.98/5.21 thf(fact_370_power__decreasing,axiom,
% 4.98/5.21 ! [N2: nat,N4: nat,A: int] :
% 4.98/5.21 ( ( ord_less_eq_nat @ N2 @ N4 )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_eq_int @ A @ one_one_int )
% 4.98/5.21 => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_decreasing
% 4.98/5.21 thf(fact_371_power__le__imp__le__exp,axiom,
% 4.98/5.21 ! [A: real,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ one_one_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 4.98/5.21 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_imp_le_exp
% 4.98/5.21 thf(fact_372_power__le__imp__le__exp,axiom,
% 4.98/5.21 ! [A: rat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 4.98/5.21 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_imp_le_exp
% 4.98/5.21 thf(fact_373_power__le__imp__le__exp,axiom,
% 4.98/5.21 ! [A: nat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 4.98/5.21 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_imp_le_exp
% 4.98/5.21 thf(fact_374_power__le__imp__le__exp,axiom,
% 4.98/5.21 ! [A: int,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ one_one_int @ A )
% 4.98/5.21 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 4.98/5.21 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_imp_le_exp
% 4.98/5.21 thf(fact_375_self__le__power,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_real @ one_one_real @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % self_le_power
% 4.98/5.21 thf(fact_376_self__le__power,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % self_le_power
% 4.98/5.21 thf(fact_377_self__le__power,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % self_le_power
% 4.98/5.21 thf(fact_378_self__le__power,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_int @ one_one_int @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % self_le_power
% 4.98/5.21 thf(fact_379_one__power2,axiom,
% 4.98/5.21 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = one_one_rat ) ).
% 4.98/5.21
% 4.98/5.21 % one_power2
% 4.98/5.21 thf(fact_380_one__power2,axiom,
% 4.98/5.21 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = one_one_nat ) ).
% 4.98/5.21
% 4.98/5.21 % one_power2
% 4.98/5.21 thf(fact_381_one__power2,axiom,
% 4.98/5.21 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = one_one_int ) ).
% 4.98/5.21
% 4.98/5.21 % one_power2
% 4.98/5.21 thf(fact_382_one__power2,axiom,
% 4.98/5.21 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = one_one_real ) ).
% 4.98/5.21
% 4.98/5.21 % one_power2
% 4.98/5.21 thf(fact_383_one__power2,axiom,
% 4.98/5.21 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = one_one_complex ) ).
% 4.98/5.21
% 4.98/5.21 % one_power2
% 4.98/5.21 thf(fact_384_one__less__power,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ one_one_real @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_less_power
% 4.98/5.21 thf(fact_385_one__less__power,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ one_one_rat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_less_power
% 4.98/5.21 thf(fact_386_one__less__power,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ one_one_nat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_less_power
% 4.98/5.21 thf(fact_387_one__less__power,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ one_one_int @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % one_less_power
% 4.98/5.21 thf(fact_388_nat__1__add__1,axiom,
% 4.98/5.21 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 4.98/5.21 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % nat_1_add_1
% 4.98/5.21 thf(fact_389_not__numeral__le__zero,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_le_zero
% 4.98/5.21 thf(fact_390_not__numeral__le__zero,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_le_zero
% 4.98/5.21 thf(fact_391_not__numeral__le__zero,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_le_zero
% 4.98/5.21 thf(fact_392_not__numeral__le__zero,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_le_zero
% 4.98/5.21 thf(fact_393_zero__le__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_numeral
% 4.98/5.21 thf(fact_394_zero__le__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_numeral
% 4.98/5.21 thf(fact_395_zero__le__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_numeral
% 4.98/5.21 thf(fact_396_zero__le__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_numeral
% 4.98/5.21 thf(fact_397_not__numeral__less__zero,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_less_zero
% 4.98/5.21 thf(fact_398_not__numeral__less__zero,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_less_zero
% 4.98/5.21 thf(fact_399_not__numeral__less__zero,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_less_zero
% 4.98/5.21 thf(fact_400_not__numeral__less__zero,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % not_numeral_less_zero
% 4.98/5.21 thf(fact_401_zero__less__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_numeral
% 4.98/5.21 thf(fact_402_zero__less__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_numeral
% 4.98/5.21 thf(fact_403_zero__less__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_numeral
% 4.98/5.21 thf(fact_404_zero__less__numeral,axiom,
% 4.98/5.21 ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_numeral
% 4.98/5.21 thf(fact_405_zero__le__power,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_power
% 4.98/5.21 thf(fact_406_zero__le__power,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_power
% 4.98/5.21 thf(fact_407_zero__le__power,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_power
% 4.98/5.21 thf(fact_408_zero__le__power,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_power
% 4.98/5.21 thf(fact_409_power__mono,axiom,
% 4.98/5.21 ! [A: real,B: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_mono
% 4.98/5.21 thf(fact_410_power__mono,axiom,
% 4.98/5.21 ! [A: rat,B: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_mono
% 4.98/5.21 thf(fact_411_power__mono,axiom,
% 4.98/5.21 ! [A: nat,B: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_mono
% 4.98/5.21 thf(fact_412_power__mono,axiom,
% 4.98/5.21 ! [A: int,B: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_mono
% 4.98/5.21 thf(fact_413_zero__less__power,axiom,
% 4.98/5.21 ! [A: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_power
% 4.98/5.21 thf(fact_414_zero__less__power,axiom,
% 4.98/5.21 ! [A: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_power
% 4.98/5.21 thf(fact_415_zero__less__power,axiom,
% 4.98/5.21 ! [A: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_power
% 4.98/5.21 thf(fact_416_zero__less__power,axiom,
% 4.98/5.21 ! [A: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_less_power
% 4.98/5.21 thf(fact_417_numeral__Bit0,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 4.98/5.21 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_Bit0
% 4.98/5.21 thf(fact_418_numeral__Bit0,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 4.98/5.21 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_Bit0
% 4.98/5.21 thf(fact_419_numeral__Bit0,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 4.98/5.21 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_Bit0
% 4.98/5.21 thf(fact_420_numeral__Bit0,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 4.98/5.21 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_Bit0
% 4.98/5.21 thf(fact_421_numeral__Bit0,axiom,
% 4.98/5.21 ! [N2: num] :
% 4.98/5.21 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 4.98/5.21 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_Bit0
% 4.98/5.21 thf(fact_422_nat__power__less__imp__less,axiom,
% 4.98/5.21 ! [I3: nat,M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ I3 )
% 4.98/5.21 => ( ( ord_less_nat @ ( power_power_nat @ I3 @ M ) @ ( power_power_nat @ I3 @ N2 ) )
% 4.98/5.21 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % nat_power_less_imp_less
% 4.98/5.21 thf(fact_423_ex__power__ivl2,axiom,
% 4.98/5.21 ! [B: nat,K: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.98/5.21 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.98/5.21 => ? [N: nat] :
% 4.98/5.21 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 4.98/5.21 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % ex_power_ivl2
% 4.98/5.21 thf(fact_424_ex__power__ivl1,axiom,
% 4.98/5.21 ! [B: nat,K: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 4.98/5.21 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 4.98/5.21 => ? [N: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 4.98/5.21 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % ex_power_ivl1
% 4.98/5.21 thf(fact_425_power__less__imp__less__base,axiom,
% 4.98/5.21 ! [A: real,N2: nat,B: real] :
% 4.98/5.21 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.21 => ( ord_less_real @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_less_imp_less_base
% 4.98/5.21 thf(fact_426_power__less__imp__less__base,axiom,
% 4.98/5.21 ! [A: rat,N2: nat,B: rat] :
% 4.98/5.21 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.21 => ( ord_less_rat @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_less_imp_less_base
% 4.98/5.21 thf(fact_427_power__less__imp__less__base,axiom,
% 4.98/5.21 ! [A: nat,N2: nat,B: nat] :
% 4.98/5.21 ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.21 => ( ord_less_nat @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_less_imp_less_base
% 4.98/5.21 thf(fact_428_power__less__imp__less__base,axiom,
% 4.98/5.21 ! [A: int,N2: nat,B: int] :
% 4.98/5.21 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.21 => ( ord_less_int @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_less_imp_less_base
% 4.98/5.21 thf(fact_429_power__le__imp__le__base,axiom,
% 4.98/5.21 ! [A: real,N2: nat,B: real] :
% 4.98/5.21 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.21 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_imp_le_base
% 4.98/5.21 thf(fact_430_power__le__imp__le__base,axiom,
% 4.98/5.21 ! [A: rat,N2: nat,B: rat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.21 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_imp_le_base
% 4.98/5.21 thf(fact_431_power__le__imp__le__base,axiom,
% 4.98/5.21 ! [A: nat,N2: nat,B: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.21 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_imp_le_base
% 4.98/5.21 thf(fact_432_power__le__imp__le__base,axiom,
% 4.98/5.21 ! [A: int,N2: nat,B: int] :
% 4.98/5.21 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.21 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_le_imp_le_base
% 4.98/5.21 thf(fact_433_power__inject__base,axiom,
% 4.98/5.21 ! [A: real,N2: nat,B: real] :
% 4.98/5.21 ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 4.98/5.21 = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.21 => ( A = B ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_inject_base
% 4.98/5.21 thf(fact_434_power__inject__base,axiom,
% 4.98/5.21 ! [A: rat,N2: nat,B: rat] :
% 4.98/5.21 ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 4.98/5.21 = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.21 => ( A = B ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_inject_base
% 4.98/5.21 thf(fact_435_power__inject__base,axiom,
% 4.98/5.21 ! [A: nat,N2: nat,B: nat] :
% 4.98/5.21 ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 4.98/5.21 = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.21 => ( A = B ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_inject_base
% 4.98/5.21 thf(fact_436_power__inject__base,axiom,
% 4.98/5.21 ! [A: int,N2: nat,B: int] :
% 4.98/5.21 ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 4.98/5.21 = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.21 => ( A = B ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_inject_base
% 4.98/5.21 thf(fact_437_zero__power,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 4.98/5.21 = zero_zero_rat ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power
% 4.98/5.21 thf(fact_438_zero__power,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 = zero_zero_nat ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power
% 4.98/5.21 thf(fact_439_zero__power,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( power_power_int @ zero_zero_int @ N2 )
% 4.98/5.21 = zero_zero_int ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power
% 4.98/5.21 thf(fact_440_zero__power,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( power_power_real @ zero_zero_real @ N2 )
% 4.98/5.21 = zero_zero_real ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power
% 4.98/5.21 thf(fact_441_zero__power,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 4.98/5.21 = zero_zero_complex ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power
% 4.98/5.21 thf(fact_442_numeral__1__eq__Suc__0,axiom,
% 4.98/5.21 ( ( numeral_numeral_nat @ one )
% 4.98/5.21 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_1_eq_Suc_0
% 4.98/5.21 thf(fact_443_power__gt__expt,axiom,
% 4.98/5.21 ! [N2: nat,K: nat] :
% 4.98/5.21 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 4.98/5.21 => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_gt_expt
% 4.98/5.21 thf(fact_444_nat__one__le__power,axiom,
% 4.98/5.21 ! [I3: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I3 )
% 4.98/5.21 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I3 @ N2 ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % nat_one_le_power
% 4.98/5.21 thf(fact_445_power__eq__imp__eq__base,axiom,
% 4.98/5.21 ! [A: real,N2: nat,B: real] :
% 4.98/5.21 ( ( ( power_power_real @ A @ N2 )
% 4.98/5.21 = ( power_power_real @ B @ N2 ) )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( A = B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_imp_eq_base
% 4.98/5.21 thf(fact_446_power__eq__imp__eq__base,axiom,
% 4.98/5.21 ! [A: rat,N2: nat,B: rat] :
% 4.98/5.21 ( ( ( power_power_rat @ A @ N2 )
% 4.98/5.21 = ( power_power_rat @ B @ N2 ) )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( A = B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_imp_eq_base
% 4.98/5.21 thf(fact_447_power__eq__imp__eq__base,axiom,
% 4.98/5.21 ! [A: nat,N2: nat,B: nat] :
% 4.98/5.21 ( ( ( power_power_nat @ A @ N2 )
% 4.98/5.21 = ( power_power_nat @ B @ N2 ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( A = B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_imp_eq_base
% 4.98/5.21 thf(fact_448_power__eq__imp__eq__base,axiom,
% 4.98/5.21 ! [A: int,N2: nat,B: int] :
% 4.98/5.21 ( ( ( power_power_int @ A @ N2 )
% 4.98/5.21 = ( power_power_int @ B @ N2 ) )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( A = B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_imp_eq_base
% 4.98/5.21 thf(fact_449_power__eq__iff__eq__base,axiom,
% 4.98/5.21 ! [N2: nat,A: real,B: real] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.21 => ( ( ( power_power_real @ A @ N2 )
% 4.98/5.21 = ( power_power_real @ B @ N2 ) )
% 4.98/5.21 = ( A = B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_iff_eq_base
% 4.98/5.21 thf(fact_450_power__eq__iff__eq__base,axiom,
% 4.98/5.21 ! [N2: nat,A: rat,B: rat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.21 => ( ( ( power_power_rat @ A @ N2 )
% 4.98/5.21 = ( power_power_rat @ B @ N2 ) )
% 4.98/5.21 = ( A = B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_iff_eq_base
% 4.98/5.21 thf(fact_451_power__eq__iff__eq__base,axiom,
% 4.98/5.21 ! [N2: nat,A: nat,B: nat] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.21 => ( ( ( power_power_nat @ A @ N2 )
% 4.98/5.21 = ( power_power_nat @ B @ N2 ) )
% 4.98/5.21 = ( A = B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_iff_eq_base
% 4.98/5.21 thf(fact_452_power__eq__iff__eq__base,axiom,
% 4.98/5.21 ! [N2: nat,A: int,B: int] :
% 4.98/5.21 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.21 => ( ( ( power_power_int @ A @ N2 )
% 4.98/5.21 = ( power_power_int @ B @ N2 ) )
% 4.98/5.21 = ( A = B ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_eq_iff_eq_base
% 4.98/5.21 thf(fact_453_zero__power2,axiom,
% 4.98/5.21 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_rat ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power2
% 4.98/5.21 thf(fact_454_zero__power2,axiom,
% 4.98/5.21 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_nat ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power2
% 4.98/5.21 thf(fact_455_zero__power2,axiom,
% 4.98/5.21 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power2
% 4.98/5.21 thf(fact_456_zero__power2,axiom,
% 4.98/5.21 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_real ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power2
% 4.98/5.21 thf(fact_457_zero__power2,axiom,
% 4.98/5.21 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_complex ) ).
% 4.98/5.21
% 4.98/5.21 % zero_power2
% 4.98/5.21 thf(fact_458_numeral__2__eq__2,axiom,
% 4.98/5.21 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 4.98/5.21 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % numeral_2_eq_2
% 4.98/5.21 thf(fact_459_less__exp,axiom,
% 4.98/5.21 ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % less_exp
% 4.98/5.21 thf(fact_460_power2__nat__le__imp__le,axiom,
% 4.98/5.21 ! [M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 4.98/5.21 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_nat_le_imp_le
% 4.98/5.21 thf(fact_461_power2__nat__le__eq__le,axiom,
% 4.98/5.21 ! [M: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_nat_le_eq_le
% 4.98/5.21 thf(fact_462_self__le__ge2__pow,axiom,
% 4.98/5.21 ! [K: nat,M: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 4.98/5.21 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % self_le_ge2_pow
% 4.98/5.21 thf(fact_463_power2__le__imp__le,axiom,
% 4.98/5.21 ! [X2: real,Y: real] :
% 4.98/5.21 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.21 => ( ord_less_eq_real @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_le_imp_le
% 4.98/5.21 thf(fact_464_power2__le__imp__le,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.21 => ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_le_imp_le
% 4.98/5.21 thf(fact_465_power2__le__imp__le,axiom,
% 4.98/5.21 ! [X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_eq_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.98/5.21 => ( ord_less_eq_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_le_imp_le
% 4.98/5.21 thf(fact_466_power2__le__imp__le,axiom,
% 4.98/5.21 ! [X2: int,Y: int] :
% 4.98/5.21 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.98/5.21 => ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_le_imp_le
% 4.98/5.21 thf(fact_467_power2__eq__imp__eq,axiom,
% 4.98/5.21 ! [X2: real,Y: real] :
% 4.98/5.21 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.21 => ( X2 = Y ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_eq_imp_eq
% 4.98/5.21 thf(fact_468_power2__eq__imp__eq,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] :
% 4.98/5.21 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.21 => ( X2 = Y ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_eq_imp_eq
% 4.98/5.21 thf(fact_469_power2__eq__imp__eq,axiom,
% 4.98/5.21 ! [X2: nat,Y: nat] :
% 4.98/5.21 ( ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.98/5.21 => ( X2 = Y ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_eq_imp_eq
% 4.98/5.21 thf(fact_470_power2__eq__imp__eq,axiom,
% 4.98/5.21 ! [X2: int,Y: int] :
% 4.98/5.21 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.98/5.21 => ( X2 = Y ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_eq_imp_eq
% 4.98/5.21 thf(fact_471_zero__le__power2,axiom,
% 4.98/5.21 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_power2
% 4.98/5.21 thf(fact_472_zero__le__power2,axiom,
% 4.98/5.21 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_power2
% 4.98/5.21 thf(fact_473_zero__le__power2,axiom,
% 4.98/5.21 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % zero_le_power2
% 4.98/5.21 thf(fact_474_power__strict__mono,axiom,
% 4.98/5.21 ! [A: real,B: real,N2: nat] :
% 4.98/5.21 ( ( ord_less_real @ A @ B )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_mono
% 4.98/5.21 thf(fact_475_power__strict__mono,axiom,
% 4.98/5.21 ! [A: rat,B: rat,N2: nat] :
% 4.98/5.21 ( ( ord_less_rat @ A @ B )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_mono
% 4.98/5.21 thf(fact_476_power__strict__mono,axiom,
% 4.98/5.21 ! [A: nat,B: nat,N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ A @ B )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_mono
% 4.98/5.21 thf(fact_477_power__strict__mono,axiom,
% 4.98/5.21 ! [A: int,B: int,N2: nat] :
% 4.98/5.21 ( ( ord_less_int @ A @ B )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.21 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.21 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power_strict_mono
% 4.98/5.21 thf(fact_478_power2__less__0,axiom,
% 4.98/5.21 ! [A: real] :
% 4.98/5.21 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_0
% 4.98/5.21 thf(fact_479_power2__less__0,axiom,
% 4.98/5.21 ! [A: rat] :
% 4.98/5.21 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_0
% 4.98/5.21 thf(fact_480_power2__less__0,axiom,
% 4.98/5.21 ! [A: int] :
% 4.98/5.21 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_0
% 4.98/5.21 thf(fact_481_less__2__cases__iff,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( ( N2 = zero_zero_nat )
% 4.98/5.21 | ( N2
% 4.98/5.21 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % less_2_cases_iff
% 4.98/5.21 thf(fact_482_less__2__cases,axiom,
% 4.98/5.21 ! [N2: nat] :
% 4.98/5.21 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 => ( ( N2 = zero_zero_nat )
% 4.98/5.21 | ( N2
% 4.98/5.21 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % less_2_cases
% 4.98/5.21 thf(fact_483_power2__less__imp__less,axiom,
% 4.98/5.21 ! [X2: real,Y: real] :
% 4.98/5.21 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.21 => ( ord_less_real @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_imp_less
% 4.98/5.21 thf(fact_484_power2__less__imp__less,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] :
% 4.98/5.21 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.21 => ( ord_less_rat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_imp_less
% 4.98/5.21 thf(fact_485_power2__less__imp__less,axiom,
% 4.98/5.21 ! [X2: nat,Y: nat] :
% 4.98/5.21 ( ( ord_less_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.98/5.21 => ( ord_less_nat @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_imp_less
% 4.98/5.21 thf(fact_486_power2__less__imp__less,axiom,
% 4.98/5.21 ! [X2: int,Y: int] :
% 4.98/5.21 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.21 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.98/5.21 => ( ord_less_int @ X2 @ Y ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % power2_less_imp_less
% 4.98/5.21 thf(fact_487_sum__power2__le__zero__iff,axiom,
% 4.98/5.21 ! [X2: real,Y: real] :
% 4.98/5.21 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 4.98/5.21 = ( ( X2 = zero_zero_real )
% 4.98/5.21 & ( Y = zero_zero_real ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_le_zero_iff
% 4.98/5.21 thf(fact_488_sum__power2__le__zero__iff,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] :
% 4.98/5.21 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 4.98/5.21 = ( ( X2 = zero_zero_rat )
% 4.98/5.21 & ( Y = zero_zero_rat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_le_zero_iff
% 4.98/5.21 thf(fact_489_sum__power2__le__zero__iff,axiom,
% 4.98/5.21 ! [X2: int,Y: int] :
% 4.98/5.21 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 4.98/5.21 = ( ( X2 = zero_zero_int )
% 4.98/5.21 & ( Y = zero_zero_int ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_le_zero_iff
% 4.98/5.21 thf(fact_490_sum__power2__ge__zero,axiom,
% 4.98/5.21 ! [X2: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_ge_zero
% 4.98/5.21 thf(fact_491_sum__power2__ge__zero,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_ge_zero
% 4.98/5.21 thf(fact_492_sum__power2__ge__zero,axiom,
% 4.98/5.21 ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_ge_zero
% 4.98/5.21 thf(fact_493_sum__power2__gt__zero__iff,axiom,
% 4.98/5.21 ! [X2: real,Y: real] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.98/5.21 = ( ( X2 != zero_zero_real )
% 4.98/5.21 | ( Y != zero_zero_real ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_gt_zero_iff
% 4.98/5.21 thf(fact_494_sum__power2__gt__zero__iff,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.98/5.21 = ( ( X2 != zero_zero_rat )
% 4.98/5.21 | ( Y != zero_zero_rat ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_gt_zero_iff
% 4.98/5.21 thf(fact_495_sum__power2__gt__zero__iff,axiom,
% 4.98/5.21 ! [X2: int,Y: int] :
% 4.98/5.21 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.98/5.21 = ( ( X2 != zero_zero_int )
% 4.98/5.21 | ( Y != zero_zero_int ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % sum_power2_gt_zero_iff
% 4.98/5.21 thf(fact_496_not__sum__power2__lt__zero,axiom,
% 4.98/5.21 ! [X2: real,Y: real] :
% 4.98/5.21 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 4.98/5.21
% 4.98/5.21 % not_sum_power2_lt_zero
% 4.98/5.21 thf(fact_497_not__sum__power2__lt__zero,axiom,
% 4.98/5.21 ! [X2: rat,Y: rat] :
% 4.98/5.21 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 4.98/5.21
% 4.98/5.21 % not_sum_power2_lt_zero
% 4.98/5.21 thf(fact_498_not__sum__power2__lt__zero,axiom,
% 4.98/5.21 ! [X2: int,Y: int] :
% 4.98/5.21 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % not_sum_power2_lt_zero
% 4.98/5.21 thf(fact_499__092_060open_062vebt__insert_A_INode_A_ISome_A_Imi_M_Ama_J_J_Adeg_AtreeList_Asummary_J_Ax_A_061_ANode_A_ISome_A_Ix_M_Amax_Ami_Ama_J_J_Adeg_A_ItreeList_091high_Ami_An_A_058_061_Avebt__insert_A_ItreeList_A_B_Ahigh_Ami_An_J_A_Ilow_Ami_An_J_093_J_A_Iif_AminNull_A_ItreeList_A_B_Ahigh_Ami_An_J_Athen_Avebt__insert_Asummary_A_Ihigh_Ami_An_J_Aelse_Asummary_J_092_060close_062,axiom,
% 4.98/5.21 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 4.98/5.21 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ xa @ ( ord_max_nat @ mi @ ma ) ) ) @ deg @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) @ ( vEBT_VEBT_low @ mi @ na ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ mi @ na ) ) ) @ ( vEBT_vebt_insert @ summary @ ( vEBT_VEBT_high @ mi @ na ) ) @ summary ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % \<open>vebt_insert (Node (Some (mi, ma)) deg treeList summary) x = Node (Some (x, max mi ma)) deg (treeList[high mi n := vebt_insert (treeList ! high mi n) (low mi n)]) (if minNull (treeList ! high mi n) then vebt_insert summary (high mi n) else summary)\<close>
% 4.98/5.21 thf(fact_500_one__div__two__eq__zero,axiom,
% 4.98/5.21 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_nat ) ).
% 4.98/5.21
% 4.98/5.21 % one_div_two_eq_zero
% 4.98/5.21 thf(fact_501_one__div__two__eq__zero,axiom,
% 4.98/5.21 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % one_div_two_eq_zero
% 4.98/5.21 thf(fact_502_bits__1__div__2,axiom,
% 4.98/5.21 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_nat ) ).
% 4.98/5.21
% 4.98/5.21 % bits_1_div_2
% 4.98/5.21 thf(fact_503_bits__1__div__2,axiom,
% 4.98/5.21 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.21 = zero_zero_int ) ).
% 4.98/5.21
% 4.98/5.21 % bits_1_div_2
% 4.98/5.21 thf(fact_504_set__swap,axiom,
% 4.98/5.21 ! [I3: nat,Xs: list_VEBT_VEBT,J: nat] :
% 4.98/5.21 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.21 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.21 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) )
% 4.98/5.21 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % set_swap
% 4.98/5.21 thf(fact_505_set__swap,axiom,
% 4.98/5.21 ! [I3: nat,Xs: list_o,J: nat] :
% 4.98/5.21 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 4.98/5.21 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 4.98/5.21 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I3 @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I3 ) ) )
% 4.98/5.21 = ( set_o2 @ Xs ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % set_swap
% 4.98/5.21 thf(fact_506_set__swap,axiom,
% 4.98/5.21 ! [I3: nat,Xs: list_nat,J: nat] :
% 4.98/5.21 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.21 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 4.98/5.21 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I3 ) ) )
% 4.98/5.21 = ( set_nat2 @ Xs ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % set_swap
% 4.98/5.21 thf(fact_507_set__swap,axiom,
% 4.98/5.21 ! [I3: nat,Xs: list_int,J: nat] :
% 4.98/5.21 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 4.98/5.21 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 4.98/5.21 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I3 @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I3 ) ) )
% 4.98/5.21 = ( set_int2 @ Xs ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % set_swap
% 4.98/5.21 thf(fact_508_add__self__div__2,axiom,
% 4.98/5.21 ! [M: nat] :
% 4.98/5.21 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = M ) ).
% 4.98/5.21
% 4.98/5.21 % add_self_div_2
% 4.98/5.21 thf(fact_509_div2__Suc__Suc,axiom,
% 4.98/5.21 ! [M: nat] :
% 4.98/5.21 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.21 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % div2_Suc_Suc
% 4.98/5.21 thf(fact_510_le__divide__eq__1__pos,axiom,
% 4.98/5.21 ! [A: real,B: real] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.98/5.21 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % le_divide_eq_1_pos
% 4.98/5.21 thf(fact_511_le__divide__eq__1__pos,axiom,
% 4.98/5.21 ! [A: rat,B: rat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.98/5.21 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % le_divide_eq_1_pos
% 4.98/5.21 thf(fact_512_le__divide__eq__1__neg,axiom,
% 4.98/5.21 ! [A: real,B: real] :
% 4.98/5.21 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.21 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.98/5.21 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % le_divide_eq_1_neg
% 4.98/5.21 thf(fact_513_le__divide__eq__1__neg,axiom,
% 4.98/5.21 ! [A: rat,B: rat] :
% 4.98/5.21 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.21 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.98/5.21 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % le_divide_eq_1_neg
% 4.98/5.21 thf(fact_514_divide__le__eq__1__pos,axiom,
% 4.98/5.21 ! [A: real,B: real] :
% 4.98/5.21 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.21 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.98/5.21 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % divide_le_eq_1_pos
% 4.98/5.21 thf(fact_515_divide__le__eq__1__pos,axiom,
% 4.98/5.21 ! [A: rat,B: rat] :
% 4.98/5.21 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.21 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.98/5.21 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 4.98/5.21
% 4.98/5.21 % divide_le_eq_1_pos
% 4.98/5.21 thf(fact_516_divide__le__eq__1__neg,axiom,
% 4.98/5.21 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.98/5.22 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_eq_1_neg
% 4.98/5.22 thf(fact_517_divide__le__eq__1__neg,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.98/5.22 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_eq_1_neg
% 4.98/5.22 thf(fact_518_insert__simp__excp,axiom,
% 4.98/5.22 ! [Mi: nat,Deg: nat,TreeList: list_VEBT_VEBT,X2: nat,Ma: nat,Summary: vEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.98/5.22 => ( ( ord_less_nat @ X2 @ Mi )
% 4.98/5.22 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.98/5.22 => ( ( X2 != Ma )
% 4.98/5.22 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 4.98/5.22 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % insert_simp_excp
% 4.98/5.22 thf(fact_519_insert__simp__norm,axiom,
% 4.98/5.22 ! [X2: nat,Deg: nat,TreeList: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 4.98/5.22 => ( ( ord_less_nat @ Mi @ X2 )
% 4.98/5.22 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 4.98/5.22 => ( ( X2 != Ma )
% 4.98/5.22 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList @ Summary ) @ X2 )
% 4.98/5.22 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X2 @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % insert_simp_norm
% 4.98/5.22 thf(fact_520_list__update__overwrite,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,I3: nat,X2: vEBT_VEBT,Y: vEBT_VEBT] :
% 4.98/5.22 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) @ I3 @ Y )
% 4.98/5.22 = ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ Y ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_overwrite
% 4.98/5.22 thf(fact_521_divide__eq__0__iff,axiom,
% 4.98/5.22 ! [A: complex,B: complex] :
% 4.98/5.22 ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.98/5.22 = zero_zero_complex )
% 4.98/5.22 = ( ( A = zero_zero_complex )
% 4.98/5.22 | ( B = zero_zero_complex ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_eq_0_iff
% 4.98/5.22 thf(fact_522_divide__eq__0__iff,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ( divide_divide_real @ A @ B )
% 4.98/5.22 = zero_zero_real )
% 4.98/5.22 = ( ( A = zero_zero_real )
% 4.98/5.22 | ( B = zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_eq_0_iff
% 4.98/5.22 thf(fact_523_divide__eq__0__iff,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ( divide_divide_rat @ A @ B )
% 4.98/5.22 = zero_zero_rat )
% 4.98/5.22 = ( ( A = zero_zero_rat )
% 4.98/5.22 | ( B = zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_eq_0_iff
% 4.98/5.22 thf(fact_524_divide__cancel__left,axiom,
% 4.98/5.22 ! [C: complex,A: complex,B: complex] :
% 4.98/5.22 ( ( ( divide1717551699836669952omplex @ C @ A )
% 4.98/5.22 = ( divide1717551699836669952omplex @ C @ B ) )
% 4.98/5.22 = ( ( C = zero_zero_complex )
% 4.98/5.22 | ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_cancel_left
% 4.98/5.22 thf(fact_525_divide__cancel__left,axiom,
% 4.98/5.22 ! [C: real,A: real,B: real] :
% 4.98/5.22 ( ( ( divide_divide_real @ C @ A )
% 4.98/5.22 = ( divide_divide_real @ C @ B ) )
% 4.98/5.22 = ( ( C = zero_zero_real )
% 4.98/5.22 | ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_cancel_left
% 4.98/5.22 thf(fact_526_divide__cancel__left,axiom,
% 4.98/5.22 ! [C: rat,A: rat,B: rat] :
% 4.98/5.22 ( ( ( divide_divide_rat @ C @ A )
% 4.98/5.22 = ( divide_divide_rat @ C @ B ) )
% 4.98/5.22 = ( ( C = zero_zero_rat )
% 4.98/5.22 | ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_cancel_left
% 4.98/5.22 thf(fact_527_divide__cancel__right,axiom,
% 4.98/5.22 ! [A: complex,C: complex,B: complex] :
% 4.98/5.22 ( ( ( divide1717551699836669952omplex @ A @ C )
% 4.98/5.22 = ( divide1717551699836669952omplex @ B @ C ) )
% 4.98/5.22 = ( ( C = zero_zero_complex )
% 4.98/5.22 | ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_cancel_right
% 4.98/5.22 thf(fact_528_divide__cancel__right,axiom,
% 4.98/5.22 ! [A: real,C: real,B: real] :
% 4.98/5.22 ( ( ( divide_divide_real @ A @ C )
% 4.98/5.22 = ( divide_divide_real @ B @ C ) )
% 4.98/5.22 = ( ( C = zero_zero_real )
% 4.98/5.22 | ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_cancel_right
% 4.98/5.22 thf(fact_529_divide__cancel__right,axiom,
% 4.98/5.22 ! [A: rat,C: rat,B: rat] :
% 4.98/5.22 ( ( ( divide_divide_rat @ A @ C )
% 4.98/5.22 = ( divide_divide_rat @ B @ C ) )
% 4.98/5.22 = ( ( C = zero_zero_rat )
% 4.98/5.22 | ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_cancel_right
% 4.98/5.22 thf(fact_530_bits__div__0,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 4.98/5.22 = zero_zero_nat ) ).
% 4.98/5.22
% 4.98/5.22 % bits_div_0
% 4.98/5.22 thf(fact_531_bits__div__0,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( divide_divide_int @ zero_zero_int @ A )
% 4.98/5.22 = zero_zero_int ) ).
% 4.98/5.22
% 4.98/5.22 % bits_div_0
% 4.98/5.22 thf(fact_532_bits__div__by__0,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 4.98/5.22 = zero_zero_nat ) ).
% 4.98/5.22
% 4.98/5.22 % bits_div_by_0
% 4.98/5.22 thf(fact_533_bits__div__by__0,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( divide_divide_int @ A @ zero_zero_int )
% 4.98/5.22 = zero_zero_int ) ).
% 4.98/5.22
% 4.98/5.22 % bits_div_by_0
% 4.98/5.22 thf(fact_534_division__ring__divide__zero,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 4.98/5.22 = zero_zero_complex ) ).
% 4.98/5.22
% 4.98/5.22 % division_ring_divide_zero
% 4.98/5.22 thf(fact_535_division__ring__divide__zero,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( divide_divide_real @ A @ zero_zero_real )
% 4.98/5.22 = zero_zero_real ) ).
% 4.98/5.22
% 4.98/5.22 % division_ring_divide_zero
% 4.98/5.22 thf(fact_536_division__ring__divide__zero,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 4.98/5.22 = zero_zero_rat ) ).
% 4.98/5.22
% 4.98/5.22 % division_ring_divide_zero
% 4.98/5.22 thf(fact_537_half__nonnegative__int__iff,axiom,
% 4.98/5.22 ! [K: int] :
% 4.98/5.22 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 4.98/5.22 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.98/5.22
% 4.98/5.22 % half_nonnegative_int_iff
% 4.98/5.22 thf(fact_538_half__negative__int__iff,axiom,
% 4.98/5.22 ! [K: int] :
% 4.98/5.22 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 4.98/5.22 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % half_negative_int_iff
% 4.98/5.22 thf(fact_539_bits__div__by__1,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( divide_divide_nat @ A @ one_one_nat )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % bits_div_by_1
% 4.98/5.22 thf(fact_540_bits__div__by__1,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( divide_divide_int @ A @ one_one_int )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % bits_div_by_1
% 4.98/5.22 thf(fact_541_length__list__update,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,I3: nat,X2: vEBT_VEBT] :
% 4.98/5.22 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) )
% 4.98/5.22 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_list_update
% 4.98/5.22 thf(fact_542_length__list__update,axiom,
% 4.98/5.22 ! [Xs: list_o,I3: nat,X2: $o] :
% 4.98/5.22 ( ( size_size_list_o @ ( list_update_o @ Xs @ I3 @ X2 ) )
% 4.98/5.22 = ( size_size_list_o @ Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_list_update
% 4.98/5.22 thf(fact_543_length__list__update,axiom,
% 4.98/5.22 ! [Xs: list_nat,I3: nat,X2: nat] :
% 4.98/5.22 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) )
% 4.98/5.22 = ( size_size_list_nat @ Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_list_update
% 4.98/5.22 thf(fact_544_length__list__update,axiom,
% 4.98/5.22 ! [Xs: list_int,I3: nat,X2: int] :
% 4.98/5.22 ( ( size_size_list_int @ ( list_update_int @ Xs @ I3 @ X2 ) )
% 4.98/5.22 = ( size_size_list_int @ Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_list_update
% 4.98/5.22 thf(fact_545_list__update__id,axiom,
% 4.98/5.22 ! [Xs: list_nat,I3: nat] :
% 4.98/5.22 ( ( list_update_nat @ Xs @ I3 @ ( nth_nat @ Xs @ I3 ) )
% 4.98/5.22 = Xs ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_id
% 4.98/5.22 thf(fact_546_list__update__id,axiom,
% 4.98/5.22 ! [Xs: list_int,I3: nat] :
% 4.98/5.22 ( ( list_update_int @ Xs @ I3 @ ( nth_int @ Xs @ I3 ) )
% 4.98/5.22 = Xs ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_id
% 4.98/5.22 thf(fact_547_list__update__id,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,I3: nat] :
% 4.98/5.22 ( ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ ( nth_VEBT_VEBT @ Xs @ I3 ) )
% 4.98/5.22 = Xs ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_id
% 4.98/5.22 thf(fact_548_nth__list__update__neq,axiom,
% 4.98/5.22 ! [I3: nat,J: nat,Xs: list_nat,X2: nat] :
% 4.98/5.22 ( ( I3 != J )
% 4.98/5.22 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = ( nth_nat @ Xs @ J ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update_neq
% 4.98/5.22 thf(fact_549_nth__list__update__neq,axiom,
% 4.98/5.22 ! [I3: nat,J: nat,Xs: list_int,X2: int] :
% 4.98/5.22 ( ( I3 != J )
% 4.98/5.22 => ( ( nth_int @ ( list_update_int @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = ( nth_int @ Xs @ J ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update_neq
% 4.98/5.22 thf(fact_550_nth__list__update__neq,axiom,
% 4.98/5.22 ! [I3: nat,J: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 4.98/5.22 ( ( I3 != J )
% 4.98/5.22 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update_neq
% 4.98/5.22 thf(fact_551_divide__eq__1__iff,axiom,
% 4.98/5.22 ! [A: complex,B: complex] :
% 4.98/5.22 ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.98/5.22 = one_one_complex )
% 4.98/5.22 = ( ( B != zero_zero_complex )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_eq_1_iff
% 4.98/5.22 thf(fact_552_divide__eq__1__iff,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ( divide_divide_real @ A @ B )
% 4.98/5.22 = one_one_real )
% 4.98/5.22 = ( ( B != zero_zero_real )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_eq_1_iff
% 4.98/5.22 thf(fact_553_divide__eq__1__iff,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ( divide_divide_rat @ A @ B )
% 4.98/5.22 = one_one_rat )
% 4.98/5.22 = ( ( B != zero_zero_rat )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_eq_1_iff
% 4.98/5.22 thf(fact_554_one__eq__divide__iff,axiom,
% 4.98/5.22 ! [A: complex,B: complex] :
% 4.98/5.22 ( ( one_one_complex
% 4.98/5.22 = ( divide1717551699836669952omplex @ A @ B ) )
% 4.98/5.22 = ( ( B != zero_zero_complex )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % one_eq_divide_iff
% 4.98/5.22 thf(fact_555_one__eq__divide__iff,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( one_one_real
% 4.98/5.22 = ( divide_divide_real @ A @ B ) )
% 4.98/5.22 = ( ( B != zero_zero_real )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % one_eq_divide_iff
% 4.98/5.22 thf(fact_556_one__eq__divide__iff,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( one_one_rat
% 4.98/5.22 = ( divide_divide_rat @ A @ B ) )
% 4.98/5.22 = ( ( B != zero_zero_rat )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % one_eq_divide_iff
% 4.98/5.22 thf(fact_557_divide__self,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( A != zero_zero_complex )
% 4.98/5.22 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.98/5.22 = one_one_complex ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_self
% 4.98/5.22 thf(fact_558_divide__self,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( A != zero_zero_real )
% 4.98/5.22 => ( ( divide_divide_real @ A @ A )
% 4.98/5.22 = one_one_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_self
% 4.98/5.22 thf(fact_559_divide__self,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( A != zero_zero_rat )
% 4.98/5.22 => ( ( divide_divide_rat @ A @ A )
% 4.98/5.22 = one_one_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_self
% 4.98/5.22 thf(fact_560_divide__self__if,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( ( A = zero_zero_complex )
% 4.98/5.22 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.98/5.22 = zero_zero_complex ) )
% 4.98/5.22 & ( ( A != zero_zero_complex )
% 4.98/5.22 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.98/5.22 = one_one_complex ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_self_if
% 4.98/5.22 thf(fact_561_divide__self__if,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( ( A = zero_zero_real )
% 4.98/5.22 => ( ( divide_divide_real @ A @ A )
% 4.98/5.22 = zero_zero_real ) )
% 4.98/5.22 & ( ( A != zero_zero_real )
% 4.98/5.22 => ( ( divide_divide_real @ A @ A )
% 4.98/5.22 = one_one_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_self_if
% 4.98/5.22 thf(fact_562_divide__self__if,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( ( A = zero_zero_rat )
% 4.98/5.22 => ( ( divide_divide_rat @ A @ A )
% 4.98/5.22 = zero_zero_rat ) )
% 4.98/5.22 & ( ( A != zero_zero_rat )
% 4.98/5.22 => ( ( divide_divide_rat @ A @ A )
% 4.98/5.22 = one_one_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_self_if
% 4.98/5.22 thf(fact_563_divide__eq__eq__1,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( ( divide_divide_real @ B @ A )
% 4.98/5.22 = one_one_real )
% 4.98/5.22 = ( ( A != zero_zero_real )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_eq_eq_1
% 4.98/5.22 thf(fact_564_divide__eq__eq__1,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( ( divide_divide_rat @ B @ A )
% 4.98/5.22 = one_one_rat )
% 4.98/5.22 = ( ( A != zero_zero_rat )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_eq_eq_1
% 4.98/5.22 thf(fact_565_eq__divide__eq__1,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( one_one_real
% 4.98/5.22 = ( divide_divide_real @ B @ A ) )
% 4.98/5.22 = ( ( A != zero_zero_real )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % eq_divide_eq_1
% 4.98/5.22 thf(fact_566_eq__divide__eq__1,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( one_one_rat
% 4.98/5.22 = ( divide_divide_rat @ B @ A ) )
% 4.98/5.22 = ( ( A != zero_zero_rat )
% 4.98/5.22 & ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % eq_divide_eq_1
% 4.98/5.22 thf(fact_567_one__divide__eq__0__iff,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( ( divide_divide_real @ one_one_real @ A )
% 4.98/5.22 = zero_zero_real )
% 4.98/5.22 = ( A = zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % one_divide_eq_0_iff
% 4.98/5.22 thf(fact_568_one__divide__eq__0__iff,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 4.98/5.22 = zero_zero_rat )
% 4.98/5.22 = ( A = zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % one_divide_eq_0_iff
% 4.98/5.22 thf(fact_569_zero__eq__1__divide__iff,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( zero_zero_real
% 4.98/5.22 = ( divide_divide_real @ one_one_real @ A ) )
% 4.98/5.22 = ( A = zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_eq_1_divide_iff
% 4.98/5.22 thf(fact_570_zero__eq__1__divide__iff,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( zero_zero_rat
% 4.98/5.22 = ( divide_divide_rat @ one_one_rat @ A ) )
% 4.98/5.22 = ( A = zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_eq_1_divide_iff
% 4.98/5.22 thf(fact_571_max__number__of_I1_J,axiom,
% 4.98/5.22 ! [U: num,V: num] :
% 4.98/5.22 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 4.98/5.22 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 4.98/5.22 = ( numeral_numeral_real @ V ) ) )
% 4.98/5.22 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 4.98/5.22 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 4.98/5.22 = ( numeral_numeral_real @ U ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_number_of(1)
% 4.98/5.22 thf(fact_572_max__number__of_I1_J,axiom,
% 4.98/5.22 ! [U: num,V: num] :
% 4.98/5.22 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 4.98/5.22 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 4.98/5.22 = ( numeral_numeral_rat @ V ) ) )
% 4.98/5.22 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 4.98/5.22 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 4.98/5.22 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_number_of(1)
% 4.98/5.22 thf(fact_573_max__number__of_I1_J,axiom,
% 4.98/5.22 ! [U: num,V: num] :
% 4.98/5.22 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 4.98/5.22 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 4.98/5.22 = ( numeral_numeral_nat @ V ) ) )
% 4.98/5.22 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 4.98/5.22 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 4.98/5.22 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_number_of(1)
% 4.98/5.22 thf(fact_574_max__number__of_I1_J,axiom,
% 4.98/5.22 ! [U: num,V: num] :
% 4.98/5.22 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 4.98/5.22 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 4.98/5.22 = ( numeral_numeral_int @ V ) ) )
% 4.98/5.22 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 4.98/5.22 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 4.98/5.22 = ( numeral_numeral_int @ U ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_number_of(1)
% 4.98/5.22 thf(fact_575_max__0__1_I4_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ zero_zero_real )
% 4.98/5.22 = ( numeral_numeral_real @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(4)
% 4.98/5.22 thf(fact_576_max__0__1_I4_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ zero_zero_rat )
% 4.98/5.22 = ( numeral_numeral_rat @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(4)
% 4.98/5.22 thf(fact_577_max__0__1_I4_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ zero_zero_nat )
% 4.98/5.22 = ( numeral_numeral_nat @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(4)
% 4.98/5.22 thf(fact_578_max__0__1_I4_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ zero_zero_int )
% 4.98/5.22 = ( numeral_numeral_int @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(4)
% 4.98/5.22 thf(fact_579_max__0__1_I3_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X2 ) )
% 4.98/5.22 = ( numeral_numeral_real @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(3)
% 4.98/5.22 thf(fact_580_max__0__1_I3_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X2 ) )
% 4.98/5.22 = ( numeral_numeral_rat @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(3)
% 4.98/5.22 thf(fact_581_max__0__1_I3_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X2 ) )
% 4.98/5.22 = ( numeral_numeral_nat @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(3)
% 4.98/5.22 thf(fact_582_max__0__1_I3_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X2 ) )
% 4.98/5.22 = ( numeral_numeral_int @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(3)
% 4.98/5.22 thf(fact_583_max__0__1_I2_J,axiom,
% 4.98/5.22 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 4.98/5.22 = one_one_real ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(2)
% 4.98/5.22 thf(fact_584_max__0__1_I2_J,axiom,
% 4.98/5.22 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 4.98/5.22 = one_one_rat ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(2)
% 4.98/5.22 thf(fact_585_max__0__1_I2_J,axiom,
% 4.98/5.22 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 4.98/5.22 = one_one_nat ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(2)
% 4.98/5.22 thf(fact_586_max__0__1_I2_J,axiom,
% 4.98/5.22 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 4.98/5.22 = one_one_int ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(2)
% 4.98/5.22 thf(fact_587_max__0__1_I1_J,axiom,
% 4.98/5.22 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 4.98/5.22 = one_one_real ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(1)
% 4.98/5.22 thf(fact_588_max__0__1_I1_J,axiom,
% 4.98/5.22 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 4.98/5.22 = one_one_rat ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(1)
% 4.98/5.22 thf(fact_589_max__0__1_I1_J,axiom,
% 4.98/5.22 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 4.98/5.22 = one_one_nat ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(1)
% 4.98/5.22 thf(fact_590_max__0__1_I1_J,axiom,
% 4.98/5.22 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 4.98/5.22 = one_one_int ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(1)
% 4.98/5.22 thf(fact_591_max__0__1_I6_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_real @ ( numeral_numeral_real @ X2 ) @ one_one_real )
% 4.98/5.22 = ( numeral_numeral_real @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(6)
% 4.98/5.22 thf(fact_592_max__0__1_I6_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat )
% 4.98/5.22 = ( numeral_numeral_rat @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(6)
% 4.98/5.22 thf(fact_593_max__0__1_I6_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat )
% 4.98/5.22 = ( numeral_numeral_nat @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(6)
% 4.98/5.22 thf(fact_594_max__0__1_I6_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_int @ ( numeral_numeral_int @ X2 ) @ one_one_int )
% 4.98/5.22 = ( numeral_numeral_int @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(6)
% 4.98/5.22 thf(fact_595_max__0__1_I5_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X2 ) )
% 4.98/5.22 = ( numeral_numeral_real @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(5)
% 4.98/5.22 thf(fact_596_max__0__1_I5_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X2 ) )
% 4.98/5.22 = ( numeral_numeral_rat @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(5)
% 4.98/5.22 thf(fact_597_max__0__1_I5_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X2 ) )
% 4.98/5.22 = ( numeral_numeral_nat @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(5)
% 4.98/5.22 thf(fact_598_max__0__1_I5_J,axiom,
% 4.98/5.22 ! [X2: num] :
% 4.98/5.22 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X2 ) )
% 4.98/5.22 = ( numeral_numeral_int @ X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % max_0_1(5)
% 4.98/5.22 thf(fact_599_div__by__Suc__0,axiom,
% 4.98/5.22 ! [M: nat] :
% 4.98/5.22 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 4.98/5.22 = M ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_Suc_0
% 4.98/5.22 thf(fact_600_div__less,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.22 => ( ( divide_divide_nat @ M @ N2 )
% 4.98/5.22 = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_less
% 4.98/5.22 thf(fact_601_list__update__beyond,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,I3: nat,X2: vEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I3 )
% 4.98/5.22 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 )
% 4.98/5.22 = Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_beyond
% 4.98/5.22 thf(fact_602_list__update__beyond,axiom,
% 4.98/5.22 ! [Xs: list_o,I3: nat,X2: $o] :
% 4.98/5.22 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I3 )
% 4.98/5.22 => ( ( list_update_o @ Xs @ I3 @ X2 )
% 4.98/5.22 = Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_beyond
% 4.98/5.22 thf(fact_603_list__update__beyond,axiom,
% 4.98/5.22 ! [Xs: list_nat,I3: nat,X2: nat] :
% 4.98/5.22 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I3 )
% 4.98/5.22 => ( ( list_update_nat @ Xs @ I3 @ X2 )
% 4.98/5.22 = Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_beyond
% 4.98/5.22 thf(fact_604_list__update__beyond,axiom,
% 4.98/5.22 ! [Xs: list_int,I3: nat,X2: int] :
% 4.98/5.22 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I3 )
% 4.98/5.22 => ( ( list_update_int @ Xs @ I3 @ X2 )
% 4.98/5.22 = Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_beyond
% 4.98/5.22 thf(fact_605_divide__le__0__1__iff,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 4.98/5.22 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_0_1_iff
% 4.98/5.22 thf(fact_606_divide__le__0__1__iff,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 4.98/5.22 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_0_1_iff
% 4.98/5.22 thf(fact_607_zero__le__divide__1__iff,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 4.98/5.22 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_le_divide_1_iff
% 4.98/5.22 thf(fact_608_zero__le__divide__1__iff,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 4.98/5.22 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_le_divide_1_iff
% 4.98/5.22 thf(fact_609_divide__less__0__1__iff,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 4.98/5.22 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_0_1_iff
% 4.98/5.22 thf(fact_610_divide__less__0__1__iff,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 4.98/5.22 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_0_1_iff
% 4.98/5.22 thf(fact_611_divide__less__eq__1__neg,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.98/5.22 = ( ord_less_real @ A @ B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_eq_1_neg
% 4.98/5.22 thf(fact_612_divide__less__eq__1__neg,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.98/5.22 = ( ord_less_rat @ A @ B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_eq_1_neg
% 4.98/5.22 thf(fact_613_divide__less__eq__1__pos,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.22 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.98/5.22 = ( ord_less_real @ B @ A ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_eq_1_pos
% 4.98/5.22 thf(fact_614_divide__less__eq__1__pos,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.22 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.98/5.22 = ( ord_less_rat @ B @ A ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_eq_1_pos
% 4.98/5.22 thf(fact_615_less__divide__eq__1__neg,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.98/5.22 = ( ord_less_real @ B @ A ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_divide_eq_1_neg
% 4.98/5.22 thf(fact_616_less__divide__eq__1__neg,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.98/5.22 = ( ord_less_rat @ B @ A ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_divide_eq_1_neg
% 4.98/5.22 thf(fact_617_less__divide__eq__1__pos,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.22 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.98/5.22 = ( ord_less_real @ A @ B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_divide_eq_1_pos
% 4.98/5.22 thf(fact_618_less__divide__eq__1__pos,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.22 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.98/5.22 = ( ord_less_rat @ A @ B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_divide_eq_1_pos
% 4.98/5.22 thf(fact_619_zero__less__divide__1__iff,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 4.98/5.22 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_less_divide_1_iff
% 4.98/5.22 thf(fact_620_zero__less__divide__1__iff,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 4.98/5.22 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_less_divide_1_iff
% 4.98/5.22 thf(fact_621_nth__list__update__eq,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) @ I3 )
% 4.98/5.22 = X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update_eq
% 4.98/5.22 thf(fact_622_nth__list__update__eq,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_o,X2: $o] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( ( nth_o @ ( list_update_o @ Xs @ I3 @ X2 ) @ I3 )
% 4.98/5.22 = X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update_eq
% 4.98/5.22 thf(fact_623_nth__list__update__eq,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_nat,X2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ I3 )
% 4.98/5.22 = X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update_eq
% 4.98/5.22 thf(fact_624_nth__list__update__eq,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_int,X2: int] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( ( nth_int @ ( list_update_int @ Xs @ I3 @ X2 ) @ I3 )
% 4.98/5.22 = X2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update_eq
% 4.98/5.22 thf(fact_625_not__exp__less__eq__0__int,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 4.98/5.22
% 4.98/5.22 % not_exp_less_eq_0_int
% 4.98/5.22 thf(fact_626_linordered__field__no__lb,axiom,
% 4.98/5.22 ! [X3: real] :
% 4.98/5.22 ? [Y3: real] : ( ord_less_real @ Y3 @ X3 ) ).
% 4.98/5.22
% 4.98/5.22 % linordered_field_no_lb
% 4.98/5.22 thf(fact_627_linordered__field__no__lb,axiom,
% 4.98/5.22 ! [X3: rat] :
% 4.98/5.22 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X3 ) ).
% 4.98/5.22
% 4.98/5.22 % linordered_field_no_lb
% 4.98/5.22 thf(fact_628_linordered__field__no__ub,axiom,
% 4.98/5.22 ! [X3: real] :
% 4.98/5.22 ? [X_12: real] : ( ord_less_real @ X3 @ X_12 ) ).
% 4.98/5.22
% 4.98/5.22 % linordered_field_no_ub
% 4.98/5.22 thf(fact_629_linordered__field__no__ub,axiom,
% 4.98/5.22 ! [X3: rat] :
% 4.98/5.22 ? [X_12: rat] : ( ord_less_rat @ X3 @ X_12 ) ).
% 4.98/5.22
% 4.98/5.22 % linordered_field_no_ub
% 4.98/5.22 thf(fact_630_subset__code_I1_J,axiom,
% 4.98/5.22 ! [Xs: list_complex,B4: set_complex] :
% 4.98/5.22 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B4 )
% 4.98/5.22 = ( ! [X: complex] :
% 4.98/5.22 ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 4.98/5.22 => ( member_complex @ X @ B4 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % subset_code(1)
% 4.98/5.22 thf(fact_631_subset__code_I1_J,axiom,
% 4.98/5.22 ! [Xs: list_real,B4: set_real] :
% 4.98/5.22 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B4 )
% 4.98/5.22 = ( ! [X: real] :
% 4.98/5.22 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 4.98/5.22 => ( member_real @ X @ B4 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % subset_code(1)
% 4.98/5.22 thf(fact_632_subset__code_I1_J,axiom,
% 4.98/5.22 ! [Xs: list_set_nat,B4: set_set_nat] :
% 4.98/5.22 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B4 )
% 4.98/5.22 = ( ! [X: set_nat] :
% 4.98/5.22 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 4.98/5.22 => ( member_set_nat @ X @ B4 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % subset_code(1)
% 4.98/5.22 thf(fact_633_subset__code_I1_J,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,B4: set_VEBT_VEBT] :
% 4.98/5.22 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B4 )
% 4.98/5.22 = ( ! [X: vEBT_VEBT] :
% 4.98/5.22 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.98/5.22 => ( member_VEBT_VEBT @ X @ B4 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % subset_code(1)
% 4.98/5.22 thf(fact_634_subset__code_I1_J,axiom,
% 4.98/5.22 ! [Xs: list_int,B4: set_int] :
% 4.98/5.22 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B4 )
% 4.98/5.22 = ( ! [X: int] :
% 4.98/5.22 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 4.98/5.22 => ( member_int @ X @ B4 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % subset_code(1)
% 4.98/5.22 thf(fact_635_subset__code_I1_J,axiom,
% 4.98/5.22 ! [Xs: list_nat,B4: set_nat] :
% 4.98/5.22 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B4 )
% 4.98/5.22 = ( ! [X: nat] :
% 4.98/5.22 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 4.98/5.22 => ( member_nat @ X @ B4 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % subset_code(1)
% 4.98/5.22 thf(fact_636_Ex__list__of__length,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ? [Xs2: list_VEBT_VEBT] :
% 4.98/5.22 ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 4.98/5.22 = N2 ) ).
% 4.98/5.22
% 4.98/5.22 % Ex_list_of_length
% 4.98/5.22 thf(fact_637_Ex__list__of__length,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ? [Xs2: list_o] :
% 4.98/5.22 ( ( size_size_list_o @ Xs2 )
% 4.98/5.22 = N2 ) ).
% 4.98/5.22
% 4.98/5.22 % Ex_list_of_length
% 4.98/5.22 thf(fact_638_Ex__list__of__length,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ? [Xs2: list_nat] :
% 4.98/5.22 ( ( size_size_list_nat @ Xs2 )
% 4.98/5.22 = N2 ) ).
% 4.98/5.22
% 4.98/5.22 % Ex_list_of_length
% 4.98/5.22 thf(fact_639_Ex__list__of__length,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ? [Xs2: list_int] :
% 4.98/5.22 ( ( size_size_list_int @ Xs2 )
% 4.98/5.22 = N2 ) ).
% 4.98/5.22
% 4.98/5.22 % Ex_list_of_length
% 4.98/5.22 thf(fact_640_neq__if__length__neq,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 4.98/5.22 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 4.98/5.22 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 4.98/5.22 => ( Xs != Ys ) ) ).
% 4.98/5.22
% 4.98/5.22 % neq_if_length_neq
% 4.98/5.22 thf(fact_641_neq__if__length__neq,axiom,
% 4.98/5.22 ! [Xs: list_o,Ys: list_o] :
% 4.98/5.22 ( ( ( size_size_list_o @ Xs )
% 4.98/5.22 != ( size_size_list_o @ Ys ) )
% 4.98/5.22 => ( Xs != Ys ) ) ).
% 4.98/5.22
% 4.98/5.22 % neq_if_length_neq
% 4.98/5.22 thf(fact_642_neq__if__length__neq,axiom,
% 4.98/5.22 ! [Xs: list_nat,Ys: list_nat] :
% 4.98/5.22 ( ( ( size_size_list_nat @ Xs )
% 4.98/5.22 != ( size_size_list_nat @ Ys ) )
% 4.98/5.22 => ( Xs != Ys ) ) ).
% 4.98/5.22
% 4.98/5.22 % neq_if_length_neq
% 4.98/5.22 thf(fact_643_neq__if__length__neq,axiom,
% 4.98/5.22 ! [Xs: list_int,Ys: list_int] :
% 4.98/5.22 ( ( ( size_size_list_int @ Xs )
% 4.98/5.22 != ( size_size_list_int @ Ys ) )
% 4.98/5.22 => ( Xs != Ys ) ) ).
% 4.98/5.22
% 4.98/5.22 % neq_if_length_neq
% 4.98/5.22 thf(fact_644_list__update__swap,axiom,
% 4.98/5.22 ! [I3: nat,I4: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT,X6: vEBT_VEBT] :
% 4.98/5.22 ( ( I3 != I4 )
% 4.98/5.22 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) @ I4 @ X6 )
% 4.98/5.22 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I4 @ X6 ) @ I3 @ X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_swap
% 4.98/5.22 thf(fact_645_add__divide__distrib,axiom,
% 4.98/5.22 ! [A: complex,B: complex,C: complex] :
% 4.98/5.22 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 4.98/5.22 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_divide_distrib
% 4.98/5.22 thf(fact_646_add__divide__distrib,axiom,
% 4.98/5.22 ! [A: real,B: real,C: real] :
% 4.98/5.22 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.98/5.22 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_divide_distrib
% 4.98/5.22 thf(fact_647_add__divide__distrib,axiom,
% 4.98/5.22 ! [A: rat,B: rat,C: rat] :
% 4.98/5.22 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.98/5.22 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_divide_distrib
% 4.98/5.22 thf(fact_648_length__induct,axiom,
% 4.98/5.22 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 4.98/5.22 ( ! [Xs2: list_VEBT_VEBT] :
% 4.98/5.22 ( ! [Ys2: list_VEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 4.98/5.22 => ( P @ Ys2 ) )
% 4.98/5.22 => ( P @ Xs2 ) )
% 4.98/5.22 => ( P @ Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_induct
% 4.98/5.22 thf(fact_649_length__induct,axiom,
% 4.98/5.22 ! [P: list_o > $o,Xs: list_o] :
% 4.98/5.22 ( ! [Xs2: list_o] :
% 4.98/5.22 ( ! [Ys2: list_o] :
% 4.98/5.22 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 4.98/5.22 => ( P @ Ys2 ) )
% 4.98/5.22 => ( P @ Xs2 ) )
% 4.98/5.22 => ( P @ Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_induct
% 4.98/5.22 thf(fact_650_length__induct,axiom,
% 4.98/5.22 ! [P: list_nat > $o,Xs: list_nat] :
% 4.98/5.22 ( ! [Xs2: list_nat] :
% 4.98/5.22 ( ! [Ys2: list_nat] :
% 4.98/5.22 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 4.98/5.22 => ( P @ Ys2 ) )
% 4.98/5.22 => ( P @ Xs2 ) )
% 4.98/5.22 => ( P @ Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_induct
% 4.98/5.22 thf(fact_651_length__induct,axiom,
% 4.98/5.22 ! [P: list_int > $o,Xs: list_int] :
% 4.98/5.22 ( ! [Xs2: list_int] :
% 4.98/5.22 ( ! [Ys2: list_int] :
% 4.98/5.22 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 4.98/5.22 => ( P @ Ys2 ) )
% 4.98/5.22 => ( P @ Xs2 ) )
% 4.98/5.22 => ( P @ Xs ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_induct
% 4.98/5.22 thf(fact_652_div__le__mono,axiom,
% 4.98/5.22 ! [M: nat,N2: nat,K: nat] :
% 4.98/5.22 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.22 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_le_mono
% 4.98/5.22 thf(fact_653_div__le__dividend,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 4.98/5.22
% 4.98/5.22 % div_le_dividend
% 4.98/5.22 thf(fact_654_set__update__subsetI,axiom,
% 4.98/5.22 ! [Xs: list_complex,A3: set_complex,X2: complex,I3: nat] :
% 4.98/5.22 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A3 )
% 4.98/5.22 => ( ( member_complex @ X2 @ A3 )
% 4.98/5.22 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs @ I3 @ X2 ) ) @ A3 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_subsetI
% 4.98/5.22 thf(fact_655_set__update__subsetI,axiom,
% 4.98/5.22 ! [Xs: list_real,A3: set_real,X2: real,I3: nat] :
% 4.98/5.22 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A3 )
% 4.98/5.22 => ( ( member_real @ X2 @ A3 )
% 4.98/5.22 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I3 @ X2 ) ) @ A3 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_subsetI
% 4.98/5.22 thf(fact_656_set__update__subsetI,axiom,
% 4.98/5.22 ! [Xs: list_set_nat,A3: set_set_nat,X2: set_nat,I3: nat] :
% 4.98/5.22 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A3 )
% 4.98/5.22 => ( ( member_set_nat @ X2 @ A3 )
% 4.98/5.22 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I3 @ X2 ) ) @ A3 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_subsetI
% 4.98/5.22 thf(fact_657_set__update__subsetI,axiom,
% 4.98/5.22 ! [Xs: list_int,A3: set_int,X2: int,I3: nat] :
% 4.98/5.22 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A3 )
% 4.98/5.22 => ( ( member_int @ X2 @ A3 )
% 4.98/5.22 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I3 @ X2 ) ) @ A3 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_subsetI
% 4.98/5.22 thf(fact_658_set__update__subsetI,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,A3: set_VEBT_VEBT,X2: vEBT_VEBT,I3: nat] :
% 4.98/5.22 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A3 )
% 4.98/5.22 => ( ( member_VEBT_VEBT @ X2 @ A3 )
% 4.98/5.22 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) ) @ A3 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_subsetI
% 4.98/5.22 thf(fact_659_set__update__subsetI,axiom,
% 4.98/5.22 ! [Xs: list_nat,A3: set_nat,X2: nat,I3: nat] :
% 4.98/5.22 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A3 )
% 4.98/5.22 => ( ( member_nat @ X2 @ A3 )
% 4.98/5.22 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I3 @ X2 ) ) @ A3 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_subsetI
% 4.98/5.22 thf(fact_660_divide__le__0__iff,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 4.98/5.22 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.22 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 4.98/5.22 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.22 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_0_iff
% 4.98/5.22 thf(fact_661_divide__le__0__iff,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 4.98/5.22 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.22 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 4.98/5.22 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.22 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_0_iff
% 4.98/5.22 thf(fact_662_divide__right__mono,axiom,
% 4.98/5.22 ! [A: real,B: real,C: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.22 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_right_mono
% 4.98/5.22 thf(fact_663_divide__right__mono,axiom,
% 4.98/5.22 ! [A: rat,B: rat,C: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.22 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_right_mono
% 4.98/5.22 thf(fact_664_zero__le__divide__iff,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 4.98/5.22 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.22 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 4.98/5.22 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.22 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_le_divide_iff
% 4.98/5.22 thf(fact_665_zero__le__divide__iff,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 4.98/5.22 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.22 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 4.98/5.22 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.22 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_le_divide_iff
% 4.98/5.22 thf(fact_666_divide__nonneg__nonneg,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.22 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonneg_nonneg
% 4.98/5.22 thf(fact_667_divide__nonneg__nonneg,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonneg_nonneg
% 4.98/5.22 thf(fact_668_divide__nonneg__nonpos,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.22 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 4.98/5.22 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonneg_nonpos
% 4.98/5.22 thf(fact_669_divide__nonneg__nonpos,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.22 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonneg_nonpos
% 4.98/5.22 thf(fact_670_divide__nonpos__nonneg,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.22 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonpos_nonneg
% 4.98/5.22 thf(fact_671_divide__nonpos__nonneg,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.22 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonpos_nonneg
% 4.98/5.22 thf(fact_672_divide__nonpos__nonpos,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 4.98/5.22 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonpos_nonpos
% 4.98/5.22 thf(fact_673_divide__nonpos__nonpos,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonpos_nonpos
% 4.98/5.22 thf(fact_674_divide__right__mono__neg,axiom,
% 4.98/5.22 ! [A: real,B: real,C: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.22 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.22 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_right_mono_neg
% 4.98/5.22 thf(fact_675_divide__right__mono__neg,axiom,
% 4.98/5.22 ! [A: rat,B: rat,C: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.22 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_right_mono_neg
% 4.98/5.22 thf(fact_676_divide__neg__neg,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_real @ X2 @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_real @ Y @ zero_zero_real )
% 4.98/5.22 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_neg_neg
% 4.98/5.22 thf(fact_677_divide__neg__neg,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_neg_neg
% 4.98/5.22 thf(fact_678_divide__neg__pos,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_real @ X2 @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.22 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_neg_pos
% 4.98/5.22 thf(fact_679_divide__neg__pos,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.98/5.22 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_neg_pos
% 4.98/5.22 thf(fact_680_divide__pos__neg,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_real @ zero_zero_real @ X2 )
% 4.98/5.22 => ( ( ord_less_real @ Y @ zero_zero_real )
% 4.98/5.22 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_pos_neg
% 4.98/5.22 thf(fact_681_divide__pos__neg,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 4.98/5.22 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_pos_neg
% 4.98/5.22 thf(fact_682_divide__pos__pos,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_real @ zero_zero_real @ X2 )
% 4.98/5.22 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.22 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_pos_pos
% 4.98/5.22 thf(fact_683_divide__pos__pos,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 4.98/5.22 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.98/5.22 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_pos_pos
% 4.98/5.22 thf(fact_684_divide__less__0__iff,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 4.98/5.22 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.22 & ( ord_less_real @ B @ zero_zero_real ) )
% 4.98/5.22 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_0_iff
% 4.98/5.22 thf(fact_685_divide__less__0__iff,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 4.98/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.22 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 4.98/5.22 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_0_iff
% 4.98/5.22 thf(fact_686_divide__less__cancel,axiom,
% 4.98/5.22 ! [A: real,C: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 4.98/5.22 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.22 => ( ord_less_real @ A @ B ) )
% 4.98/5.22 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.22 => ( ord_less_real @ B @ A ) )
% 4.98/5.22 & ( C != zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_cancel
% 4.98/5.22 thf(fact_687_divide__less__cancel,axiom,
% 4.98/5.22 ! [A: rat,C: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.22 => ( ord_less_rat @ A @ B ) )
% 4.98/5.22 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_rat @ B @ A ) )
% 4.98/5.22 & ( C != zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_cancel
% 4.98/5.22 thf(fact_688_zero__less__divide__iff,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 4.98/5.22 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.22 & ( ord_less_real @ zero_zero_real @ B ) )
% 4.98/5.22 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_less_divide_iff
% 4.98/5.22 thf(fact_689_zero__less__divide__iff,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 4.98/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.22 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 4.98/5.22 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_less_divide_iff
% 4.98/5.22 thf(fact_690_divide__strict__right__mono,axiom,
% 4.98/5.22 ! [A: real,B: real,C: real] :
% 4.98/5.22 ( ( ord_less_real @ A @ B )
% 4.98/5.22 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.22 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_strict_right_mono
% 4.98/5.22 thf(fact_691_divide__strict__right__mono,axiom,
% 4.98/5.22 ! [A: rat,B: rat,C: rat] :
% 4.98/5.22 ( ( ord_less_rat @ A @ B )
% 4.98/5.22 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.22 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_strict_right_mono
% 4.98/5.22 thf(fact_692_divide__strict__right__mono__neg,axiom,
% 4.98/5.22 ! [B: real,A: real,C: real] :
% 4.98/5.22 ( ( ord_less_real @ B @ A )
% 4.98/5.22 => ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.22 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_strict_right_mono_neg
% 4.98/5.22 thf(fact_693_divide__strict__right__mono__neg,axiom,
% 4.98/5.22 ! [B: rat,A: rat,C: rat] :
% 4.98/5.22 ( ( ord_less_rat @ B @ A )
% 4.98/5.22 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_strict_right_mono_neg
% 4.98/5.22 thf(fact_694_right__inverse__eq,axiom,
% 4.98/5.22 ! [B: complex,A: complex] :
% 4.98/5.22 ( ( B != zero_zero_complex )
% 4.98/5.22 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.98/5.22 = one_one_complex )
% 4.98/5.22 = ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % right_inverse_eq
% 4.98/5.22 thf(fact_695_right__inverse__eq,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( B != zero_zero_real )
% 4.98/5.22 => ( ( ( divide_divide_real @ A @ B )
% 4.98/5.22 = one_one_real )
% 4.98/5.22 = ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % right_inverse_eq
% 4.98/5.22 thf(fact_696_right__inverse__eq,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( B != zero_zero_rat )
% 4.98/5.22 => ( ( ( divide_divide_rat @ A @ B )
% 4.98/5.22 = one_one_rat )
% 4.98/5.22 = ( A = B ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % right_inverse_eq
% 4.98/5.22 thf(fact_697_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ( divide_divide_nat @ M @ N2 )
% 4.98/5.22 = zero_zero_nat )
% 4.98/5.22 = ( ( ord_less_nat @ M @ N2 )
% 4.98/5.22 | ( N2 = zero_zero_nat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % Euclidean_Division.div_eq_0_iff
% 4.98/5.22 thf(fact_698_Suc__div__le__mono,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % Suc_div_le_mono
% 4.98/5.22 thf(fact_699_nth__equalityI,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 4.98/5.22 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 4.98/5.22 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 4.98/5.22 => ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( ( nth_VEBT_VEBT @ Xs @ I2 )
% 4.98/5.22 = ( nth_VEBT_VEBT @ Ys @ I2 ) ) )
% 4.98/5.22 => ( Xs = Ys ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_equalityI
% 4.98/5.22 thf(fact_700_nth__equalityI,axiom,
% 4.98/5.22 ! [Xs: list_o,Ys: list_o] :
% 4.98/5.22 ( ( ( size_size_list_o @ Xs )
% 4.98/5.22 = ( size_size_list_o @ Ys ) )
% 4.98/5.22 => ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( ( nth_o @ Xs @ I2 )
% 4.98/5.22 = ( nth_o @ Ys @ I2 ) ) )
% 4.98/5.22 => ( Xs = Ys ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_equalityI
% 4.98/5.22 thf(fact_701_nth__equalityI,axiom,
% 4.98/5.22 ! [Xs: list_nat,Ys: list_nat] :
% 4.98/5.22 ( ( ( size_size_list_nat @ Xs )
% 4.98/5.22 = ( size_size_list_nat @ Ys ) )
% 4.98/5.22 => ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( ( nth_nat @ Xs @ I2 )
% 4.98/5.22 = ( nth_nat @ Ys @ I2 ) ) )
% 4.98/5.22 => ( Xs = Ys ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_equalityI
% 4.98/5.22 thf(fact_702_nth__equalityI,axiom,
% 4.98/5.22 ! [Xs: list_int,Ys: list_int] :
% 4.98/5.22 ( ( ( size_size_list_int @ Xs )
% 4.98/5.22 = ( size_size_list_int @ Ys ) )
% 4.98/5.22 => ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( ( nth_int @ Xs @ I2 )
% 4.98/5.22 = ( nth_int @ Ys @ I2 ) ) )
% 4.98/5.22 => ( Xs = Ys ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_equalityI
% 4.98/5.22 thf(fact_703_Skolem__list__nth,axiom,
% 4.98/5.22 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 4.98/5.22 ( ( ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ K )
% 4.98/5.22 => ? [X4: vEBT_VEBT] : ( P @ I5 @ X4 ) ) )
% 4.98/5.22 = ( ? [Xs3: list_VEBT_VEBT] :
% 4.98/5.22 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 4.98/5.22 = K )
% 4.98/5.22 & ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ K )
% 4.98/5.22 => ( P @ I5 @ ( nth_VEBT_VEBT @ Xs3 @ I5 ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % Skolem_list_nth
% 4.98/5.22 thf(fact_704_Skolem__list__nth,axiom,
% 4.98/5.22 ! [K: nat,P: nat > $o > $o] :
% 4.98/5.22 ( ( ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ K )
% 4.98/5.22 => ? [X4: $o] : ( P @ I5 @ X4 ) ) )
% 4.98/5.22 = ( ? [Xs3: list_o] :
% 4.98/5.22 ( ( ( size_size_list_o @ Xs3 )
% 4.98/5.22 = K )
% 4.98/5.22 & ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ K )
% 4.98/5.22 => ( P @ I5 @ ( nth_o @ Xs3 @ I5 ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % Skolem_list_nth
% 4.98/5.22 thf(fact_705_Skolem__list__nth,axiom,
% 4.98/5.22 ! [K: nat,P: nat > nat > $o] :
% 4.98/5.22 ( ( ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ K )
% 4.98/5.22 => ? [X4: nat] : ( P @ I5 @ X4 ) ) )
% 4.98/5.22 = ( ? [Xs3: list_nat] :
% 4.98/5.22 ( ( ( size_size_list_nat @ Xs3 )
% 4.98/5.22 = K )
% 4.98/5.22 & ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ K )
% 4.98/5.22 => ( P @ I5 @ ( nth_nat @ Xs3 @ I5 ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % Skolem_list_nth
% 4.98/5.22 thf(fact_706_Skolem__list__nth,axiom,
% 4.98/5.22 ! [K: nat,P: nat > int > $o] :
% 4.98/5.22 ( ( ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ K )
% 4.98/5.22 => ? [X4: int] : ( P @ I5 @ X4 ) ) )
% 4.98/5.22 = ( ? [Xs3: list_int] :
% 4.98/5.22 ( ( ( size_size_list_int @ Xs3 )
% 4.98/5.22 = K )
% 4.98/5.22 & ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ K )
% 4.98/5.22 => ( P @ I5 @ ( nth_int @ Xs3 @ I5 ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % Skolem_list_nth
% 4.98/5.22 thf(fact_707_list__eq__iff__nth__eq,axiom,
% 4.98/5.22 ( ( ^ [Y4: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y4 = Z2 ) )
% 4.98/5.22 = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 4.98/5.22 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 4.98/5.22 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 4.98/5.22 & ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 4.98/5.22 => ( ( nth_VEBT_VEBT @ Xs3 @ I5 )
% 4.98/5.22 = ( nth_VEBT_VEBT @ Ys3 @ I5 ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_eq_iff_nth_eq
% 4.98/5.22 thf(fact_708_list__eq__iff__nth__eq,axiom,
% 4.98/5.22 ( ( ^ [Y4: list_o,Z2: list_o] : ( Y4 = Z2 ) )
% 4.98/5.22 = ( ^ [Xs3: list_o,Ys3: list_o] :
% 4.98/5.22 ( ( ( size_size_list_o @ Xs3 )
% 4.98/5.22 = ( size_size_list_o @ Ys3 ) )
% 4.98/5.22 & ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs3 ) )
% 4.98/5.22 => ( ( nth_o @ Xs3 @ I5 )
% 4.98/5.22 = ( nth_o @ Ys3 @ I5 ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_eq_iff_nth_eq
% 4.98/5.22 thf(fact_709_list__eq__iff__nth__eq,axiom,
% 4.98/5.22 ( ( ^ [Y4: list_nat,Z2: list_nat] : ( Y4 = Z2 ) )
% 4.98/5.22 = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 4.98/5.22 ( ( ( size_size_list_nat @ Xs3 )
% 4.98/5.22 = ( size_size_list_nat @ Ys3 ) )
% 4.98/5.22 & ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs3 ) )
% 4.98/5.22 => ( ( nth_nat @ Xs3 @ I5 )
% 4.98/5.22 = ( nth_nat @ Ys3 @ I5 ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_eq_iff_nth_eq
% 4.98/5.22 thf(fact_710_list__eq__iff__nth__eq,axiom,
% 4.98/5.22 ( ( ^ [Y4: list_int,Z2: list_int] : ( Y4 = Z2 ) )
% 4.98/5.22 = ( ^ [Xs3: list_int,Ys3: list_int] :
% 4.98/5.22 ( ( ( size_size_list_int @ Xs3 )
% 4.98/5.22 = ( size_size_list_int @ Ys3 ) )
% 4.98/5.22 & ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs3 ) )
% 4.98/5.22 => ( ( nth_int @ Xs3 @ I5 )
% 4.98/5.22 = ( nth_int @ Ys3 @ I5 ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_eq_iff_nth_eq
% 4.98/5.22 thf(fact_711_field__le__epsilon,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ! [E: real] :
% 4.98/5.22 ( ( ord_less_real @ zero_zero_real @ E )
% 4.98/5.22 => ( ord_less_eq_real @ X2 @ ( plus_plus_real @ Y @ E ) ) )
% 4.98/5.22 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 4.98/5.22
% 4.98/5.22 % field_le_epsilon
% 4.98/5.22 thf(fact_712_field__le__epsilon,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ! [E: rat] :
% 4.98/5.22 ( ( ord_less_rat @ zero_zero_rat @ E )
% 4.98/5.22 => ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ Y @ E ) ) )
% 4.98/5.22 => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 4.98/5.22
% 4.98/5.22 % field_le_epsilon
% 4.98/5.22 thf(fact_713_frac__le,axiom,
% 4.98/5.22 ! [Y: real,X2: real,W: real,Z: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.22 => ( ( ord_less_eq_real @ X2 @ Y )
% 4.98/5.22 => ( ( ord_less_real @ zero_zero_real @ W )
% 4.98/5.22 => ( ( ord_less_eq_real @ W @ Z )
% 4.98/5.22 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % frac_le
% 4.98/5.22 thf(fact_714_frac__le,axiom,
% 4.98/5.22 ! [Y: rat,X2: rat,W: rat,Z: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.22 => ( ( ord_less_eq_rat @ X2 @ Y )
% 4.98/5.22 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 4.98/5.22 => ( ( ord_less_eq_rat @ W @ Z )
% 4.98/5.22 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % frac_le
% 4.98/5.22 thf(fact_715_frac__less,axiom,
% 4.98/5.22 ! [X2: real,Y: real,W: real,Z: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.22 => ( ( ord_less_real @ X2 @ Y )
% 4.98/5.22 => ( ( ord_less_real @ zero_zero_real @ W )
% 4.98/5.22 => ( ( ord_less_eq_real @ W @ Z )
% 4.98/5.22 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % frac_less
% 4.98/5.22 thf(fact_716_frac__less,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat,W: rat,Z: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.22 => ( ( ord_less_rat @ X2 @ Y )
% 4.98/5.22 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 4.98/5.22 => ( ( ord_less_eq_rat @ W @ Z )
% 4.98/5.22 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % frac_less
% 4.98/5.22 thf(fact_717_frac__less2,axiom,
% 4.98/5.22 ! [X2: real,Y: real,W: real,Z: real] :
% 4.98/5.22 ( ( ord_less_real @ zero_zero_real @ X2 )
% 4.98/5.22 => ( ( ord_less_eq_real @ X2 @ Y )
% 4.98/5.22 => ( ( ord_less_real @ zero_zero_real @ W )
% 4.98/5.22 => ( ( ord_less_real @ W @ Z )
% 4.98/5.22 => ( ord_less_real @ ( divide_divide_real @ X2 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % frac_less2
% 4.98/5.22 thf(fact_718_frac__less2,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat,W: rat,Z: rat] :
% 4.98/5.22 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 4.98/5.22 => ( ( ord_less_eq_rat @ X2 @ Y )
% 4.98/5.22 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 4.98/5.22 => ( ( ord_less_rat @ W @ Z )
% 4.98/5.22 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % frac_less2
% 4.98/5.22 thf(fact_719_divide__le__cancel,axiom,
% 4.98/5.22 ! [A: real,C: real,B: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 4.98/5.22 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.22 => ( ord_less_eq_real @ A @ B ) )
% 4.98/5.22 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.22 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_cancel
% 4.98/5.22 thf(fact_720_divide__le__cancel,axiom,
% 4.98/5.22 ! [A: rat,C: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.22 => ( ord_less_eq_rat @ A @ B ) )
% 4.98/5.22 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_cancel
% 4.98/5.22 thf(fact_721_divide__nonneg__neg,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.22 => ( ( ord_less_real @ Y @ zero_zero_real )
% 4.98/5.22 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonneg_neg
% 4.98/5.22 thf(fact_722_divide__nonneg__neg,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.22 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonneg_neg
% 4.98/5.22 thf(fact_723_divide__nonneg__pos,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.22 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.22 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonneg_pos
% 4.98/5.22 thf(fact_724_divide__nonneg__pos,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.22 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.98/5.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonneg_pos
% 4.98/5.22 thf(fact_725_divide__nonpos__neg,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_real @ Y @ zero_zero_real )
% 4.98/5.22 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonpos_neg
% 4.98/5.22 thf(fact_726_divide__nonpos__neg,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 4.98/5.22 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonpos_neg
% 4.98/5.22 thf(fact_727_divide__nonpos__pos,axiom,
% 4.98/5.22 ! [X2: real,Y: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 4.98/5.22 => ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.22 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonpos_pos
% 4.98/5.22 thf(fact_728_divide__nonpos__pos,axiom,
% 4.98/5.22 ! [X2: rat,Y: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 4.98/5.22 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.98/5.22 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_nonpos_pos
% 4.98/5.22 thf(fact_729_divide__less__eq__1,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.98/5.22 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.22 & ( ord_less_real @ B @ A ) )
% 4.98/5.22 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 & ( ord_less_real @ A @ B ) )
% 4.98/5.22 | ( A = zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_eq_1
% 4.98/5.22 thf(fact_730_divide__less__eq__1,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.98/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.22 & ( ord_less_rat @ B @ A ) )
% 4.98/5.22 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 & ( ord_less_rat @ A @ B ) )
% 4.98/5.22 | ( A = zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_less_eq_1
% 4.98/5.22 thf(fact_731_less__divide__eq__1,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.98/5.22 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.22 & ( ord_less_real @ A @ B ) )
% 4.98/5.22 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 & ( ord_less_real @ B @ A ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_divide_eq_1
% 4.98/5.22 thf(fact_732_less__divide__eq__1,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.98/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.22 & ( ord_less_rat @ A @ B ) )
% 4.98/5.22 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_divide_eq_1
% 4.98/5.22 thf(fact_733_div__add__self1,axiom,
% 4.98/5.22 ! [B: nat,A: nat] :
% 4.98/5.22 ( ( B != zero_zero_nat )
% 4.98/5.22 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.98/5.22 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_add_self1
% 4.98/5.22 thf(fact_734_div__add__self1,axiom,
% 4.98/5.22 ! [B: int,A: int] :
% 4.98/5.22 ( ( B != zero_zero_int )
% 4.98/5.22 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.98/5.22 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_add_self1
% 4.98/5.22 thf(fact_735_div__add__self2,axiom,
% 4.98/5.22 ! [B: nat,A: nat] :
% 4.98/5.22 ( ( B != zero_zero_nat )
% 4.98/5.22 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.98/5.22 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_add_self2
% 4.98/5.22 thf(fact_736_div__add__self2,axiom,
% 4.98/5.22 ! [B: int,A: int] :
% 4.98/5.22 ( ( B != zero_zero_int )
% 4.98/5.22 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.98/5.22 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_add_self2
% 4.98/5.22 thf(fact_737_gt__half__sum,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ A @ B )
% 4.98/5.22 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % gt_half_sum
% 4.98/5.22 thf(fact_738_gt__half__sum,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ A @ B )
% 4.98/5.22 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % gt_half_sum
% 4.98/5.22 thf(fact_739_less__half__sum,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ A @ B )
% 4.98/5.22 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_half_sum
% 4.98/5.22 thf(fact_740_less__half__sum,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ A @ B )
% 4.98/5.22 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_half_sum
% 4.98/5.22 thf(fact_741_numeral__Bit0__div__2,axiom,
% 4.98/5.22 ! [N2: num] :
% 4.98/5.22 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.22 = ( numeral_numeral_nat @ N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % numeral_Bit0_div_2
% 4.98/5.22 thf(fact_742_numeral__Bit0__div__2,axiom,
% 4.98/5.22 ! [N2: num] :
% 4.98/5.22 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.22 = ( numeral_numeral_int @ N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % numeral_Bit0_div_2
% 4.98/5.22 thf(fact_743_length__pos__if__in__set,axiom,
% 4.98/5.22 ! [X2: complex,Xs: list_complex] :
% 4.98/5.22 ( ( member_complex @ X2 @ ( set_complex2 @ Xs ) )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_pos_if_in_set
% 4.98/5.22 thf(fact_744_length__pos__if__in__set,axiom,
% 4.98/5.22 ! [X2: real,Xs: list_real] :
% 4.98/5.22 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_pos_if_in_set
% 4.98/5.22 thf(fact_745_length__pos__if__in__set,axiom,
% 4.98/5.22 ! [X2: set_nat,Xs: list_set_nat] :
% 4.98/5.22 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_pos_if_in_set
% 4.98/5.22 thf(fact_746_length__pos__if__in__set,axiom,
% 4.98/5.22 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.98/5.22 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_pos_if_in_set
% 4.98/5.22 thf(fact_747_length__pos__if__in__set,axiom,
% 4.98/5.22 ! [X2: $o,Xs: list_o] :
% 4.98/5.22 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_pos_if_in_set
% 4.98/5.22 thf(fact_748_length__pos__if__in__set,axiom,
% 4.98/5.22 ! [X2: nat,Xs: list_nat] :
% 4.98/5.22 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_pos_if_in_set
% 4.98/5.22 thf(fact_749_length__pos__if__in__set,axiom,
% 4.98/5.22 ! [X2: int,Xs: list_int] :
% 4.98/5.22 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % length_pos_if_in_set
% 4.98/5.22 thf(fact_750_div__le__mono2,axiom,
% 4.98/5.22 ! [M: nat,N2: nat,K: nat] :
% 4.98/5.22 ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.98/5.22 => ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.22 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_le_mono2
% 4.98/5.22 thf(fact_751_div__greater__zero__iff,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 4.98/5.22 = ( ( ord_less_eq_nat @ N2 @ M )
% 4.98/5.22 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_greater_zero_iff
% 4.98/5.22 thf(fact_752_nth__mem,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_complex] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.98/5.22 => ( member_complex @ ( nth_complex @ Xs @ N2 ) @ ( set_complex2 @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_mem
% 4.98/5.22 thf(fact_753_nth__mem,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_real] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 4.98/5.22 => ( member_real @ ( nth_real @ Xs @ N2 ) @ ( set_real2 @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_mem
% 4.98/5.22 thf(fact_754_nth__mem,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_set_nat] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.98/5.22 => ( member_set_nat @ ( nth_set_nat @ Xs @ N2 ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_mem
% 4.98/5.22 thf(fact_755_nth__mem,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_VEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N2 ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_mem
% 4.98/5.22 thf(fact_756_nth__mem,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_o] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( member_o @ ( nth_o @ Xs @ N2 ) @ ( set_o2 @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_mem
% 4.98/5.22 thf(fact_757_nth__mem,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_nat] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ ( set_nat2 @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_mem
% 4.98/5.22 thf(fact_758_nth__mem,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_int] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( member_int @ ( nth_int @ Xs @ N2 ) @ ( set_int2 @ Xs ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_mem
% 4.98/5.22 thf(fact_759_list__ball__nth,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( ! [X5: vEBT_VEBT] :
% 4.98/5.22 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.98/5.22 => ( P @ X5 ) )
% 4.98/5.22 => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_ball_nth
% 4.98/5.22 thf(fact_760_list__ball__nth,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_o,P: $o > $o] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( ! [X5: $o] :
% 4.98/5.22 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 4.98/5.22 => ( P @ X5 ) )
% 4.98/5.22 => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_ball_nth
% 4.98/5.22 thf(fact_761_list__ball__nth,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_nat,P: nat > $o] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( ! [X5: nat] :
% 4.98/5.22 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 4.98/5.22 => ( P @ X5 ) )
% 4.98/5.22 => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_ball_nth
% 4.98/5.22 thf(fact_762_list__ball__nth,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_int,P: int > $o] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( ! [X5: int] :
% 4.98/5.22 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 4.98/5.22 => ( P @ X5 ) )
% 4.98/5.22 => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_ball_nth
% 4.98/5.22 thf(fact_763_in__set__conv__nth,axiom,
% 4.98/5.22 ! [X2: complex,Xs: list_complex] :
% 4.98/5.22 ( ( member_complex @ X2 @ ( set_complex2 @ Xs ) )
% 4.98/5.22 = ( ? [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.98/5.22 & ( ( nth_complex @ Xs @ I5 )
% 4.98/5.22 = X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % in_set_conv_nth
% 4.98/5.22 thf(fact_764_in__set__conv__nth,axiom,
% 4.98/5.22 ! [X2: real,Xs: list_real] :
% 4.98/5.22 ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 4.98/5.22 = ( ? [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_real @ Xs ) )
% 4.98/5.22 & ( ( nth_real @ Xs @ I5 )
% 4.98/5.22 = X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % in_set_conv_nth
% 4.98/5.22 thf(fact_765_in__set__conv__nth,axiom,
% 4.98/5.22 ! [X2: set_nat,Xs: list_set_nat] :
% 4.98/5.22 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 4.98/5.22 = ( ? [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.98/5.22 & ( ( nth_set_nat @ Xs @ I5 )
% 4.98/5.22 = X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % in_set_conv_nth
% 4.98/5.22 thf(fact_766_in__set__conv__nth,axiom,
% 4.98/5.22 ! [X2: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 4.98/5.22 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.98/5.22 = ( ? [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 & ( ( nth_VEBT_VEBT @ Xs @ I5 )
% 4.98/5.22 = X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % in_set_conv_nth
% 4.98/5.22 thf(fact_767_in__set__conv__nth,axiom,
% 4.98/5.22 ! [X2: $o,Xs: list_o] :
% 4.98/5.22 ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 4.98/5.22 = ( ? [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 & ( ( nth_o @ Xs @ I5 )
% 4.98/5.22 = X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % in_set_conv_nth
% 4.98/5.22 thf(fact_768_in__set__conv__nth,axiom,
% 4.98/5.22 ! [X2: nat,Xs: list_nat] :
% 4.98/5.22 ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 4.98/5.22 = ( ? [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 & ( ( nth_nat @ Xs @ I5 )
% 4.98/5.22 = X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % in_set_conv_nth
% 4.98/5.22 thf(fact_769_in__set__conv__nth,axiom,
% 4.98/5.22 ! [X2: int,Xs: list_int] :
% 4.98/5.22 ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 4.98/5.22 = ( ? [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 & ( ( nth_int @ Xs @ I5 )
% 4.98/5.22 = X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % in_set_conv_nth
% 4.98/5.22 thf(fact_770_all__nth__imp__all__set,axiom,
% 4.98/5.22 ! [Xs: list_complex,P: complex > $o,X2: complex] :
% 4.98/5.22 ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_complex @ Xs @ I2 ) ) )
% 4.98/5.22 => ( ( member_complex @ X2 @ ( set_complex2 @ Xs ) )
% 4.98/5.22 => ( P @ X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_nth_imp_all_set
% 4.98/5.22 thf(fact_771_all__nth__imp__all__set,axiom,
% 4.98/5.22 ! [Xs: list_real,P: real > $o,X2: real] :
% 4.98/5.22 ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_size_list_real @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_real @ Xs @ I2 ) ) )
% 4.98/5.22 => ( ( member_real @ X2 @ ( set_real2 @ Xs ) )
% 4.98/5.22 => ( P @ X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_nth_imp_all_set
% 4.98/5.22 thf(fact_772_all__nth__imp__all__set,axiom,
% 4.98/5.22 ! [Xs: list_set_nat,P: set_nat > $o,X2: set_nat] :
% 4.98/5.22 ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_set_nat @ Xs @ I2 ) ) )
% 4.98/5.22 => ( ( member_set_nat @ X2 @ ( set_set_nat2 @ Xs ) )
% 4.98/5.22 => ( P @ X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_nth_imp_all_set
% 4.98/5.22 thf(fact_773_all__nth__imp__all__set,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 4.98/5.22 ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_VEBT_VEBT @ Xs @ I2 ) ) )
% 4.98/5.22 => ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.98/5.22 => ( P @ X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_nth_imp_all_set
% 4.98/5.22 thf(fact_774_all__nth__imp__all__set,axiom,
% 4.98/5.22 ! [Xs: list_o,P: $o > $o,X2: $o] :
% 4.98/5.22 ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_o @ Xs @ I2 ) ) )
% 4.98/5.22 => ( ( member_o @ X2 @ ( set_o2 @ Xs ) )
% 4.98/5.22 => ( P @ X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_nth_imp_all_set
% 4.98/5.22 thf(fact_775_all__nth__imp__all__set,axiom,
% 4.98/5.22 ! [Xs: list_nat,P: nat > $o,X2: nat] :
% 4.98/5.22 ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_nat @ Xs @ I2 ) ) )
% 4.98/5.22 => ( ( member_nat @ X2 @ ( set_nat2 @ Xs ) )
% 4.98/5.22 => ( P @ X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_nth_imp_all_set
% 4.98/5.22 thf(fact_776_all__nth__imp__all__set,axiom,
% 4.98/5.22 ! [Xs: list_int,P: int > $o,X2: int] :
% 4.98/5.22 ( ! [I2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_int @ Xs @ I2 ) ) )
% 4.98/5.22 => ( ( member_int @ X2 @ ( set_int2 @ Xs ) )
% 4.98/5.22 => ( P @ X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_nth_imp_all_set
% 4.98/5.22 thf(fact_777_all__set__conv__all__nth,axiom,
% 4.98/5.22 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 4.98/5.22 ( ( ! [X: vEBT_VEBT] :
% 4.98/5.22 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 4.98/5.22 => ( P @ X ) ) )
% 4.98/5.22 = ( ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_VEBT_VEBT @ Xs @ I5 ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_set_conv_all_nth
% 4.98/5.22 thf(fact_778_all__set__conv__all__nth,axiom,
% 4.98/5.22 ! [Xs: list_o,P: $o > $o] :
% 4.98/5.22 ( ( ! [X: $o] :
% 4.98/5.22 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 4.98/5.22 => ( P @ X ) ) )
% 4.98/5.22 = ( ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_o @ Xs @ I5 ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_set_conv_all_nth
% 4.98/5.22 thf(fact_779_all__set__conv__all__nth,axiom,
% 4.98/5.22 ! [Xs: list_nat,P: nat > $o] :
% 4.98/5.22 ( ( ! [X: nat] :
% 4.98/5.22 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 4.98/5.22 => ( P @ X ) ) )
% 4.98/5.22 = ( ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_nat @ Xs @ I5 ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_set_conv_all_nth
% 4.98/5.22 thf(fact_780_all__set__conv__all__nth,axiom,
% 4.98/5.22 ! [Xs: list_int,P: int > $o] :
% 4.98/5.22 ( ( ! [X: int] :
% 4.98/5.22 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 4.98/5.22 => ( P @ X ) ) )
% 4.98/5.22 = ( ! [I5: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( P @ ( nth_int @ Xs @ I5 ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % all_set_conv_all_nth
% 4.98/5.22 thf(fact_781_div__less__dividend,axiom,
% 4.98/5.22 ! [N2: nat,M: nat] :
% 4.98/5.22 ( ( ord_less_nat @ one_one_nat @ N2 )
% 4.98/5.22 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.98/5.22 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_less_dividend
% 4.98/5.22 thf(fact_782_div__eq__dividend__iff,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.98/5.22 => ( ( ( divide_divide_nat @ M @ N2 )
% 4.98/5.22 = M )
% 4.98/5.22 = ( N2 = one_one_nat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_eq_dividend_iff
% 4.98/5.22 thf(fact_783_set__update__memI,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_complex,X2: complex] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 4.98/5.22 => ( member_complex @ X2 @ ( set_complex2 @ ( list_update_complex @ Xs @ N2 @ X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_memI
% 4.98/5.22 thf(fact_784_set__update__memI,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_real,X2: real] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 4.98/5.22 => ( member_real @ X2 @ ( set_real2 @ ( list_update_real @ Xs @ N2 @ X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_memI
% 4.98/5.22 thf(fact_785_set__update__memI,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_set_nat,X2: set_nat] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 4.98/5.22 => ( member_set_nat @ X2 @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N2 @ X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_memI
% 4.98/5.22 thf(fact_786_set__update__memI,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N2 @ X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_memI
% 4.98/5.22 thf(fact_787_set__update__memI,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_o,X2: $o] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( member_o @ X2 @ ( set_o2 @ ( list_update_o @ Xs @ N2 @ X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_memI
% 4.98/5.22 thf(fact_788_set__update__memI,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_nat,X2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( member_nat @ X2 @ ( set_nat2 @ ( list_update_nat @ Xs @ N2 @ X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_memI
% 4.98/5.22 thf(fact_789_set__update__memI,axiom,
% 4.98/5.22 ! [N2: nat,Xs: list_int,X2: int] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( member_int @ X2 @ ( set_int2 @ ( list_update_int @ Xs @ N2 @ X2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % set_update_memI
% 4.98/5.22 thf(fact_790_nth__list__update,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_VEBT_VEBT,J: nat,X2: vEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( ( ( I3 = J )
% 4.98/5.22 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = X2 ) )
% 4.98/5.22 & ( ( I3 != J )
% 4.98/5.22 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update
% 4.98/5.22 thf(fact_791_nth__list__update,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_o,X2: $o,J: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( ( nth_o @ ( list_update_o @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = ( ( ( I3 = J )
% 4.98/5.22 => X2 )
% 4.98/5.22 & ( ( I3 != J )
% 4.98/5.22 => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update
% 4.98/5.22 thf(fact_792_nth__list__update,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_nat,J: nat,X2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( ( ( I3 = J )
% 4.98/5.22 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = X2 ) )
% 4.98/5.22 & ( ( I3 != J )
% 4.98/5.22 => ( ( nth_nat @ ( list_update_nat @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update
% 4.98/5.22 thf(fact_793_nth__list__update,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_int,J: nat,X2: int] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( ( ( I3 = J )
% 4.98/5.22 => ( ( nth_int @ ( list_update_int @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = X2 ) )
% 4.98/5.22 & ( ( I3 != J )
% 4.98/5.22 => ( ( nth_int @ ( list_update_int @ Xs @ I3 @ X2 ) @ J )
% 4.98/5.22 = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % nth_list_update
% 4.98/5.22 thf(fact_794_list__update__same__conv,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 4.98/5.22 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 )
% 4.98/5.22 = Xs )
% 4.98/5.22 = ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 4.98/5.22 = X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_same_conv
% 4.98/5.22 thf(fact_795_list__update__same__conv,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_o,X2: $o] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 4.98/5.22 => ( ( ( list_update_o @ Xs @ I3 @ X2 )
% 4.98/5.22 = Xs )
% 4.98/5.22 = ( ( nth_o @ Xs @ I3 )
% 4.98/5.22 = X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_same_conv
% 4.98/5.22 thf(fact_796_list__update__same__conv,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_nat,X2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 4.98/5.22 => ( ( ( list_update_nat @ Xs @ I3 @ X2 )
% 4.98/5.22 = Xs )
% 4.98/5.22 = ( ( nth_nat @ Xs @ I3 )
% 4.98/5.22 = X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_same_conv
% 4.98/5.22 thf(fact_797_list__update__same__conv,axiom,
% 4.98/5.22 ! [I3: nat,Xs: list_int,X2: int] :
% 4.98/5.22 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 4.98/5.22 => ( ( ( list_update_int @ Xs @ I3 @ X2 )
% 4.98/5.22 = Xs )
% 4.98/5.22 = ( ( nth_int @ Xs @ I3 )
% 4.98/5.22 = X2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % list_update_same_conv
% 4.98/5.22 thf(fact_798_divide__le__eq__1,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 4.98/5.22 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.22 & ( ord_less_eq_real @ B @ A ) )
% 4.98/5.22 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 & ( ord_less_eq_real @ A @ B ) )
% 4.98/5.22 | ( A = zero_zero_real ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_eq_1
% 4.98/5.22 thf(fact_799_divide__le__eq__1,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 4.98/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.22 & ( ord_less_eq_rat @ B @ A ) )
% 4.98/5.22 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 & ( ord_less_eq_rat @ A @ B ) )
% 4.98/5.22 | ( A = zero_zero_rat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % divide_le_eq_1
% 4.98/5.22 thf(fact_800_le__divide__eq__1,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 4.98/5.22 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.22 & ( ord_less_eq_real @ A @ B ) )
% 4.98/5.22 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.22 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % le_divide_eq_1
% 4.98/5.22 thf(fact_801_le__divide__eq__1,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 4.98/5.22 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.22 & ( ord_less_eq_rat @ A @ B ) )
% 4.98/5.22 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.22 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % le_divide_eq_1
% 4.98/5.22 thf(fact_802_exp__add__not__zero__imp__left,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.22 != zero_zero_nat )
% 4.98/5.22 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 4.98/5.22 != zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % exp_add_not_zero_imp_left
% 4.98/5.22 thf(fact_803_exp__add__not__zero__imp__left,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.22 != zero_zero_int )
% 4.98/5.22 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 4.98/5.22 != zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % exp_add_not_zero_imp_left
% 4.98/5.22 thf(fact_804_exp__add__not__zero__imp__right,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.22 != zero_zero_nat )
% 4.98/5.22 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.98/5.22 != zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % exp_add_not_zero_imp_right
% 4.98/5.22 thf(fact_805_exp__add__not__zero__imp__right,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.22 != zero_zero_int )
% 4.98/5.22 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 4.98/5.22 != zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % exp_add_not_zero_imp_right
% 4.98/5.22 thf(fact_806_div__exp__eq,axiom,
% 4.98/5.22 ! [A: nat,M: nat,N2: nat] :
% 4.98/5.22 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.22 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_exp_eq
% 4.98/5.22 thf(fact_807_div__exp__eq,axiom,
% 4.98/5.22 ! [A: int,M: nat,N2: nat] :
% 4.98/5.22 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.22 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_exp_eq
% 4.98/5.22 thf(fact_808_div__2__gt__zero,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_2_gt_zero
% 4.98/5.22 thf(fact_809_Suc__n__div__2__gt__zero,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.22 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % Suc_n_div_2_gt_zero
% 4.98/5.22 thf(fact_810_semiring__norm_I69_J,axiom,
% 4.98/5.22 ! [M: num] :
% 4.98/5.22 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 4.98/5.22
% 4.98/5.22 % semiring_norm(69)
% 4.98/5.22 thf(fact_811_semiring__norm_I76_J,axiom,
% 4.98/5.22 ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % semiring_norm(76)
% 4.98/5.22 thf(fact_812_semiring__norm_I2_J,axiom,
% 4.98/5.22 ( ( plus_plus_num @ one @ one )
% 4.98/5.22 = ( bit0 @ one ) ) ).
% 4.98/5.22
% 4.98/5.22 % semiring_norm(2)
% 4.98/5.22 thf(fact_813_less__one,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ one_one_nat )
% 4.98/5.22 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_one
% 4.98/5.22 thf(fact_814_add__gr__0,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.22 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.98/5.22 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_gr_0
% 4.98/5.22 thf(fact_815_less__Suc0,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 4.98/5.22 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % less_Suc0
% 4.98/5.22 thf(fact_816_zero__less__Suc,axiom,
% 4.98/5.22 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_less_Suc
% 4.98/5.22 thf(fact_817_div__self,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( A != zero_zero_complex )
% 4.98/5.22 => ( ( divide1717551699836669952omplex @ A @ A )
% 4.98/5.22 = one_one_complex ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_self
% 4.98/5.22 thf(fact_818_div__self,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( A != zero_zero_real )
% 4.98/5.22 => ( ( divide_divide_real @ A @ A )
% 4.98/5.22 = one_one_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_self
% 4.98/5.22 thf(fact_819_div__self,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( A != zero_zero_rat )
% 4.98/5.22 => ( ( divide_divide_rat @ A @ A )
% 4.98/5.22 = one_one_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_self
% 4.98/5.22 thf(fact_820_div__self,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( A != zero_zero_nat )
% 4.98/5.22 => ( ( divide_divide_nat @ A @ A )
% 4.98/5.22 = one_one_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_self
% 4.98/5.22 thf(fact_821_div__self,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( A != zero_zero_int )
% 4.98/5.22 => ( ( divide_divide_int @ A @ A )
% 4.98/5.22 = one_one_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % div_self
% 4.98/5.22 thf(fact_822_buildup__gives__valid,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.22 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % buildup_gives_valid
% 4.98/5.22 thf(fact_823_add__less__same__cancel1,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 4.98/5.22 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_same_cancel1
% 4.98/5.22 thf(fact_824_add__less__same__cancel1,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 4.98/5.22 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_same_cancel1
% 4.98/5.22 thf(fact_825_add__less__same__cancel1,axiom,
% 4.98/5.22 ! [B: nat,A: nat] :
% 4.98/5.22 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.98/5.22 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_same_cancel1
% 4.98/5.22 thf(fact_826_add__less__same__cancel1,axiom,
% 4.98/5.22 ! [B: int,A: int] :
% 4.98/5.22 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.98/5.22 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_same_cancel1
% 4.98/5.22 thf(fact_827_add__less__same__cancel2,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.98/5.22 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_same_cancel2
% 4.98/5.22 thf(fact_828_add__less__same__cancel2,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.98/5.22 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_same_cancel2
% 4.98/5.22 thf(fact_829_add__less__same__cancel2,axiom,
% 4.98/5.22 ! [A: nat,B: nat] :
% 4.98/5.22 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.98/5.22 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_same_cancel2
% 4.98/5.22 thf(fact_830_add__less__same__cancel2,axiom,
% 4.98/5.22 ! [A: int,B: int] :
% 4.98/5.22 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.98/5.22 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_same_cancel2
% 4.98/5.22 thf(fact_831_buildup__nothing__in__min__max,axiom,
% 4.98/5.22 ! [N2: nat,X2: nat] :
% 4.98/5.22 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X2 ) ).
% 4.98/5.22
% 4.98/5.22 % buildup_nothing_in_min_max
% 4.98/5.22 thf(fact_832_buildup__nothing__in__leaf,axiom,
% 4.98/5.22 ! [N2: nat,X2: nat] :
% 4.98/5.22 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X2 ) ).
% 4.98/5.22
% 4.98/5.22 % buildup_nothing_in_leaf
% 4.98/5.22 thf(fact_833_semiring__norm_I87_J,axiom,
% 4.98/5.22 ! [M: num,N2: num] :
% 4.98/5.22 ( ( ( bit0 @ M )
% 4.98/5.22 = ( bit0 @ N2 ) )
% 4.98/5.22 = ( M = N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % semiring_norm(87)
% 4.98/5.22 thf(fact_834_add__right__cancel,axiom,
% 4.98/5.22 ! [B: real,A: real,C: real] :
% 4.98/5.22 ( ( ( plus_plus_real @ B @ A )
% 4.98/5.22 = ( plus_plus_real @ C @ A ) )
% 4.98/5.22 = ( B = C ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_right_cancel
% 4.98/5.22 thf(fact_835_add__right__cancel,axiom,
% 4.98/5.22 ! [B: rat,A: rat,C: rat] :
% 4.98/5.22 ( ( ( plus_plus_rat @ B @ A )
% 4.98/5.22 = ( plus_plus_rat @ C @ A ) )
% 4.98/5.22 = ( B = C ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_right_cancel
% 4.98/5.22 thf(fact_836_add__right__cancel,axiom,
% 4.98/5.22 ! [B: nat,A: nat,C: nat] :
% 4.98/5.22 ( ( ( plus_plus_nat @ B @ A )
% 4.98/5.22 = ( plus_plus_nat @ C @ A ) )
% 4.98/5.22 = ( B = C ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_right_cancel
% 4.98/5.22 thf(fact_837_add__right__cancel,axiom,
% 4.98/5.22 ! [B: int,A: int,C: int] :
% 4.98/5.22 ( ( ( plus_plus_int @ B @ A )
% 4.98/5.22 = ( plus_plus_int @ C @ A ) )
% 4.98/5.22 = ( B = C ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_right_cancel
% 4.98/5.22 thf(fact_838_add__left__cancel,axiom,
% 4.98/5.22 ! [A: real,B: real,C: real] :
% 4.98/5.22 ( ( ( plus_plus_real @ A @ B )
% 4.98/5.22 = ( plus_plus_real @ A @ C ) )
% 4.98/5.22 = ( B = C ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_left_cancel
% 4.98/5.22 thf(fact_839_add__left__cancel,axiom,
% 4.98/5.22 ! [A: rat,B: rat,C: rat] :
% 4.98/5.22 ( ( ( plus_plus_rat @ A @ B )
% 4.98/5.22 = ( plus_plus_rat @ A @ C ) )
% 4.98/5.22 = ( B = C ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_left_cancel
% 4.98/5.22 thf(fact_840_add__left__cancel,axiom,
% 4.98/5.22 ! [A: nat,B: nat,C: nat] :
% 4.98/5.22 ( ( ( plus_plus_nat @ A @ B )
% 4.98/5.22 = ( plus_plus_nat @ A @ C ) )
% 4.98/5.22 = ( B = C ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_left_cancel
% 4.98/5.22 thf(fact_841_add__left__cancel,axiom,
% 4.98/5.22 ! [A: int,B: int,C: int] :
% 4.98/5.22 ( ( ( plus_plus_int @ A @ B )
% 4.98/5.22 = ( plus_plus_int @ A @ C ) )
% 4.98/5.22 = ( B = C ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_left_cancel
% 4.98/5.22 thf(fact_842_old_Onat_Oinject,axiom,
% 4.98/5.22 ! [Nat: nat,Nat2: nat] :
% 4.98/5.22 ( ( ( suc @ Nat )
% 4.98/5.22 = ( suc @ Nat2 ) )
% 4.98/5.22 = ( Nat = Nat2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % old.nat.inject
% 4.98/5.22 thf(fact_843_nat_Oinject,axiom,
% 4.98/5.22 ! [X22: nat,Y2: nat] :
% 4.98/5.22 ( ( ( suc @ X22 )
% 4.98/5.22 = ( suc @ Y2 ) )
% 4.98/5.22 = ( X22 = Y2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % nat.inject
% 4.98/5.22 thf(fact_844_le__zero__eq,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 4.98/5.22 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % le_zero_eq
% 4.98/5.22 thf(fact_845_not__gr__zero,axiom,
% 4.98/5.22 ! [N2: nat] :
% 4.98/5.22 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 4.98/5.22 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % not_gr_zero
% 4.98/5.22 thf(fact_846_add__le__cancel__right,axiom,
% 4.98/5.22 ! [A: real,C: real,B: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.98/5.22 = ( ord_less_eq_real @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_le_cancel_right
% 4.98/5.22 thf(fact_847_add__le__cancel__right,axiom,
% 4.98/5.22 ! [A: rat,C: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.22 = ( ord_less_eq_rat @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_le_cancel_right
% 4.98/5.22 thf(fact_848_add__le__cancel__right,axiom,
% 4.98/5.22 ! [A: nat,C: nat,B: nat] :
% 4.98/5.22 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.22 = ( ord_less_eq_nat @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_le_cancel_right
% 4.98/5.22 thf(fact_849_add__le__cancel__right,axiom,
% 4.98/5.22 ! [A: int,C: int,B: int] :
% 4.98/5.22 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.98/5.22 = ( ord_less_eq_int @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_le_cancel_right
% 4.98/5.22 thf(fact_850_add__le__cancel__left,axiom,
% 4.98/5.22 ! [C: real,A: real,B: real] :
% 4.98/5.22 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.98/5.22 = ( ord_less_eq_real @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_le_cancel_left
% 4.98/5.22 thf(fact_851_add__le__cancel__left,axiom,
% 4.98/5.22 ! [C: rat,A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.98/5.22 = ( ord_less_eq_rat @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_le_cancel_left
% 4.98/5.22 thf(fact_852_add__le__cancel__left,axiom,
% 4.98/5.22 ! [C: nat,A: nat,B: nat] :
% 4.98/5.22 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.98/5.22 = ( ord_less_eq_nat @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_le_cancel_left
% 4.98/5.22 thf(fact_853_add__le__cancel__left,axiom,
% 4.98/5.22 ! [C: int,A: int,B: int] :
% 4.98/5.22 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.98/5.22 = ( ord_less_eq_int @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_le_cancel_left
% 4.98/5.22 thf(fact_854_add__0,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add_0
% 4.98/5.22 thf(fact_855_add__0,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( plus_plus_real @ zero_zero_real @ A )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add_0
% 4.98/5.22 thf(fact_856_add__0,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add_0
% 4.98/5.22 thf(fact_857_add__0,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add_0
% 4.98/5.22 thf(fact_858_add__0,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( plus_plus_int @ zero_zero_int @ A )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add_0
% 4.98/5.22 thf(fact_859_zero__eq__add__iff__both__eq__0,axiom,
% 4.98/5.22 ! [X2: nat,Y: nat] :
% 4.98/5.22 ( ( zero_zero_nat
% 4.98/5.22 = ( plus_plus_nat @ X2 @ Y ) )
% 4.98/5.22 = ( ( X2 = zero_zero_nat )
% 4.98/5.22 & ( Y = zero_zero_nat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % zero_eq_add_iff_both_eq_0
% 4.98/5.22 thf(fact_860_add__eq__0__iff__both__eq__0,axiom,
% 4.98/5.22 ! [X2: nat,Y: nat] :
% 4.98/5.22 ( ( ( plus_plus_nat @ X2 @ Y )
% 4.98/5.22 = zero_zero_nat )
% 4.98/5.22 = ( ( X2 = zero_zero_nat )
% 4.98/5.22 & ( Y = zero_zero_nat ) ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_eq_0_iff_both_eq_0
% 4.98/5.22 thf(fact_861_add__cancel__right__right,axiom,
% 4.98/5.22 ! [A: complex,B: complex] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_complex @ A @ B ) )
% 4.98/5.22 = ( B = zero_zero_complex ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_right
% 4.98/5.22 thf(fact_862_add__cancel__right__right,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_real @ A @ B ) )
% 4.98/5.22 = ( B = zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_right
% 4.98/5.22 thf(fact_863_add__cancel__right__right,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_rat @ A @ B ) )
% 4.98/5.22 = ( B = zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_right
% 4.98/5.22 thf(fact_864_add__cancel__right__right,axiom,
% 4.98/5.22 ! [A: nat,B: nat] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_nat @ A @ B ) )
% 4.98/5.22 = ( B = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_right
% 4.98/5.22 thf(fact_865_add__cancel__right__right,axiom,
% 4.98/5.22 ! [A: int,B: int] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_int @ A @ B ) )
% 4.98/5.22 = ( B = zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_right
% 4.98/5.22 thf(fact_866_add__cancel__right__left,axiom,
% 4.98/5.22 ! [A: complex,B: complex] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_complex @ B @ A ) )
% 4.98/5.22 = ( B = zero_zero_complex ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_left
% 4.98/5.22 thf(fact_867_add__cancel__right__left,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_real @ B @ A ) )
% 4.98/5.22 = ( B = zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_left
% 4.98/5.22 thf(fact_868_add__cancel__right__left,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_rat @ B @ A ) )
% 4.98/5.22 = ( B = zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_left
% 4.98/5.22 thf(fact_869_add__cancel__right__left,axiom,
% 4.98/5.22 ! [A: nat,B: nat] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_nat @ B @ A ) )
% 4.98/5.22 = ( B = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_left
% 4.98/5.22 thf(fact_870_add__cancel__right__left,axiom,
% 4.98/5.22 ! [A: int,B: int] :
% 4.98/5.22 ( ( A
% 4.98/5.22 = ( plus_plus_int @ B @ A ) )
% 4.98/5.22 = ( B = zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_right_left
% 4.98/5.22 thf(fact_871_add__cancel__left__right,axiom,
% 4.98/5.22 ! [A: complex,B: complex] :
% 4.98/5.22 ( ( ( plus_plus_complex @ A @ B )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_complex ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_right
% 4.98/5.22 thf(fact_872_add__cancel__left__right,axiom,
% 4.98/5.22 ! [A: real,B: real] :
% 4.98/5.22 ( ( ( plus_plus_real @ A @ B )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_right
% 4.98/5.22 thf(fact_873_add__cancel__left__right,axiom,
% 4.98/5.22 ! [A: rat,B: rat] :
% 4.98/5.22 ( ( ( plus_plus_rat @ A @ B )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_right
% 4.98/5.22 thf(fact_874_add__cancel__left__right,axiom,
% 4.98/5.22 ! [A: nat,B: nat] :
% 4.98/5.22 ( ( ( plus_plus_nat @ A @ B )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_right
% 4.98/5.22 thf(fact_875_add__cancel__left__right,axiom,
% 4.98/5.22 ! [A: int,B: int] :
% 4.98/5.22 ( ( ( plus_plus_int @ A @ B )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_right
% 4.98/5.22 thf(fact_876_add__cancel__left__left,axiom,
% 4.98/5.22 ! [B: complex,A: complex] :
% 4.98/5.22 ( ( ( plus_plus_complex @ B @ A )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_complex ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_left
% 4.98/5.22 thf(fact_877_add__cancel__left__left,axiom,
% 4.98/5.22 ! [B: real,A: real] :
% 4.98/5.22 ( ( ( plus_plus_real @ B @ A )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_left
% 4.98/5.22 thf(fact_878_add__cancel__left__left,axiom,
% 4.98/5.22 ! [B: rat,A: rat] :
% 4.98/5.22 ( ( ( plus_plus_rat @ B @ A )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_left
% 4.98/5.22 thf(fact_879_add__cancel__left__left,axiom,
% 4.98/5.22 ! [B: nat,A: nat] :
% 4.98/5.22 ( ( ( plus_plus_nat @ B @ A )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_nat ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_left
% 4.98/5.22 thf(fact_880_add__cancel__left__left,axiom,
% 4.98/5.22 ! [B: int,A: int] :
% 4.98/5.22 ( ( ( plus_plus_int @ B @ A )
% 4.98/5.22 = A )
% 4.98/5.22 = ( B = zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_cancel_left_left
% 4.98/5.22 thf(fact_881_double__zero__sym,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( zero_zero_real
% 4.98/5.22 = ( plus_plus_real @ A @ A ) )
% 4.98/5.22 = ( A = zero_zero_real ) ) ).
% 4.98/5.22
% 4.98/5.22 % double_zero_sym
% 4.98/5.22 thf(fact_882_double__zero__sym,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( zero_zero_rat
% 4.98/5.22 = ( plus_plus_rat @ A @ A ) )
% 4.98/5.22 = ( A = zero_zero_rat ) ) ).
% 4.98/5.22
% 4.98/5.22 % double_zero_sym
% 4.98/5.22 thf(fact_883_double__zero__sym,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( zero_zero_int
% 4.98/5.22 = ( plus_plus_int @ A @ A ) )
% 4.98/5.22 = ( A = zero_zero_int ) ) ).
% 4.98/5.22
% 4.98/5.22 % double_zero_sym
% 4.98/5.22 thf(fact_884_add_Oright__neutral,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add.right_neutral
% 4.98/5.22 thf(fact_885_add_Oright__neutral,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( plus_plus_real @ A @ zero_zero_real )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add.right_neutral
% 4.98/5.22 thf(fact_886_add_Oright__neutral,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add.right_neutral
% 4.98/5.22 thf(fact_887_add_Oright__neutral,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add.right_neutral
% 4.98/5.22 thf(fact_888_add_Oright__neutral,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( plus_plus_int @ A @ zero_zero_int )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % add.right_neutral
% 4.98/5.22 thf(fact_889_add__less__cancel__right,axiom,
% 4.98/5.22 ! [A: real,C: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.98/5.22 = ( ord_less_real @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_cancel_right
% 4.98/5.22 thf(fact_890_add__less__cancel__right,axiom,
% 4.98/5.22 ! [A: rat,C: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.22 = ( ord_less_rat @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_cancel_right
% 4.98/5.22 thf(fact_891_add__less__cancel__right,axiom,
% 4.98/5.22 ! [A: nat,C: nat,B: nat] :
% 4.98/5.22 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.22 = ( ord_less_nat @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_cancel_right
% 4.98/5.22 thf(fact_892_add__less__cancel__right,axiom,
% 4.98/5.22 ! [A: int,C: int,B: int] :
% 4.98/5.22 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.98/5.22 = ( ord_less_int @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_cancel_right
% 4.98/5.22 thf(fact_893_add__less__cancel__left,axiom,
% 4.98/5.22 ! [C: real,A: real,B: real] :
% 4.98/5.22 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.98/5.22 = ( ord_less_real @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_cancel_left
% 4.98/5.22 thf(fact_894_add__less__cancel__left,axiom,
% 4.98/5.22 ! [C: rat,A: rat,B: rat] :
% 4.98/5.22 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.98/5.22 = ( ord_less_rat @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_cancel_left
% 4.98/5.22 thf(fact_895_add__less__cancel__left,axiom,
% 4.98/5.22 ! [C: nat,A: nat,B: nat] :
% 4.98/5.22 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.98/5.22 = ( ord_less_nat @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_cancel_left
% 4.98/5.22 thf(fact_896_add__less__cancel__left,axiom,
% 4.98/5.22 ! [C: int,A: int,B: int] :
% 4.98/5.22 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.98/5.22 = ( ord_less_int @ A @ B ) ) ).
% 4.98/5.22
% 4.98/5.22 % add_less_cancel_left
% 4.98/5.22 thf(fact_897_div__by__0,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 4.98/5.22 = zero_zero_complex ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_0
% 4.98/5.22 thf(fact_898_div__by__0,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( divide_divide_real @ A @ zero_zero_real )
% 4.98/5.22 = zero_zero_real ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_0
% 4.98/5.22 thf(fact_899_div__by__0,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 4.98/5.22 = zero_zero_rat ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_0
% 4.98/5.22 thf(fact_900_div__by__0,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 4.98/5.22 = zero_zero_nat ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_0
% 4.98/5.22 thf(fact_901_div__by__0,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( divide_divide_int @ A @ zero_zero_int )
% 4.98/5.22 = zero_zero_int ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_0
% 4.98/5.22 thf(fact_902_div__0,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 4.98/5.22 = zero_zero_complex ) ).
% 4.98/5.22
% 4.98/5.22 % div_0
% 4.98/5.22 thf(fact_903_div__0,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( divide_divide_real @ zero_zero_real @ A )
% 4.98/5.22 = zero_zero_real ) ).
% 4.98/5.22
% 4.98/5.22 % div_0
% 4.98/5.22 thf(fact_904_div__0,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 4.98/5.22 = zero_zero_rat ) ).
% 4.98/5.22
% 4.98/5.22 % div_0
% 4.98/5.22 thf(fact_905_div__0,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 4.98/5.22 = zero_zero_nat ) ).
% 4.98/5.22
% 4.98/5.22 % div_0
% 4.98/5.22 thf(fact_906_div__0,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( divide_divide_int @ zero_zero_int @ A )
% 4.98/5.22 = zero_zero_int ) ).
% 4.98/5.22
% 4.98/5.22 % div_0
% 4.98/5.22 thf(fact_907_semiring__norm_I83_J,axiom,
% 4.98/5.22 ! [N2: num] :
% 4.98/5.22 ( one
% 4.98/5.22 != ( bit0 @ N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % semiring_norm(83)
% 4.98/5.22 thf(fact_908_semiring__norm_I85_J,axiom,
% 4.98/5.22 ! [M: num] :
% 4.98/5.22 ( ( bit0 @ M )
% 4.98/5.22 != one ) ).
% 4.98/5.22
% 4.98/5.22 % semiring_norm(85)
% 4.98/5.22 thf(fact_909_div__by__1,axiom,
% 4.98/5.22 ! [A: complex] :
% 4.98/5.22 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_1
% 4.98/5.22 thf(fact_910_div__by__1,axiom,
% 4.98/5.22 ! [A: real] :
% 4.98/5.22 ( ( divide_divide_real @ A @ one_one_real )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_1
% 4.98/5.22 thf(fact_911_div__by__1,axiom,
% 4.98/5.22 ! [A: rat] :
% 4.98/5.22 ( ( divide_divide_rat @ A @ one_one_rat )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_1
% 4.98/5.22 thf(fact_912_div__by__1,axiom,
% 4.98/5.22 ! [A: nat] :
% 4.98/5.22 ( ( divide_divide_nat @ A @ one_one_nat )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_1
% 4.98/5.22 thf(fact_913_div__by__1,axiom,
% 4.98/5.22 ! [A: int] :
% 4.98/5.22 ( ( divide_divide_int @ A @ one_one_int )
% 4.98/5.22 = A ) ).
% 4.98/5.22
% 4.98/5.22 % div_by_1
% 4.98/5.22 thf(fact_914_Suc__less__eq,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 4.98/5.22 = ( ord_less_nat @ M @ N2 ) ) ).
% 4.98/5.22
% 4.98/5.22 % Suc_less_eq
% 4.98/5.22 thf(fact_915_Suc__mono,axiom,
% 4.98/5.22 ! [M: nat,N2: nat] :
% 4.98/5.22 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.22 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_mono
% 4.98/5.23 thf(fact_916_lessI,axiom,
% 4.98/5.23 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % lessI
% 4.98/5.23 thf(fact_917_less__nat__zero__code,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % less_nat_zero_code
% 4.98/5.23 thf(fact_918_neq0__conv,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( N2 != zero_zero_nat )
% 4.98/5.23 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % neq0_conv
% 4.98/5.23 thf(fact_919_bot__nat__0_Onot__eq__extremum,axiom,
% 4.98/5.23 ! [A: nat] :
% 4.98/5.23 ( ( A != zero_zero_nat )
% 4.98/5.23 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 4.98/5.23
% 4.98/5.23 % bot_nat_0.not_eq_extremum
% 4.98/5.23 thf(fact_920_Suc__le__mono,axiom,
% 4.98/5.23 ! [N2: nat,M: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 4.98/5.23 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_le_mono
% 4.98/5.23 thf(fact_921_le0,axiom,
% 4.98/5.23 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 4.98/5.23
% 4.98/5.23 % le0
% 4.98/5.23 thf(fact_922_bot__nat__0_Oextremum,axiom,
% 4.98/5.23 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 4.98/5.23
% 4.98/5.23 % bot_nat_0.extremum
% 4.98/5.23 thf(fact_923_add__Suc__right,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 4.98/5.23 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_Suc_right
% 4.98/5.23 thf(fact_924_Nat_Oadd__0__right,axiom,
% 4.98/5.23 ! [M: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 4.98/5.23 = M ) ).
% 4.98/5.23
% 4.98/5.23 % Nat.add_0_right
% 4.98/5.23 thf(fact_925_add__is__0,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ( plus_plus_nat @ M @ N2 )
% 4.98/5.23 = zero_zero_nat )
% 4.98/5.23 = ( ( M = zero_zero_nat )
% 4.98/5.23 & ( N2 = zero_zero_nat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_is_0
% 4.98/5.23 thf(fact_926_nat__add__left__cancel__less,axiom,
% 4.98/5.23 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 4.98/5.23 = ( ord_less_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_add_left_cancel_less
% 4.98/5.23 thf(fact_927_nat__add__left__cancel__le,axiom,
% 4.98/5.23 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 4.98/5.23 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_add_left_cancel_le
% 4.98/5.23 thf(fact_928_semiring__norm_I6_J,axiom,
% 4.98/5.23 ! [M: num,N2: num] :
% 4.98/5.23 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 4.98/5.23 = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % semiring_norm(6)
% 4.98/5.23 thf(fact_929_max__Suc__Suc,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 4.98/5.23 = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_Suc_Suc
% 4.98/5.23 thf(fact_930_max__0R,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 4.98/5.23 = N2 ) ).
% 4.98/5.23
% 4.98/5.23 % max_0R
% 4.98/5.23 thf(fact_931_max__0L,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 4.98/5.23 = N2 ) ).
% 4.98/5.23
% 4.98/5.23 % max_0L
% 4.98/5.23 thf(fact_932_max__nat_Oright__neutral,axiom,
% 4.98/5.23 ! [A: nat] :
% 4.98/5.23 ( ( ord_max_nat @ A @ zero_zero_nat )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % max_nat.right_neutral
% 4.98/5.23 thf(fact_933_max__nat_Oneutr__eq__iff,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( zero_zero_nat
% 4.98/5.23 = ( ord_max_nat @ A @ B ) )
% 4.98/5.23 = ( ( A = zero_zero_nat )
% 4.98/5.23 & ( B = zero_zero_nat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_nat.neutr_eq_iff
% 4.98/5.23 thf(fact_934_max__nat_Oleft__neutral,axiom,
% 4.98/5.23 ! [A: nat] :
% 4.98/5.23 ( ( ord_max_nat @ zero_zero_nat @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % max_nat.left_neutral
% 4.98/5.23 thf(fact_935_max__nat_Oeq__neutr__iff,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ( ord_max_nat @ A @ B )
% 4.98/5.23 = zero_zero_nat )
% 4.98/5.23 = ( ( A = zero_zero_nat )
% 4.98/5.23 & ( B = zero_zero_nat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_nat.eq_neutr_iff
% 4.98/5.23 thf(fact_936_semiring__norm_I78_J,axiom,
% 4.98/5.23 ! [M: num,N2: num] :
% 4.98/5.23 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 4.98/5.23 = ( ord_less_num @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % semiring_norm(78)
% 4.98/5.23 thf(fact_937_semiring__norm_I71_J,axiom,
% 4.98/5.23 ! [M: num,N2: num] :
% 4.98/5.23 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 4.98/5.23 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % semiring_norm(71)
% 4.98/5.23 thf(fact_938_semiring__norm_I75_J,axiom,
% 4.98/5.23 ! [M: num] :
% 4.98/5.23 ~ ( ord_less_num @ M @ one ) ).
% 4.98/5.23
% 4.98/5.23 % semiring_norm(75)
% 4.98/5.23 thf(fact_939_semiring__norm_I68_J,axiom,
% 4.98/5.23 ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 4.98/5.23
% 4.98/5.23 % semiring_norm(68)
% 4.98/5.23 thf(fact_940_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.98/5.23 ! [A: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 4.98/5.23 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_le_double_add_iff_zero_le_single_add
% 4.98/5.23 thf(fact_941_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.98/5.23 ! [A: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 4.98/5.23 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_le_double_add_iff_zero_le_single_add
% 4.98/5.23 thf(fact_942_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.98/5.23 ! [A: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 4.98/5.23 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_le_double_add_iff_zero_le_single_add
% 4.98/5.23 thf(fact_943_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.98/5.23 ! [A: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 4.98/5.23 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.98/5.23
% 4.98/5.23 % double_add_le_zero_iff_single_add_le_zero
% 4.98/5.23 thf(fact_944_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.98/5.23 ! [A: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 4.98/5.23 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.98/5.23
% 4.98/5.23 % double_add_le_zero_iff_single_add_le_zero
% 4.98/5.23 thf(fact_945_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.98/5.23 ! [A: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 4.98/5.23 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.98/5.23
% 4.98/5.23 % double_add_le_zero_iff_single_add_le_zero
% 4.98/5.23 thf(fact_946_le__add__same__cancel2,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 4.98/5.23 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add_same_cancel2
% 4.98/5.23 thf(fact_947_le__add__same__cancel2,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 4.98/5.23 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add_same_cancel2
% 4.98/5.23 thf(fact_948_le__add__same__cancel2,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 4.98/5.23 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add_same_cancel2
% 4.98/5.23 thf(fact_949_le__add__same__cancel2,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 4.98/5.23 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add_same_cancel2
% 4.98/5.23 thf(fact_950_le__add__same__cancel1,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.98/5.23 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add_same_cancel1
% 4.98/5.23 thf(fact_951_le__add__same__cancel1,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.98/5.23 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add_same_cancel1
% 4.98/5.23 thf(fact_952_le__add__same__cancel1,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.98/5.23 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add_same_cancel1
% 4.98/5.23 thf(fact_953_le__add__same__cancel1,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.98/5.23 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add_same_cancel1
% 4.98/5.23 thf(fact_954_add__le__same__cancel2,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.98/5.23 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_same_cancel2
% 4.98/5.23 thf(fact_955_add__le__same__cancel2,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.98/5.23 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_same_cancel2
% 4.98/5.23 thf(fact_956_add__le__same__cancel2,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.98/5.23 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_same_cancel2
% 4.98/5.23 thf(fact_957_add__le__same__cancel2,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.98/5.23 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_same_cancel2
% 4.98/5.23 thf(fact_958_add__le__same__cancel1,axiom,
% 4.98/5.23 ! [B: real,A: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 4.98/5.23 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_same_cancel1
% 4.98/5.23 thf(fact_959_add__le__same__cancel1,axiom,
% 4.98/5.23 ! [B: rat,A: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 4.98/5.23 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_same_cancel1
% 4.98/5.23 thf(fact_960_add__le__same__cancel1,axiom,
% 4.98/5.23 ! [B: nat,A: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.98/5.23 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_same_cancel1
% 4.98/5.23 thf(fact_961_add__le__same__cancel1,axiom,
% 4.98/5.23 ! [B: int,A: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.98/5.23 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_same_cancel1
% 4.98/5.23 thf(fact_962_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.98/5.23 ! [A: real] :
% 4.98/5.23 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 4.98/5.23 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_less_double_add_iff_zero_less_single_add
% 4.98/5.23 thf(fact_963_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.98/5.23 ! [A: rat] :
% 4.98/5.23 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 4.98/5.23 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_less_double_add_iff_zero_less_single_add
% 4.98/5.23 thf(fact_964_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.98/5.23 ! [A: int] :
% 4.98/5.23 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 4.98/5.23 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_less_double_add_iff_zero_less_single_add
% 4.98/5.23 thf(fact_965_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.98/5.23 ! [A: real] :
% 4.98/5.23 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 4.98/5.23 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 4.98/5.23
% 4.98/5.23 % double_add_less_zero_iff_single_add_less_zero
% 4.98/5.23 thf(fact_966_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.98/5.23 ! [A: rat] :
% 4.98/5.23 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 4.98/5.23 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 4.98/5.23
% 4.98/5.23 % double_add_less_zero_iff_single_add_less_zero
% 4.98/5.23 thf(fact_967_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.98/5.23 ! [A: int] :
% 4.98/5.23 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 4.98/5.23 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 4.98/5.23
% 4.98/5.23 % double_add_less_zero_iff_single_add_less_zero
% 4.98/5.23 thf(fact_968_less__add__same__cancel2,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 4.98/5.23 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_same_cancel2
% 4.98/5.23 thf(fact_969_less__add__same__cancel2,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 4.98/5.23 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_same_cancel2
% 4.98/5.23 thf(fact_970_less__add__same__cancel2,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 4.98/5.23 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_same_cancel2
% 4.98/5.23 thf(fact_971_less__add__same__cancel2,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 4.98/5.23 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_same_cancel2
% 4.98/5.23 thf(fact_972_less__add__same__cancel1,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.98/5.23 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_same_cancel1
% 4.98/5.23 thf(fact_973_less__add__same__cancel1,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.98/5.23 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_same_cancel1
% 4.98/5.23 thf(fact_974_less__add__same__cancel1,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.98/5.23 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_same_cancel1
% 4.98/5.23 thf(fact_975_less__add__same__cancel1,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.98/5.23 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_same_cancel1
% 4.98/5.23 thf(fact_976_div__neg__neg__trivial,axiom,
% 4.98/5.23 ! [K: int,L: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 4.98/5.23 => ( ( ord_less_int @ L @ K )
% 4.98/5.23 => ( ( divide_divide_int @ K @ L )
% 4.98/5.23 = zero_zero_int ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % div_neg_neg_trivial
% 4.98/5.23 thf(fact_977_div__pos__pos__trivial,axiom,
% 4.98/5.23 ! [K: int,L: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.98/5.23 => ( ( ord_less_int @ K @ L )
% 4.98/5.23 => ( ( divide_divide_int @ K @ L )
% 4.98/5.23 = zero_zero_int ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % div_pos_pos_trivial
% 4.98/5.23 thf(fact_978_zero__reorient,axiom,
% 4.98/5.23 ! [X2: complex] :
% 4.98/5.23 ( ( zero_zero_complex = X2 )
% 4.98/5.23 = ( X2 = zero_zero_complex ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_reorient
% 4.98/5.23 thf(fact_979_zero__reorient,axiom,
% 4.98/5.23 ! [X2: real] :
% 4.98/5.23 ( ( zero_zero_real = X2 )
% 4.98/5.23 = ( X2 = zero_zero_real ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_reorient
% 4.98/5.23 thf(fact_980_zero__reorient,axiom,
% 4.98/5.23 ! [X2: rat] :
% 4.98/5.23 ( ( zero_zero_rat = X2 )
% 4.98/5.23 = ( X2 = zero_zero_rat ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_reorient
% 4.98/5.23 thf(fact_981_zero__reorient,axiom,
% 4.98/5.23 ! [X2: nat] :
% 4.98/5.23 ( ( zero_zero_nat = X2 )
% 4.98/5.23 = ( X2 = zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_reorient
% 4.98/5.23 thf(fact_982_zero__reorient,axiom,
% 4.98/5.23 ! [X2: int] :
% 4.98/5.23 ( ( zero_zero_int = X2 )
% 4.98/5.23 = ( X2 = zero_zero_int ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_reorient
% 4.98/5.23 thf(fact_983_linorder__neqE__linordered__idom,axiom,
% 4.98/5.23 ! [X2: real,Y: real] :
% 4.98/5.23 ( ( X2 != Y )
% 4.98/5.23 => ( ~ ( ord_less_real @ X2 @ Y )
% 4.98/5.23 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % linorder_neqE_linordered_idom
% 4.98/5.23 thf(fact_984_linorder__neqE__linordered__idom,axiom,
% 4.98/5.23 ! [X2: rat,Y: rat] :
% 4.98/5.23 ( ( X2 != Y )
% 4.98/5.23 => ( ~ ( ord_less_rat @ X2 @ Y )
% 4.98/5.23 => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % linorder_neqE_linordered_idom
% 4.98/5.23 thf(fact_985_linorder__neqE__linordered__idom,axiom,
% 4.98/5.23 ! [X2: int,Y: int] :
% 4.98/5.23 ( ( X2 != Y )
% 4.98/5.23 => ( ~ ( ord_less_int @ X2 @ Y )
% 4.98/5.23 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % linorder_neqE_linordered_idom
% 4.98/5.23 thf(fact_986_one__reorient,axiom,
% 4.98/5.23 ! [X2: complex] :
% 4.98/5.23 ( ( one_one_complex = X2 )
% 4.98/5.23 = ( X2 = one_one_complex ) ) ).
% 4.98/5.23
% 4.98/5.23 % one_reorient
% 4.98/5.23 thf(fact_987_one__reorient,axiom,
% 4.98/5.23 ! [X2: real] :
% 4.98/5.23 ( ( one_one_real = X2 )
% 4.98/5.23 = ( X2 = one_one_real ) ) ).
% 4.98/5.23
% 4.98/5.23 % one_reorient
% 4.98/5.23 thf(fact_988_one__reorient,axiom,
% 4.98/5.23 ! [X2: rat] :
% 4.98/5.23 ( ( one_one_rat = X2 )
% 4.98/5.23 = ( X2 = one_one_rat ) ) ).
% 4.98/5.23
% 4.98/5.23 % one_reorient
% 4.98/5.23 thf(fact_989_one__reorient,axiom,
% 4.98/5.23 ! [X2: nat] :
% 4.98/5.23 ( ( one_one_nat = X2 )
% 4.98/5.23 = ( X2 = one_one_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % one_reorient
% 4.98/5.23 thf(fact_990_one__reorient,axiom,
% 4.98/5.23 ! [X2: int] :
% 4.98/5.23 ( ( one_one_int = X2 )
% 4.98/5.23 = ( X2 = one_one_int ) ) ).
% 4.98/5.23
% 4.98/5.23 % one_reorient
% 4.98/5.23 thf(fact_991_add__right__imp__eq,axiom,
% 4.98/5.23 ! [B: real,A: real,C: real] :
% 4.98/5.23 ( ( ( plus_plus_real @ B @ A )
% 4.98/5.23 = ( plus_plus_real @ C @ A ) )
% 4.98/5.23 => ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_right_imp_eq
% 4.98/5.23 thf(fact_992_add__right__imp__eq,axiom,
% 4.98/5.23 ! [B: rat,A: rat,C: rat] :
% 4.98/5.23 ( ( ( plus_plus_rat @ B @ A )
% 4.98/5.23 = ( plus_plus_rat @ C @ A ) )
% 4.98/5.23 => ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_right_imp_eq
% 4.98/5.23 thf(fact_993_add__right__imp__eq,axiom,
% 4.98/5.23 ! [B: nat,A: nat,C: nat] :
% 4.98/5.23 ( ( ( plus_plus_nat @ B @ A )
% 4.98/5.23 = ( plus_plus_nat @ C @ A ) )
% 4.98/5.23 => ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_right_imp_eq
% 4.98/5.23 thf(fact_994_add__right__imp__eq,axiom,
% 4.98/5.23 ! [B: int,A: int,C: int] :
% 4.98/5.23 ( ( ( plus_plus_int @ B @ A )
% 4.98/5.23 = ( plus_plus_int @ C @ A ) )
% 4.98/5.23 => ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_right_imp_eq
% 4.98/5.23 thf(fact_995_add__left__imp__eq,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( ( plus_plus_real @ A @ B )
% 4.98/5.23 = ( plus_plus_real @ A @ C ) )
% 4.98/5.23 => ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_left_imp_eq
% 4.98/5.23 thf(fact_996_add__left__imp__eq,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( ( plus_plus_rat @ A @ B )
% 4.98/5.23 = ( plus_plus_rat @ A @ C ) )
% 4.98/5.23 => ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_left_imp_eq
% 4.98/5.23 thf(fact_997_add__left__imp__eq,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( ( plus_plus_nat @ A @ B )
% 4.98/5.23 = ( plus_plus_nat @ A @ C ) )
% 4.98/5.23 => ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_left_imp_eq
% 4.98/5.23 thf(fact_998_add__left__imp__eq,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( ( plus_plus_int @ A @ B )
% 4.98/5.23 = ( plus_plus_int @ A @ C ) )
% 4.98/5.23 => ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_left_imp_eq
% 4.98/5.23 thf(fact_999_add_Oleft__commute,axiom,
% 4.98/5.23 ! [B: real,A: real,C: real] :
% 4.98/5.23 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 4.98/5.23 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.left_commute
% 4.98/5.23 thf(fact_1000_add_Oleft__commute,axiom,
% 4.98/5.23 ! [B: rat,A: rat,C: rat] :
% 4.98/5.23 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 4.98/5.23 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.left_commute
% 4.98/5.23 thf(fact_1001_add_Oleft__commute,axiom,
% 4.98/5.23 ! [B: nat,A: nat,C: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 4.98/5.23 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.left_commute
% 4.98/5.23 thf(fact_1002_add_Oleft__commute,axiom,
% 4.98/5.23 ! [B: int,A: int,C: int] :
% 4.98/5.23 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 4.98/5.23 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.left_commute
% 4.98/5.23 thf(fact_1003_add_Ocommute,axiom,
% 4.98/5.23 ( plus_plus_real
% 4.98/5.23 = ( ^ [A5: real,B5: real] : ( plus_plus_real @ B5 @ A5 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.commute
% 4.98/5.23 thf(fact_1004_add_Ocommute,axiom,
% 4.98/5.23 ( plus_plus_rat
% 4.98/5.23 = ( ^ [A5: rat,B5: rat] : ( plus_plus_rat @ B5 @ A5 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.commute
% 4.98/5.23 thf(fact_1005_add_Ocommute,axiom,
% 4.98/5.23 ( plus_plus_nat
% 4.98/5.23 = ( ^ [A5: nat,B5: nat] : ( plus_plus_nat @ B5 @ A5 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.commute
% 4.98/5.23 thf(fact_1006_add_Ocommute,axiom,
% 4.98/5.23 ( plus_plus_int
% 4.98/5.23 = ( ^ [A5: int,B5: int] : ( plus_plus_int @ B5 @ A5 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.commute
% 4.98/5.23 thf(fact_1007_add_Oright__cancel,axiom,
% 4.98/5.23 ! [B: real,A: real,C: real] :
% 4.98/5.23 ( ( ( plus_plus_real @ B @ A )
% 4.98/5.23 = ( plus_plus_real @ C @ A ) )
% 4.98/5.23 = ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.right_cancel
% 4.98/5.23 thf(fact_1008_add_Oright__cancel,axiom,
% 4.98/5.23 ! [B: rat,A: rat,C: rat] :
% 4.98/5.23 ( ( ( plus_plus_rat @ B @ A )
% 4.98/5.23 = ( plus_plus_rat @ C @ A ) )
% 4.98/5.23 = ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.right_cancel
% 4.98/5.23 thf(fact_1009_add_Oright__cancel,axiom,
% 4.98/5.23 ! [B: int,A: int,C: int] :
% 4.98/5.23 ( ( ( plus_plus_int @ B @ A )
% 4.98/5.23 = ( plus_plus_int @ C @ A ) )
% 4.98/5.23 = ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.right_cancel
% 4.98/5.23 thf(fact_1010_add_Oleft__cancel,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( ( plus_plus_real @ A @ B )
% 4.98/5.23 = ( plus_plus_real @ A @ C ) )
% 4.98/5.23 = ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.left_cancel
% 4.98/5.23 thf(fact_1011_add_Oleft__cancel,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( ( plus_plus_rat @ A @ B )
% 4.98/5.23 = ( plus_plus_rat @ A @ C ) )
% 4.98/5.23 = ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.left_cancel
% 4.98/5.23 thf(fact_1012_add_Oleft__cancel,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( ( plus_plus_int @ A @ B )
% 4.98/5.23 = ( plus_plus_int @ A @ C ) )
% 4.98/5.23 = ( B = C ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.left_cancel
% 4.98/5.23 thf(fact_1013_add_Oassoc,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.98/5.23 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.assoc
% 4.98/5.23 thf(fact_1014_add_Oassoc,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.98/5.23 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.assoc
% 4.98/5.23 thf(fact_1015_add_Oassoc,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.23 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.assoc
% 4.98/5.23 thf(fact_1016_add_Oassoc,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.23 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add.assoc
% 4.98/5.23 thf(fact_1017_group__cancel_Oadd2,axiom,
% 4.98/5.23 ! [B4: real,K: real,B: real,A: real] :
% 4.98/5.23 ( ( B4
% 4.98/5.23 = ( plus_plus_real @ K @ B ) )
% 4.98/5.23 => ( ( plus_plus_real @ A @ B4 )
% 4.98/5.23 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % group_cancel.add2
% 4.98/5.23 thf(fact_1018_group__cancel_Oadd2,axiom,
% 4.98/5.23 ! [B4: rat,K: rat,B: rat,A: rat] :
% 4.98/5.23 ( ( B4
% 4.98/5.23 = ( plus_plus_rat @ K @ B ) )
% 4.98/5.23 => ( ( plus_plus_rat @ A @ B4 )
% 4.98/5.23 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % group_cancel.add2
% 4.98/5.23 thf(fact_1019_group__cancel_Oadd2,axiom,
% 4.98/5.23 ! [B4: nat,K: nat,B: nat,A: nat] :
% 4.98/5.23 ( ( B4
% 4.98/5.23 = ( plus_plus_nat @ K @ B ) )
% 4.98/5.23 => ( ( plus_plus_nat @ A @ B4 )
% 4.98/5.23 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % group_cancel.add2
% 4.98/5.23 thf(fact_1020_group__cancel_Oadd2,axiom,
% 4.98/5.23 ! [B4: int,K: int,B: int,A: int] :
% 4.98/5.23 ( ( B4
% 4.98/5.23 = ( plus_plus_int @ K @ B ) )
% 4.98/5.23 => ( ( plus_plus_int @ A @ B4 )
% 4.98/5.23 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % group_cancel.add2
% 4.98/5.23 thf(fact_1021_group__cancel_Oadd1,axiom,
% 4.98/5.23 ! [A3: real,K: real,A: real,B: real] :
% 4.98/5.23 ( ( A3
% 4.98/5.23 = ( plus_plus_real @ K @ A ) )
% 4.98/5.23 => ( ( plus_plus_real @ A3 @ B )
% 4.98/5.23 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % group_cancel.add1
% 4.98/5.23 thf(fact_1022_group__cancel_Oadd1,axiom,
% 4.98/5.23 ! [A3: rat,K: rat,A: rat,B: rat] :
% 4.98/5.23 ( ( A3
% 4.98/5.23 = ( plus_plus_rat @ K @ A ) )
% 4.98/5.23 => ( ( plus_plus_rat @ A3 @ B )
% 4.98/5.23 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % group_cancel.add1
% 4.98/5.23 thf(fact_1023_group__cancel_Oadd1,axiom,
% 4.98/5.23 ! [A3: nat,K: nat,A: nat,B: nat] :
% 4.98/5.23 ( ( A3
% 4.98/5.23 = ( plus_plus_nat @ K @ A ) )
% 4.98/5.23 => ( ( plus_plus_nat @ A3 @ B )
% 4.98/5.23 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % group_cancel.add1
% 4.98/5.23 thf(fact_1024_group__cancel_Oadd1,axiom,
% 4.98/5.23 ! [A3: int,K: int,A: int,B: int] :
% 4.98/5.23 ( ( A3
% 4.98/5.23 = ( plus_plus_int @ K @ A ) )
% 4.98/5.23 => ( ( plus_plus_int @ A3 @ B )
% 4.98/5.23 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % group_cancel.add1
% 4.98/5.23 thf(fact_1025_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ( plus_plus_real @ I3 @ K )
% 4.98/5.23 = ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(4)
% 4.98/5.23 thf(fact_1026_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ( plus_plus_rat @ I3 @ K )
% 4.98/5.23 = ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(4)
% 4.98/5.23 thf(fact_1027_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ( plus_plus_nat @ I3 @ K )
% 4.98/5.23 = ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(4)
% 4.98/5.23 thf(fact_1028_add__mono__thms__linordered__semiring_I4_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ( plus_plus_int @ I3 @ K )
% 4.98/5.23 = ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(4)
% 4.98/5.23 thf(fact_1029_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.98/5.23 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % ab_semigroup_add_class.add_ac(1)
% 4.98/5.23 thf(fact_1030_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.98/5.23 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % ab_semigroup_add_class.add_ac(1)
% 4.98/5.23 thf(fact_1031_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.23 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % ab_semigroup_add_class.add_ac(1)
% 4.98/5.23 thf(fact_1032_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.23 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % ab_semigroup_add_class.add_ac(1)
% 4.98/5.23 thf(fact_1033_n__not__Suc__n,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( N2
% 4.98/5.23 != ( suc @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % n_not_Suc_n
% 4.98/5.23 thf(fact_1034_Suc__inject,axiom,
% 4.98/5.23 ! [X2: nat,Y: nat] :
% 4.98/5.23 ( ( ( suc @ X2 )
% 4.98/5.23 = ( suc @ Y ) )
% 4.98/5.23 => ( X2 = Y ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_inject
% 4.98/5.23 thf(fact_1035_linorder__neqE__nat,axiom,
% 4.98/5.23 ! [X2: nat,Y: nat] :
% 4.98/5.23 ( ( X2 != Y )
% 4.98/5.23 => ( ~ ( ord_less_nat @ X2 @ Y )
% 4.98/5.23 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % linorder_neqE_nat
% 4.98/5.23 thf(fact_1036_infinite__descent,axiom,
% 4.98/5.23 ! [P: nat > $o,N2: nat] :
% 4.98/5.23 ( ! [N: nat] :
% 4.98/5.23 ( ~ ( P @ N )
% 4.98/5.23 => ? [M2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M2 @ N )
% 4.98/5.23 & ~ ( P @ M2 ) ) )
% 4.98/5.23 => ( P @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % infinite_descent
% 4.98/5.23 thf(fact_1037_nat__less__induct,axiom,
% 4.98/5.23 ! [P: nat > $o,N2: nat] :
% 4.98/5.23 ( ! [N: nat] :
% 4.98/5.23 ( ! [M2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M2 @ N )
% 4.98/5.23 => ( P @ M2 ) )
% 4.98/5.23 => ( P @ N ) )
% 4.98/5.23 => ( P @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_less_induct
% 4.98/5.23 thf(fact_1038_less__irrefl__nat,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 4.98/5.23
% 4.98/5.23 % less_irrefl_nat
% 4.98/5.23 thf(fact_1039_less__not__refl3,axiom,
% 4.98/5.23 ! [S2: nat,T2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ S2 @ T2 )
% 4.98/5.23 => ( S2 != T2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_not_refl3
% 4.98/5.23 thf(fact_1040_less__not__refl2,axiom,
% 4.98/5.23 ! [N2: nat,M: nat] :
% 4.98/5.23 ( ( ord_less_nat @ N2 @ M )
% 4.98/5.23 => ( M != N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_not_refl2
% 4.98/5.23 thf(fact_1041_less__not__refl,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 4.98/5.23
% 4.98/5.23 % less_not_refl
% 4.98/5.23 thf(fact_1042_nat__neq__iff,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( M != N2 )
% 4.98/5.23 = ( ( ord_less_nat @ M @ N2 )
% 4.98/5.23 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_neq_iff
% 4.98/5.23 thf(fact_1043_Nat_Oex__has__greatest__nat,axiom,
% 4.98/5.23 ! [P: nat > $o,K: nat,B: nat] :
% 4.98/5.23 ( ( P @ K )
% 4.98/5.23 => ( ! [Y3: nat] :
% 4.98/5.23 ( ( P @ Y3 )
% 4.98/5.23 => ( ord_less_eq_nat @ Y3 @ B ) )
% 4.98/5.23 => ? [X5: nat] :
% 4.98/5.23 ( ( P @ X5 )
% 4.98/5.23 & ! [Y5: nat] :
% 4.98/5.23 ( ( P @ Y5 )
% 4.98/5.23 => ( ord_less_eq_nat @ Y5 @ X5 ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Nat.ex_has_greatest_nat
% 4.98/5.23 thf(fact_1044_nat__le__linear,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_le_linear
% 4.98/5.23 thf(fact_1045_le__antisym,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ M )
% 4.98/5.23 => ( M = N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_antisym
% 4.98/5.23 thf(fact_1046_eq__imp__le,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( M = N2 )
% 4.98/5.23 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % eq_imp_le
% 4.98/5.23 thf(fact_1047_le__trans,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 => ( ( ord_less_eq_nat @ J @ K )
% 4.98/5.23 => ( ord_less_eq_nat @ I3 @ K ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_trans
% 4.98/5.23 thf(fact_1048_le__refl,axiom,
% 4.98/5.23 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 4.98/5.23
% 4.98/5.23 % le_refl
% 4.98/5.23 thf(fact_1049_size__neq__size__imp__neq,axiom,
% 4.98/5.23 ! [X2: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 4.98/5.23 ( ( ( size_s6755466524823107622T_VEBT @ X2 )
% 4.98/5.23 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 4.98/5.23 => ( X2 != Y ) ) ).
% 4.98/5.23
% 4.98/5.23 % size_neq_size_imp_neq
% 4.98/5.23 thf(fact_1050_size__neq__size__imp__neq,axiom,
% 4.98/5.23 ! [X2: list_o,Y: list_o] :
% 4.98/5.23 ( ( ( size_size_list_o @ X2 )
% 4.98/5.23 != ( size_size_list_o @ Y ) )
% 4.98/5.23 => ( X2 != Y ) ) ).
% 4.98/5.23
% 4.98/5.23 % size_neq_size_imp_neq
% 4.98/5.23 thf(fact_1051_size__neq__size__imp__neq,axiom,
% 4.98/5.23 ! [X2: list_nat,Y: list_nat] :
% 4.98/5.23 ( ( ( size_size_list_nat @ X2 )
% 4.98/5.23 != ( size_size_list_nat @ Y ) )
% 4.98/5.23 => ( X2 != Y ) ) ).
% 4.98/5.23
% 4.98/5.23 % size_neq_size_imp_neq
% 4.98/5.23 thf(fact_1052_size__neq__size__imp__neq,axiom,
% 4.98/5.23 ! [X2: list_int,Y: list_int] :
% 4.98/5.23 ( ( ( size_size_list_int @ X2 )
% 4.98/5.23 != ( size_size_list_int @ Y ) )
% 4.98/5.23 => ( X2 != Y ) ) ).
% 4.98/5.23
% 4.98/5.23 % size_neq_size_imp_neq
% 4.98/5.23 thf(fact_1053_size__neq__size__imp__neq,axiom,
% 4.98/5.23 ! [X2: num,Y: num] :
% 4.98/5.23 ( ( ( size_size_num @ X2 )
% 4.98/5.23 != ( size_size_num @ Y ) )
% 4.98/5.23 => ( X2 != Y ) ) ).
% 4.98/5.23
% 4.98/5.23 % size_neq_size_imp_neq
% 4.98/5.23 thf(fact_1054_zero__le,axiom,
% 4.98/5.23 ! [X2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X2 ) ).
% 4.98/5.23
% 4.98/5.23 % zero_le
% 4.98/5.23 thf(fact_1055_zero__less__iff__neq__zero,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.23 = ( N2 != zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_less_iff_neq_zero
% 4.98/5.23 thf(fact_1056_gr__implies__not__zero,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.23 => ( N2 != zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % gr_implies_not_zero
% 4.98/5.23 thf(fact_1057_not__less__zero,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % not_less_zero
% 4.98/5.23 thf(fact_1058_gr__zeroI,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( N2 != zero_zero_nat )
% 4.98/5.23 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % gr_zeroI
% 4.98/5.23 thf(fact_1059_add__le__imp__le__right,axiom,
% 4.98/5.23 ! [A: real,C: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.98/5.23 => ( ord_less_eq_real @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_imp_le_right
% 4.98/5.23 thf(fact_1060_add__le__imp__le__right,axiom,
% 4.98/5.23 ! [A: rat,C: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.23 => ( ord_less_eq_rat @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_imp_le_right
% 4.98/5.23 thf(fact_1061_add__le__imp__le__right,axiom,
% 4.98/5.23 ! [A: nat,C: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.23 => ( ord_less_eq_nat @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_imp_le_right
% 4.98/5.23 thf(fact_1062_add__le__imp__le__right,axiom,
% 4.98/5.23 ! [A: int,C: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.98/5.23 => ( ord_less_eq_int @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_imp_le_right
% 4.98/5.23 thf(fact_1063_add__le__imp__le__left,axiom,
% 4.98/5.23 ! [C: real,A: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.98/5.23 => ( ord_less_eq_real @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_imp_le_left
% 4.98/5.23 thf(fact_1064_add__le__imp__le__left,axiom,
% 4.98/5.23 ! [C: rat,A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.98/5.23 => ( ord_less_eq_rat @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_imp_le_left
% 4.98/5.23 thf(fact_1065_add__le__imp__le__left,axiom,
% 4.98/5.23 ! [C: nat,A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.98/5.23 => ( ord_less_eq_nat @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_imp_le_left
% 4.98/5.23 thf(fact_1066_add__le__imp__le__left,axiom,
% 4.98/5.23 ! [C: int,A: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.98/5.23 => ( ord_less_eq_int @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_imp_le_left
% 4.98/5.23 thf(fact_1067_le__iff__add,axiom,
% 4.98/5.23 ( ord_less_eq_nat
% 4.98/5.23 = ( ^ [A5: nat,B5: nat] :
% 4.98/5.23 ? [C2: nat] :
% 4.98/5.23 ( B5
% 4.98/5.23 = ( plus_plus_nat @ A5 @ C2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_iff_add
% 4.98/5.23 thf(fact_1068_add__right__mono,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_right_mono
% 4.98/5.23 thf(fact_1069_add__right__mono,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_right_mono
% 4.98/5.23 thf(fact_1070_add__right__mono,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_right_mono
% 4.98/5.23 thf(fact_1071_add__right__mono,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_right_mono
% 4.98/5.23 thf(fact_1072_less__eqE,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.23 => ~ ! [C3: nat] :
% 4.98/5.23 ( B
% 4.98/5.23 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_eqE
% 4.98/5.23 thf(fact_1073_add__left__mono,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_left_mono
% 4.98/5.23 thf(fact_1074_add__left__mono,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_left_mono
% 4.98/5.23 thf(fact_1075_add__left__mono,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_left_mono
% 4.98/5.23 thf(fact_1076_add__left__mono,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_left_mono
% 4.98/5.23 thf(fact_1077_add__mono,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.23 => ( ( ord_less_eq_real @ C @ D )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono
% 4.98/5.23 thf(fact_1078_add__mono,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.23 => ( ( ord_less_eq_rat @ C @ D )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono
% 4.98/5.23 thf(fact_1079_add__mono,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.23 => ( ( ord_less_eq_nat @ C @ D )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono
% 4.98/5.23 thf(fact_1080_add__mono,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.23 => ( ( ord_less_eq_int @ C @ D )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono
% 4.98/5.23 thf(fact_1081_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( ord_less_eq_real @ I3 @ J )
% 4.98/5.23 & ( ord_less_eq_real @ K @ L ) )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(1)
% 4.98/5.23 thf(fact_1082_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( ord_less_eq_rat @ I3 @ J )
% 4.98/5.23 & ( ord_less_eq_rat @ K @ L ) )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ I3 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(1)
% 4.98/5.23 thf(fact_1083_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 & ( ord_less_eq_nat @ K @ L ) )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(1)
% 4.98/5.23 thf(fact_1084_add__mono__thms__linordered__semiring_I1_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( ord_less_eq_int @ I3 @ J )
% 4.98/5.23 & ( ord_less_eq_int @ K @ L ) )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(1)
% 4.98/5.23 thf(fact_1085_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( ord_less_eq_real @ K @ L ) )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(2)
% 4.98/5.23 thf(fact_1086_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( ord_less_eq_rat @ K @ L ) )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ I3 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(2)
% 4.98/5.23 thf(fact_1087_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( ord_less_eq_nat @ K @ L ) )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(2)
% 4.98/5.23 thf(fact_1088_add__mono__thms__linordered__semiring_I2_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( ord_less_eq_int @ K @ L ) )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(2)
% 4.98/5.23 thf(fact_1089_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( ord_less_eq_real @ I3 @ J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(3)
% 4.98/5.23 thf(fact_1090_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( ord_less_eq_rat @ I3 @ J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ I3 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(3)
% 4.98/5.23 thf(fact_1091_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(3)
% 4.98/5.23 thf(fact_1092_add__mono__thms__linordered__semiring_I3_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( ord_less_eq_int @ I3 @ J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_semiring(3)
% 4.98/5.23 thf(fact_1093_zero__neq__one,axiom,
% 4.98/5.23 zero_zero_complex != one_one_complex ).
% 4.98/5.23
% 4.98/5.23 % zero_neq_one
% 4.98/5.23 thf(fact_1094_zero__neq__one,axiom,
% 4.98/5.23 zero_zero_real != one_one_real ).
% 4.98/5.23
% 4.98/5.23 % zero_neq_one
% 4.98/5.23 thf(fact_1095_zero__neq__one,axiom,
% 4.98/5.23 zero_zero_rat != one_one_rat ).
% 4.98/5.23
% 4.98/5.23 % zero_neq_one
% 4.98/5.23 thf(fact_1096_zero__neq__one,axiom,
% 4.98/5.23 zero_zero_nat != one_one_nat ).
% 4.98/5.23
% 4.98/5.23 % zero_neq_one
% 4.98/5.23 thf(fact_1097_zero__neq__one,axiom,
% 4.98/5.23 zero_zero_int != one_one_int ).
% 4.98/5.23
% 4.98/5.23 % zero_neq_one
% 4.98/5.23 thf(fact_1098_add_Ogroup__left__neutral,axiom,
% 4.98/5.23 ! [A: complex] :
% 4.98/5.23 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.group_left_neutral
% 4.98/5.23 thf(fact_1099_add_Ogroup__left__neutral,axiom,
% 4.98/5.23 ! [A: real] :
% 4.98/5.23 ( ( plus_plus_real @ zero_zero_real @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.group_left_neutral
% 4.98/5.23 thf(fact_1100_add_Ogroup__left__neutral,axiom,
% 4.98/5.23 ! [A: rat] :
% 4.98/5.23 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.group_left_neutral
% 4.98/5.23 thf(fact_1101_add_Ogroup__left__neutral,axiom,
% 4.98/5.23 ! [A: int] :
% 4.98/5.23 ( ( plus_plus_int @ zero_zero_int @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.group_left_neutral
% 4.98/5.23 thf(fact_1102_add_Ocomm__neutral,axiom,
% 4.98/5.23 ! [A: complex] :
% 4.98/5.23 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.comm_neutral
% 4.98/5.23 thf(fact_1103_add_Ocomm__neutral,axiom,
% 4.98/5.23 ! [A: real] :
% 4.98/5.23 ( ( plus_plus_real @ A @ zero_zero_real )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.comm_neutral
% 4.98/5.23 thf(fact_1104_add_Ocomm__neutral,axiom,
% 4.98/5.23 ! [A: rat] :
% 4.98/5.23 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.comm_neutral
% 4.98/5.23 thf(fact_1105_add_Ocomm__neutral,axiom,
% 4.98/5.23 ! [A: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.comm_neutral
% 4.98/5.23 thf(fact_1106_add_Ocomm__neutral,axiom,
% 4.98/5.23 ! [A: int] :
% 4.98/5.23 ( ( plus_plus_int @ A @ zero_zero_int )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % add.comm_neutral
% 4.98/5.23 thf(fact_1107_comm__monoid__add__class_Oadd__0,axiom,
% 4.98/5.23 ! [A: complex] :
% 4.98/5.23 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % comm_monoid_add_class.add_0
% 4.98/5.23 thf(fact_1108_comm__monoid__add__class_Oadd__0,axiom,
% 4.98/5.23 ! [A: real] :
% 4.98/5.23 ( ( plus_plus_real @ zero_zero_real @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % comm_monoid_add_class.add_0
% 4.98/5.23 thf(fact_1109_comm__monoid__add__class_Oadd__0,axiom,
% 4.98/5.23 ! [A: rat] :
% 4.98/5.23 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % comm_monoid_add_class.add_0
% 4.98/5.23 thf(fact_1110_comm__monoid__add__class_Oadd__0,axiom,
% 4.98/5.23 ! [A: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % comm_monoid_add_class.add_0
% 4.98/5.23 thf(fact_1111_comm__monoid__add__class_Oadd__0,axiom,
% 4.98/5.23 ! [A: int] :
% 4.98/5.23 ( ( plus_plus_int @ zero_zero_int @ A )
% 4.98/5.23 = A ) ).
% 4.98/5.23
% 4.98/5.23 % comm_monoid_add_class.add_0
% 4.98/5.23 thf(fact_1112_add__less__imp__less__right,axiom,
% 4.98/5.23 ! [A: real,C: real,B: real] :
% 4.98/5.23 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.98/5.23 => ( ord_less_real @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_imp_less_right
% 4.98/5.23 thf(fact_1113_add__less__imp__less__right,axiom,
% 4.98/5.23 ! [A: rat,C: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.23 => ( ord_less_rat @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_imp_less_right
% 4.98/5.23 thf(fact_1114_add__less__imp__less__right,axiom,
% 4.98/5.23 ! [A: nat,C: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.23 => ( ord_less_nat @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_imp_less_right
% 4.98/5.23 thf(fact_1115_add__less__imp__less__right,axiom,
% 4.98/5.23 ! [A: int,C: int,B: int] :
% 4.98/5.23 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.98/5.23 => ( ord_less_int @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_imp_less_right
% 4.98/5.23 thf(fact_1116_add__less__imp__less__left,axiom,
% 4.98/5.23 ! [C: real,A: real,B: real] :
% 4.98/5.23 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.98/5.23 => ( ord_less_real @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_imp_less_left
% 4.98/5.23 thf(fact_1117_add__less__imp__less__left,axiom,
% 4.98/5.23 ! [C: rat,A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.98/5.23 => ( ord_less_rat @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_imp_less_left
% 4.98/5.23 thf(fact_1118_add__less__imp__less__left,axiom,
% 4.98/5.23 ! [C: nat,A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.98/5.23 => ( ord_less_nat @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_imp_less_left
% 4.98/5.23 thf(fact_1119_add__less__imp__less__left,axiom,
% 4.98/5.23 ! [C: int,A: int,B: int] :
% 4.98/5.23 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.98/5.23 => ( ord_less_int @ A @ B ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_imp_less_left
% 4.98/5.23 thf(fact_1120_add__strict__right__mono,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( ord_less_real @ A @ B )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_right_mono
% 4.98/5.23 thf(fact_1121_add__strict__right__mono,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( ord_less_rat @ A @ B )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_right_mono
% 4.98/5.23 thf(fact_1122_add__strict__right__mono,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ B )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_right_mono
% 4.98/5.23 thf(fact_1123_add__strict__right__mono,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( ord_less_int @ A @ B )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_right_mono
% 4.98/5.23 thf(fact_1124_add__strict__left__mono,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( ord_less_real @ A @ B )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_left_mono
% 4.98/5.23 thf(fact_1125_add__strict__left__mono,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( ord_less_rat @ A @ B )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_left_mono
% 4.98/5.23 thf(fact_1126_add__strict__left__mono,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ B )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_left_mono
% 4.98/5.23 thf(fact_1127_add__strict__left__mono,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( ord_less_int @ A @ B )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_left_mono
% 4.98/5.23 thf(fact_1128_add__strict__mono,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.23 ( ( ord_less_real @ A @ B )
% 4.98/5.23 => ( ( ord_less_real @ C @ D )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_mono
% 4.98/5.23 thf(fact_1129_add__strict__mono,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.23 ( ( ord_less_rat @ A @ B )
% 4.98/5.23 => ( ( ord_less_rat @ C @ D )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_mono
% 4.98/5.23 thf(fact_1130_add__strict__mono,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ B )
% 4.98/5.23 => ( ( ord_less_nat @ C @ D )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_mono
% 4.98/5.23 thf(fact_1131_add__strict__mono,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.23 ( ( ord_less_int @ A @ B )
% 4.98/5.23 => ( ( ord_less_int @ C @ D )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_strict_mono
% 4.98/5.23 thf(fact_1132_add__mono__thms__linordered__field_I1_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( ord_less_real @ I3 @ J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(1)
% 4.98/5.23 thf(fact_1133_add__mono__thms__linordered__field_I1_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( ord_less_rat @ I3 @ J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ I3 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(1)
% 4.98/5.23 thf(fact_1134_add__mono__thms__linordered__field_I1_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(1)
% 4.98/5.23 thf(fact_1135_add__mono__thms__linordered__field_I1_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( ord_less_int @ I3 @ J )
% 4.98/5.23 & ( K = L ) )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(1)
% 4.98/5.23 thf(fact_1136_add__mono__thms__linordered__field_I2_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( ord_less_real @ K @ L ) )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(2)
% 4.98/5.23 thf(fact_1137_add__mono__thms__linordered__field_I2_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( ord_less_rat @ K @ L ) )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ I3 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(2)
% 4.98/5.23 thf(fact_1138_add__mono__thms__linordered__field_I2_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( ord_less_nat @ K @ L ) )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(2)
% 4.98/5.23 thf(fact_1139_add__mono__thms__linordered__field_I2_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( I3 = J )
% 4.98/5.23 & ( ord_less_int @ K @ L ) )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(2)
% 4.98/5.23 thf(fact_1140_add__mono__thms__linordered__field_I5_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( ord_less_real @ I3 @ J )
% 4.98/5.23 & ( ord_less_real @ K @ L ) )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(5)
% 4.98/5.23 thf(fact_1141_add__mono__thms__linordered__field_I5_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( ord_less_rat @ I3 @ J )
% 4.98/5.23 & ( ord_less_rat @ K @ L ) )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ I3 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(5)
% 4.98/5.23 thf(fact_1142_add__mono__thms__linordered__field_I5_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 & ( ord_less_nat @ K @ L ) )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(5)
% 4.98/5.23 thf(fact_1143_add__mono__thms__linordered__field_I5_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( ord_less_int @ I3 @ J )
% 4.98/5.23 & ( ord_less_int @ K @ L ) )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(5)
% 4.98/5.23 thf(fact_1144_not0__implies__Suc,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( N2 != zero_zero_nat )
% 4.98/5.23 => ? [M3: nat] :
% 4.98/5.23 ( N2
% 4.98/5.23 = ( suc @ M3 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % not0_implies_Suc
% 4.98/5.23 thf(fact_1145_Zero__not__Suc,axiom,
% 4.98/5.23 ! [M: nat] :
% 4.98/5.23 ( zero_zero_nat
% 4.98/5.23 != ( suc @ M ) ) ).
% 4.98/5.23
% 4.98/5.23 % Zero_not_Suc
% 4.98/5.23 thf(fact_1146_Zero__neq__Suc,axiom,
% 4.98/5.23 ! [M: nat] :
% 4.98/5.23 ( zero_zero_nat
% 4.98/5.23 != ( suc @ M ) ) ).
% 4.98/5.23
% 4.98/5.23 % Zero_neq_Suc
% 4.98/5.23 thf(fact_1147_Suc__neq__Zero,axiom,
% 4.98/5.23 ! [M: nat] :
% 4.98/5.23 ( ( suc @ M )
% 4.98/5.23 != zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_neq_Zero
% 4.98/5.23 thf(fact_1148_zero__induct,axiom,
% 4.98/5.23 ! [P: nat > $o,K: nat] :
% 4.98/5.23 ( ( P @ K )
% 4.98/5.23 => ( ! [N: nat] :
% 4.98/5.23 ( ( P @ ( suc @ N ) )
% 4.98/5.23 => ( P @ N ) )
% 4.98/5.23 => ( P @ zero_zero_nat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % zero_induct
% 4.98/5.23 thf(fact_1149_diff__induct,axiom,
% 4.98/5.23 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 4.98/5.23 ( ! [X5: nat] : ( P @ X5 @ zero_zero_nat )
% 4.98/5.23 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 4.98/5.23 => ( ! [X5: nat,Y3: nat] :
% 4.98/5.23 ( ( P @ X5 @ Y3 )
% 4.98/5.23 => ( P @ ( suc @ X5 ) @ ( suc @ Y3 ) ) )
% 4.98/5.23 => ( P @ M @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % diff_induct
% 4.98/5.23 thf(fact_1150_nat__induct,axiom,
% 4.98/5.23 ! [P: nat > $o,N2: nat] :
% 4.98/5.23 ( ( P @ zero_zero_nat )
% 4.98/5.23 => ( ! [N: nat] :
% 4.98/5.23 ( ( P @ N )
% 4.98/5.23 => ( P @ ( suc @ N ) ) )
% 4.98/5.23 => ( P @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_induct
% 4.98/5.23 thf(fact_1151_old_Onat_Oexhaust,axiom,
% 4.98/5.23 ! [Y: nat] :
% 4.98/5.23 ( ( Y != zero_zero_nat )
% 4.98/5.23 => ~ ! [Nat3: nat] :
% 4.98/5.23 ( Y
% 4.98/5.23 != ( suc @ Nat3 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % old.nat.exhaust
% 4.98/5.23 thf(fact_1152_nat_OdiscI,axiom,
% 4.98/5.23 ! [Nat: nat,X22: nat] :
% 4.98/5.23 ( ( Nat
% 4.98/5.23 = ( suc @ X22 ) )
% 4.98/5.23 => ( Nat != zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat.discI
% 4.98/5.23 thf(fact_1153_old_Onat_Odistinct_I1_J,axiom,
% 4.98/5.23 ! [Nat2: nat] :
% 4.98/5.23 ( zero_zero_nat
% 4.98/5.23 != ( suc @ Nat2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % old.nat.distinct(1)
% 4.98/5.23 thf(fact_1154_old_Onat_Odistinct_I2_J,axiom,
% 4.98/5.23 ! [Nat2: nat] :
% 4.98/5.23 ( ( suc @ Nat2 )
% 4.98/5.23 != zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % old.nat.distinct(2)
% 4.98/5.23 thf(fact_1155_nat_Odistinct_I1_J,axiom,
% 4.98/5.23 ! [X22: nat] :
% 4.98/5.23 ( zero_zero_nat
% 4.98/5.23 != ( suc @ X22 ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat.distinct(1)
% 4.98/5.23 thf(fact_1156_not__less__less__Suc__eq,axiom,
% 4.98/5.23 ! [N2: nat,M: nat] :
% 4.98/5.23 ( ~ ( ord_less_nat @ N2 @ M )
% 4.98/5.23 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 4.98/5.23 = ( N2 = M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % not_less_less_Suc_eq
% 4.98/5.23 thf(fact_1157_strict__inc__induct,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,P: nat > $o] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 => ( ! [I2: nat] :
% 4.98/5.23 ( ( J
% 4.98/5.23 = ( suc @ I2 ) )
% 4.98/5.23 => ( P @ I2 ) )
% 4.98/5.23 => ( ! [I2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I2 @ J )
% 4.98/5.23 => ( ( P @ ( suc @ I2 ) )
% 4.98/5.23 => ( P @ I2 ) ) )
% 4.98/5.23 => ( P @ I3 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % strict_inc_induct
% 4.98/5.23 thf(fact_1158_less__Suc__induct,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,P: nat > nat > $o] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 4.98/5.23 => ( ! [I2: nat,J2: nat,K2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I2 @ J2 )
% 4.98/5.23 => ( ( ord_less_nat @ J2 @ K2 )
% 4.98/5.23 => ( ( P @ I2 @ J2 )
% 4.98/5.23 => ( ( P @ J2 @ K2 )
% 4.98/5.23 => ( P @ I2 @ K2 ) ) ) ) )
% 4.98/5.23 => ( P @ I3 @ J ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_Suc_induct
% 4.98/5.23 thf(fact_1159_less__trans__Suc,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 => ( ( ord_less_nat @ J @ K )
% 4.98/5.23 => ( ord_less_nat @ ( suc @ I3 ) @ K ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_trans_Suc
% 4.98/5.23 thf(fact_1160_Suc__less__SucD,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 4.98/5.23 => ( ord_less_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_less_SucD
% 4.98/5.23 thf(fact_1161_less__antisym,axiom,
% 4.98/5.23 ! [N2: nat,M: nat] :
% 4.98/5.23 ( ~ ( ord_less_nat @ N2 @ M )
% 4.98/5.23 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 4.98/5.23 => ( M = N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_antisym
% 4.98/5.23 thf(fact_1162_Suc__less__eq2,axiom,
% 4.98/5.23 ! [N2: nat,M: nat] :
% 4.98/5.23 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 4.98/5.23 = ( ? [M4: nat] :
% 4.98/5.23 ( ( M
% 4.98/5.23 = ( suc @ M4 ) )
% 4.98/5.23 & ( ord_less_nat @ N2 @ M4 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_less_eq2
% 4.98/5.23 thf(fact_1163_All__less__Suc,axiom,
% 4.98/5.23 ! [N2: nat,P: nat > $o] :
% 4.98/5.23 ( ( ! [I5: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 4.98/5.23 => ( P @ I5 ) ) )
% 4.98/5.23 = ( ( P @ N2 )
% 4.98/5.23 & ! [I5: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I5 @ N2 )
% 4.98/5.23 => ( P @ I5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % All_less_Suc
% 4.98/5.23 thf(fact_1164_not__less__eq,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 4.98/5.23 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % not_less_eq
% 4.98/5.23 thf(fact_1165_less__Suc__eq,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 4.98/5.23 = ( ( ord_less_nat @ M @ N2 )
% 4.98/5.23 | ( M = N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_Suc_eq
% 4.98/5.23 thf(fact_1166_Ex__less__Suc,axiom,
% 4.98/5.23 ! [N2: nat,P: nat > $o] :
% 4.98/5.23 ( ( ? [I5: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 4.98/5.23 & ( P @ I5 ) ) )
% 4.98/5.23 = ( ( P @ N2 )
% 4.98/5.23 | ? [I5: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I5 @ N2 )
% 4.98/5.23 & ( P @ I5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Ex_less_Suc
% 4.98/5.23 thf(fact_1167_less__SucI,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.23 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_SucI
% 4.98/5.23 thf(fact_1168_less__SucE,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 4.98/5.23 => ( ~ ( ord_less_nat @ M @ N2 )
% 4.98/5.23 => ( M = N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_SucE
% 4.98/5.23 thf(fact_1169_Suc__lessI,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.23 => ( ( ( suc @ M )
% 4.98/5.23 != N2 )
% 4.98/5.23 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_lessI
% 4.98/5.23 thf(fact_1170_Suc__lessE,axiom,
% 4.98/5.23 ! [I3: nat,K: nat] :
% 4.98/5.23 ( ( ord_less_nat @ ( suc @ I3 ) @ K )
% 4.98/5.23 => ~ ! [J2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J2 )
% 4.98/5.23 => ( K
% 4.98/5.23 != ( suc @ J2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_lessE
% 4.98/5.23 thf(fact_1171_Suc__lessD,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 4.98/5.23 => ( ord_less_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_lessD
% 4.98/5.23 thf(fact_1172_Nat_OlessE,axiom,
% 4.98/5.23 ! [I3: nat,K: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ K )
% 4.98/5.23 => ( ( K
% 4.98/5.23 != ( suc @ I3 ) )
% 4.98/5.23 => ~ ! [J2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J2 )
% 4.98/5.23 => ( K
% 4.98/5.23 != ( suc @ J2 ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Nat.lessE
% 4.98/5.23 thf(fact_1173_infinite__descent0,axiom,
% 4.98/5.23 ! [P: nat > $o,N2: nat] :
% 4.98/5.23 ( ( P @ zero_zero_nat )
% 4.98/5.23 => ( ! [N: nat] :
% 4.98/5.23 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.98/5.23 => ( ~ ( P @ N )
% 4.98/5.23 => ? [M2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M2 @ N )
% 4.98/5.23 & ~ ( P @ M2 ) ) ) )
% 4.98/5.23 => ( P @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % infinite_descent0
% 4.98/5.23 thf(fact_1174_gr__implies__not0,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.23 => ( N2 != zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % gr_implies_not0
% 4.98/5.23 thf(fact_1175_less__zeroE,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % less_zeroE
% 4.98/5.23 thf(fact_1176_not__less0,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % not_less0
% 4.98/5.23 thf(fact_1177_not__gr0,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 4.98/5.23 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % not_gr0
% 4.98/5.23 thf(fact_1178_gr0I,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( N2 != zero_zero_nat )
% 4.98/5.23 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % gr0I
% 4.98/5.23 thf(fact_1179_bot__nat__0_Oextremum__strict,axiom,
% 4.98/5.23 ! [A: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % bot_nat_0.extremum_strict
% 4.98/5.23 thf(fact_1180_transitive__stepwise__le,axiom,
% 4.98/5.23 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 4.98/5.23 => ( ! [X5: nat,Y3: nat,Z3: nat] :
% 4.98/5.23 ( ( R @ X5 @ Y3 )
% 4.98/5.23 => ( ( R @ Y3 @ Z3 )
% 4.98/5.23 => ( R @ X5 @ Z3 ) ) )
% 4.98/5.23 => ( ! [N: nat] : ( R @ N @ ( suc @ N ) )
% 4.98/5.23 => ( R @ M @ N2 ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % transitive_stepwise_le
% 4.98/5.23 thf(fact_1181_nat__induct__at__least,axiom,
% 4.98/5.23 ! [M: nat,N2: nat,P: nat > $o] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ( ( P @ M )
% 4.98/5.23 => ( ! [N: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N )
% 4.98/5.23 => ( ( P @ N )
% 4.98/5.23 => ( P @ ( suc @ N ) ) ) )
% 4.98/5.23 => ( P @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_induct_at_least
% 4.98/5.23 thf(fact_1182_full__nat__induct,axiom,
% 4.98/5.23 ! [P: nat > $o,N2: nat] :
% 4.98/5.23 ( ! [N: nat] :
% 4.98/5.23 ( ! [M2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 4.98/5.23 => ( P @ M2 ) )
% 4.98/5.23 => ( P @ N ) )
% 4.98/5.23 => ( P @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % full_nat_induct
% 4.98/5.23 thf(fact_1183_not__less__eq__eq,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 4.98/5.23 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 4.98/5.23
% 4.98/5.23 % not_less_eq_eq
% 4.98/5.23 thf(fact_1184_Suc__n__not__le__n,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_n_not_le_n
% 4.98/5.23 thf(fact_1185_le__Suc__eq,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 4.98/5.23 = ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 | ( M
% 4.98/5.23 = ( suc @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_Suc_eq
% 4.98/5.23 thf(fact_1186_Suc__le__D,axiom,
% 4.98/5.23 ! [N2: nat,M5: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M5 )
% 4.98/5.23 => ? [M3: nat] :
% 4.98/5.23 ( M5
% 4.98/5.23 = ( suc @ M3 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_le_D
% 4.98/5.23 thf(fact_1187_le__SucI,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_SucI
% 4.98/5.23 thf(fact_1188_le__SucE,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 4.98/5.23 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ( M
% 4.98/5.23 = ( suc @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_SucE
% 4.98/5.23 thf(fact_1189_Suc__leD,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 4.98/5.23 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_leD
% 4.98/5.23 thf(fact_1190_le__0__eq,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 4.98/5.23 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_0_eq
% 4.98/5.23 thf(fact_1191_bot__nat__0_Oextremum__uniqueI,axiom,
% 4.98/5.23 ! [A: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.98/5.23 => ( A = zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % bot_nat_0.extremum_uniqueI
% 4.98/5.23 thf(fact_1192_bot__nat__0_Oextremum__unique,axiom,
% 4.98/5.23 ! [A: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.98/5.23 = ( A = zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % bot_nat_0.extremum_unique
% 4.98/5.23 thf(fact_1193_less__eq__nat_Osimps_I1_J,axiom,
% 4.98/5.23 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 4.98/5.23
% 4.98/5.23 % less_eq_nat.simps(1)
% 4.98/5.23 thf(fact_1194_add__Suc__shift,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 4.98/5.23 = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_Suc_shift
% 4.98/5.23 thf(fact_1195_add__Suc,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 4.98/5.23 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_Suc
% 4.98/5.23 thf(fact_1196_nat__arith_Osuc1,axiom,
% 4.98/5.23 ! [A3: nat,K: nat,A: nat] :
% 4.98/5.23 ( ( A3
% 4.98/5.23 = ( plus_plus_nat @ K @ A ) )
% 4.98/5.23 => ( ( suc @ A3 )
% 4.98/5.23 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_arith.suc1
% 4.98/5.23 thf(fact_1197_less__mono__imp__le__mono,axiom,
% 4.98/5.23 ! [F: nat > nat,I3: nat,J: nat] :
% 4.98/5.23 ( ! [I2: nat,J2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I2 @ J2 )
% 4.98/5.23 => ( ord_less_nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( F @ J ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_mono_imp_le_mono
% 4.98/5.23 thf(fact_1198_le__neq__implies__less,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ( ( M != N2 )
% 4.98/5.23 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_neq_implies_less
% 4.98/5.23 thf(fact_1199_less__or__eq__imp__le,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ( ord_less_nat @ M @ N2 )
% 4.98/5.23 | ( M = N2 ) )
% 4.98/5.23 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_or_eq_imp_le
% 4.98/5.23 thf(fact_1200_le__eq__less__or__eq,axiom,
% 4.98/5.23 ( ord_less_eq_nat
% 4.98/5.23 = ( ^ [M6: nat,N3: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M6 @ N3 )
% 4.98/5.23 | ( M6 = N3 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_eq_less_or_eq
% 4.98/5.23 thf(fact_1201_less__imp__le__nat,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.23 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_imp_le_nat
% 4.98/5.23 thf(fact_1202_nat__less__le,axiom,
% 4.98/5.23 ( ord_less_nat
% 4.98/5.23 = ( ^ [M6: nat,N3: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M6 @ N3 )
% 4.98/5.23 & ( M6 != N3 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_less_le
% 4.98/5.23 thf(fact_1203_add__eq__self__zero,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ( plus_plus_nat @ M @ N2 )
% 4.98/5.23 = M )
% 4.98/5.23 => ( N2 = zero_zero_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_eq_self_zero
% 4.98/5.23 thf(fact_1204_plus__nat_Oadd__0,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 4.98/5.23 = N2 ) ).
% 4.98/5.23
% 4.98/5.23 % plus_nat.add_0
% 4.98/5.23 thf(fact_1205_less__add__eq__less,axiom,
% 4.98/5.23 ! [K: nat,L: nat,M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ K @ L )
% 4.98/5.23 => ( ( ( plus_plus_nat @ M @ L )
% 4.98/5.23 = ( plus_plus_nat @ K @ N2 ) )
% 4.98/5.23 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_eq_less
% 4.98/5.23 thf(fact_1206_trans__less__add2,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,M: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 => ( ord_less_nat @ I3 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % trans_less_add2
% 4.98/5.23 thf(fact_1207_trans__less__add1,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,M: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 => ( ord_less_nat @ I3 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % trans_less_add1
% 4.98/5.23 thf(fact_1208_add__less__mono1,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_mono1
% 4.98/5.23 thf(fact_1209_not__add__less2,axiom,
% 4.98/5.23 ! [J: nat,I3: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I3 ) @ I3 ) ).
% 4.98/5.23
% 4.98/5.23 % not_add_less2
% 4.98/5.23 thf(fact_1210_not__add__less1,axiom,
% 4.98/5.23 ! [I3: nat,J: nat] :
% 4.98/5.23 ~ ( ord_less_nat @ ( plus_plus_nat @ I3 @ J ) @ I3 ) ).
% 4.98/5.23
% 4.98/5.23 % not_add_less1
% 4.98/5.23 thf(fact_1211_add__less__mono,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 => ( ( ord_less_nat @ K @ L )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_mono
% 4.98/5.23 thf(fact_1212_add__lessD1,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.23 ( ( ord_less_nat @ ( plus_plus_nat @ I3 @ J ) @ K )
% 4.98/5.23 => ( ord_less_nat @ I3 @ K ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_lessD1
% 4.98/5.23 thf(fact_1213_nat__le__iff__add,axiom,
% 4.98/5.23 ( ord_less_eq_nat
% 4.98/5.23 = ( ^ [M6: nat,N3: nat] :
% 4.98/5.23 ? [K3: nat] :
% 4.98/5.23 ( N3
% 4.98/5.23 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_le_iff_add
% 4.98/5.23 thf(fact_1214_trans__le__add2,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,M: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 => ( ord_less_eq_nat @ I3 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % trans_le_add2
% 4.98/5.23 thf(fact_1215_trans__le__add1,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,M: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 => ( ord_less_eq_nat @ I3 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % trans_le_add1
% 4.98/5.23 thf(fact_1216_add__le__mono1,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_mono1
% 4.98/5.23 thf(fact_1217_add__le__mono,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 => ( ( ord_less_eq_nat @ K @ L )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_mono
% 4.98/5.23 thf(fact_1218_le__Suc__ex,axiom,
% 4.98/5.23 ! [K: nat,L: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ K @ L )
% 4.98/5.23 => ? [N: nat] :
% 4.98/5.23 ( L
% 4.98/5.23 = ( plus_plus_nat @ K @ N ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_Suc_ex
% 4.98/5.23 thf(fact_1219_add__leD2,axiom,
% 4.98/5.23 ! [M: nat,K: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 4.98/5.23 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_leD2
% 4.98/5.23 thf(fact_1220_add__leD1,axiom,
% 4.98/5.23 ! [M: nat,K: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 4.98/5.23 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_leD1
% 4.98/5.23 thf(fact_1221_le__add2,axiom,
% 4.98/5.23 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add2
% 4.98/5.23 thf(fact_1222_le__add1,axiom,
% 4.98/5.23 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_add1
% 4.98/5.23 thf(fact_1223_add__leE,axiom,
% 4.98/5.23 ! [M: nat,K: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 4.98/5.23 => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_leE
% 4.98/5.23 thf(fact_1224_max__add__distrib__right,axiom,
% 4.98/5.23 ! [X2: real,Y: real,Z: real] :
% 4.98/5.23 ( ( plus_plus_real @ X2 @ ( ord_max_real @ Y @ Z ) )
% 4.98/5.23 = ( ord_max_real @ ( plus_plus_real @ X2 @ Y ) @ ( plus_plus_real @ X2 @ Z ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_add_distrib_right
% 4.98/5.23 thf(fact_1225_max__add__distrib__right,axiom,
% 4.98/5.23 ! [X2: rat,Y: rat,Z: rat] :
% 4.98/5.23 ( ( plus_plus_rat @ X2 @ ( ord_max_rat @ Y @ Z ) )
% 4.98/5.23 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( plus_plus_rat @ X2 @ Z ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_add_distrib_right
% 4.98/5.23 thf(fact_1226_max__add__distrib__right,axiom,
% 4.98/5.23 ! [X2: nat,Y: nat,Z: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ X2 @ ( ord_max_nat @ Y @ Z ) )
% 4.98/5.23 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Y ) @ ( plus_plus_nat @ X2 @ Z ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_add_distrib_right
% 4.98/5.23 thf(fact_1227_max__add__distrib__right,axiom,
% 4.98/5.23 ! [X2: int,Y: int,Z: int] :
% 4.98/5.23 ( ( plus_plus_int @ X2 @ ( ord_max_int @ Y @ Z ) )
% 4.98/5.23 = ( ord_max_int @ ( plus_plus_int @ X2 @ Y ) @ ( plus_plus_int @ X2 @ Z ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_add_distrib_right
% 4.98/5.23 thf(fact_1228_max__add__distrib__left,axiom,
% 4.98/5.23 ! [X2: real,Y: real,Z: real] :
% 4.98/5.23 ( ( plus_plus_real @ ( ord_max_real @ X2 @ Y ) @ Z )
% 4.98/5.23 = ( ord_max_real @ ( plus_plus_real @ X2 @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_add_distrib_left
% 4.98/5.23 thf(fact_1229_max__add__distrib__left,axiom,
% 4.98/5.23 ! [X2: rat,Y: rat,Z: rat] :
% 4.98/5.23 ( ( plus_plus_rat @ ( ord_max_rat @ X2 @ Y ) @ Z )
% 4.98/5.23 = ( ord_max_rat @ ( plus_plus_rat @ X2 @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_add_distrib_left
% 4.98/5.23 thf(fact_1230_max__add__distrib__left,axiom,
% 4.98/5.23 ! [X2: nat,Y: nat,Z: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ ( ord_max_nat @ X2 @ Y ) @ Z )
% 4.98/5.23 = ( ord_max_nat @ ( plus_plus_nat @ X2 @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_add_distrib_left
% 4.98/5.23 thf(fact_1231_max__add__distrib__left,axiom,
% 4.98/5.23 ! [X2: int,Y: int,Z: int] :
% 4.98/5.23 ( ( plus_plus_int @ ( ord_max_int @ X2 @ Y ) @ Z )
% 4.98/5.23 = ( ord_max_int @ ( plus_plus_int @ X2 @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % max_add_distrib_left
% 4.98/5.23 thf(fact_1232_nat__add__max__right,axiom,
% 4.98/5.23 ! [M: nat,N2: nat,Q2: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 4.98/5.23 = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_add_max_right
% 4.98/5.23 thf(fact_1233_nat__add__max__left,axiom,
% 4.98/5.23 ! [M: nat,N2: nat,Q2: nat] :
% 4.98/5.23 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 4.98/5.23 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N2 @ Q2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % nat_add_max_left
% 4.98/5.23 thf(fact_1234_not__one__le__zero,axiom,
% 4.98/5.23 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 4.98/5.23
% 4.98/5.23 % not_one_le_zero
% 4.98/5.23 thf(fact_1235_not__one__le__zero,axiom,
% 4.98/5.23 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 4.98/5.23
% 4.98/5.23 % not_one_le_zero
% 4.98/5.23 thf(fact_1236_not__one__le__zero,axiom,
% 4.98/5.23 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % not_one_le_zero
% 4.98/5.23 thf(fact_1237_not__one__le__zero,axiom,
% 4.98/5.23 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 4.98/5.23
% 4.98/5.23 % not_one_le_zero
% 4.98/5.23 thf(fact_1238_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.98/5.23 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 4.98/5.23
% 4.98/5.23 % linordered_nonzero_semiring_class.zero_le_one
% 4.98/5.23 thf(fact_1239_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.98/5.23 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 4.98/5.23
% 4.98/5.23 % linordered_nonzero_semiring_class.zero_le_one
% 4.98/5.23 thf(fact_1240_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.98/5.23 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 4.98/5.23
% 4.98/5.23 % linordered_nonzero_semiring_class.zero_le_one
% 4.98/5.23 thf(fact_1241_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 4.98/5.23 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 4.98/5.23
% 4.98/5.23 % linordered_nonzero_semiring_class.zero_le_one
% 4.98/5.23 thf(fact_1242_zero__less__one__class_Ozero__le__one,axiom,
% 4.98/5.23 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 4.98/5.23
% 4.98/5.23 % zero_less_one_class.zero_le_one
% 4.98/5.23 thf(fact_1243_zero__less__one__class_Ozero__le__one,axiom,
% 4.98/5.23 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 4.98/5.23
% 4.98/5.23 % zero_less_one_class.zero_le_one
% 4.98/5.23 thf(fact_1244_zero__less__one__class_Ozero__le__one,axiom,
% 4.98/5.23 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 4.98/5.23
% 4.98/5.23 % zero_less_one_class.zero_le_one
% 4.98/5.23 thf(fact_1245_zero__less__one__class_Ozero__le__one,axiom,
% 4.98/5.23 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 4.98/5.23
% 4.98/5.23 % zero_less_one_class.zero_le_one
% 4.98/5.23 thf(fact_1246_add__nonpos__eq__0__iff,axiom,
% 4.98/5.23 ! [X2: real,Y: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 4.98/5.23 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 4.98/5.23 => ( ( ( plus_plus_real @ X2 @ Y )
% 4.98/5.23 = zero_zero_real )
% 4.98/5.23 = ( ( X2 = zero_zero_real )
% 4.98/5.23 & ( Y = zero_zero_real ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonpos_eq_0_iff
% 4.98/5.23 thf(fact_1247_add__nonpos__eq__0__iff,axiom,
% 4.98/5.23 ! [X2: rat,Y: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 4.98/5.23 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 4.98/5.23 => ( ( ( plus_plus_rat @ X2 @ Y )
% 4.98/5.23 = zero_zero_rat )
% 4.98/5.23 = ( ( X2 = zero_zero_rat )
% 4.98/5.23 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonpos_eq_0_iff
% 4.98/5.23 thf(fact_1248_add__nonpos__eq__0__iff,axiom,
% 4.98/5.23 ! [X2: nat,Y: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ X2 @ zero_zero_nat )
% 4.98/5.23 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 4.98/5.23 => ( ( ( plus_plus_nat @ X2 @ Y )
% 4.98/5.23 = zero_zero_nat )
% 4.98/5.23 = ( ( X2 = zero_zero_nat )
% 4.98/5.23 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonpos_eq_0_iff
% 4.98/5.23 thf(fact_1249_add__nonpos__eq__0__iff,axiom,
% 4.98/5.23 ! [X2: int,Y: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 4.98/5.23 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 4.98/5.23 => ( ( ( plus_plus_int @ X2 @ Y )
% 4.98/5.23 = zero_zero_int )
% 4.98/5.23 = ( ( X2 = zero_zero_int )
% 4.98/5.23 & ( Y = zero_zero_int ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonpos_eq_0_iff
% 4.98/5.23 thf(fact_1250_add__nonneg__eq__0__iff,axiom,
% 4.98/5.23 ! [X2: real,Y: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.23 => ( ( ( plus_plus_real @ X2 @ Y )
% 4.98/5.23 = zero_zero_real )
% 4.98/5.23 = ( ( X2 = zero_zero_real )
% 4.98/5.23 & ( Y = zero_zero_real ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonneg_eq_0_iff
% 4.98/5.23 thf(fact_1251_add__nonneg__eq__0__iff,axiom,
% 4.98/5.23 ! [X2: rat,Y: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.23 => ( ( ( plus_plus_rat @ X2 @ Y )
% 4.98/5.23 = zero_zero_rat )
% 4.98/5.23 = ( ( X2 = zero_zero_rat )
% 4.98/5.23 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonneg_eq_0_iff
% 4.98/5.23 thf(fact_1252_add__nonneg__eq__0__iff,axiom,
% 4.98/5.23 ! [X2: nat,Y: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 4.98/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 4.98/5.23 => ( ( ( plus_plus_nat @ X2 @ Y )
% 4.98/5.23 = zero_zero_nat )
% 4.98/5.23 = ( ( X2 = zero_zero_nat )
% 4.98/5.23 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonneg_eq_0_iff
% 4.98/5.23 thf(fact_1253_add__nonneg__eq__0__iff,axiom,
% 4.98/5.23 ! [X2: int,Y: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 4.98/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.98/5.23 => ( ( ( plus_plus_int @ X2 @ Y )
% 4.98/5.23 = zero_zero_int )
% 4.98/5.23 = ( ( X2 = zero_zero_int )
% 4.98/5.23 & ( Y = zero_zero_int ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonneg_eq_0_iff
% 4.98/5.23 thf(fact_1254_add__nonpos__nonpos,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.23 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonpos_nonpos
% 4.98/5.23 thf(fact_1255_add__nonpos__nonpos,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.23 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonpos_nonpos
% 4.98/5.23 thf(fact_1256_add__nonpos__nonpos,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.98/5.23 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonpos_nonpos
% 4.98/5.23 thf(fact_1257_add__nonpos__nonpos,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.23 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonpos_nonpos
% 4.98/5.23 thf(fact_1258_add__nonneg__nonneg,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.23 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.23 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonneg_nonneg
% 4.98/5.23 thf(fact_1259_add__nonneg__nonneg,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.23 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.23 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonneg_nonneg
% 4.98/5.23 thf(fact_1260_add__nonneg__nonneg,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.23 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.23 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonneg_nonneg
% 4.98/5.23 thf(fact_1261_add__nonneg__nonneg,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.23 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.23 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_nonneg_nonneg
% 4.98/5.23 thf(fact_1262_add__increasing2,axiom,
% 4.98/5.23 ! [C: real,B: real,A: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.23 => ( ( ord_less_eq_real @ B @ A )
% 4.98/5.23 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_increasing2
% 4.98/5.23 thf(fact_1263_add__increasing2,axiom,
% 4.98/5.23 ! [C: rat,B: rat,A: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.23 => ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.23 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_increasing2
% 4.98/5.23 thf(fact_1264_add__increasing2,axiom,
% 4.98/5.23 ! [C: nat,B: nat,A: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.23 => ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.23 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_increasing2
% 4.98/5.23 thf(fact_1265_add__increasing2,axiom,
% 4.98/5.23 ! [C: int,B: int,A: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.23 => ( ( ord_less_eq_int @ B @ A )
% 4.98/5.23 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_increasing2
% 4.98/5.23 thf(fact_1266_add__decreasing2,axiom,
% 4.98/5.23 ! [C: real,A: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.23 => ( ( ord_less_eq_real @ A @ B )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_decreasing2
% 4.98/5.23 thf(fact_1267_add__decreasing2,axiom,
% 4.98/5.23 ! [C: rat,A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.23 => ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_decreasing2
% 4.98/5.23 thf(fact_1268_add__decreasing2,axiom,
% 4.98/5.23 ! [C: nat,A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 4.98/5.23 => ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_decreasing2
% 4.98/5.23 thf(fact_1269_add__decreasing2,axiom,
% 4.98/5.23 ! [C: int,A: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.23 => ( ( ord_less_eq_int @ A @ B )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_decreasing2
% 4.98/5.23 thf(fact_1270_add__increasing,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.23 => ( ( ord_less_eq_real @ B @ C )
% 4.98/5.23 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_increasing
% 4.98/5.23 thf(fact_1271_add__increasing,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.23 => ( ( ord_less_eq_rat @ B @ C )
% 4.98/5.23 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_increasing
% 4.98/5.23 thf(fact_1272_add__increasing,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.23 => ( ( ord_less_eq_nat @ B @ C )
% 4.98/5.23 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_increasing
% 4.98/5.23 thf(fact_1273_add__increasing,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.23 => ( ( ord_less_eq_int @ B @ C )
% 4.98/5.23 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_increasing
% 4.98/5.23 thf(fact_1274_add__decreasing,axiom,
% 4.98/5.23 ! [A: real,C: real,B: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.23 => ( ( ord_less_eq_real @ C @ B )
% 4.98/5.23 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_decreasing
% 4.98/5.23 thf(fact_1275_add__decreasing,axiom,
% 4.98/5.23 ! [A: rat,C: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.23 => ( ( ord_less_eq_rat @ C @ B )
% 4.98/5.23 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_decreasing
% 4.98/5.23 thf(fact_1276_add__decreasing,axiom,
% 4.98/5.23 ! [A: nat,C: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.98/5.23 => ( ( ord_less_eq_nat @ C @ B )
% 4.98/5.23 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_decreasing
% 4.98/5.23 thf(fact_1277_add__decreasing,axiom,
% 4.98/5.23 ! [A: int,C: int,B: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.23 => ( ( ord_less_eq_int @ C @ B )
% 4.98/5.23 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_decreasing
% 4.98/5.23 thf(fact_1278_add__less__le__mono,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.23 ( ( ord_less_real @ A @ B )
% 4.98/5.23 => ( ( ord_less_eq_real @ C @ D )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_le_mono
% 4.98/5.23 thf(fact_1279_add__less__le__mono,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.23 ( ( ord_less_rat @ A @ B )
% 4.98/5.23 => ( ( ord_less_eq_rat @ C @ D )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_le_mono
% 4.98/5.23 thf(fact_1280_add__less__le__mono,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ B )
% 4.98/5.23 => ( ( ord_less_eq_nat @ C @ D )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_le_mono
% 4.98/5.23 thf(fact_1281_add__less__le__mono,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.23 ( ( ord_less_int @ A @ B )
% 4.98/5.23 => ( ( ord_less_eq_int @ C @ D )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_le_mono
% 4.98/5.23 thf(fact_1282_add__le__less__mono,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.23 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.23 => ( ( ord_less_real @ C @ D )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_less_mono
% 4.98/5.23 thf(fact_1283_add__le__less__mono,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.23 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.23 => ( ( ord_less_rat @ C @ D )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_less_mono
% 4.98/5.23 thf(fact_1284_add__le__less__mono,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.23 => ( ( ord_less_nat @ C @ D )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_less_mono
% 4.98/5.23 thf(fact_1285_add__le__less__mono,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.23 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.23 => ( ( ord_less_int @ C @ D )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_le_less_mono
% 4.98/5.23 thf(fact_1286_add__mono__thms__linordered__field_I3_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( ord_less_real @ I3 @ J )
% 4.98/5.23 & ( ord_less_eq_real @ K @ L ) )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(3)
% 4.98/5.23 thf(fact_1287_add__mono__thms__linordered__field_I3_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( ord_less_rat @ I3 @ J )
% 4.98/5.23 & ( ord_less_eq_rat @ K @ L ) )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ I3 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(3)
% 4.98/5.23 thf(fact_1288_add__mono__thms__linordered__field_I3_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( ord_less_nat @ I3 @ J )
% 4.98/5.23 & ( ord_less_eq_nat @ K @ L ) )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(3)
% 4.98/5.23 thf(fact_1289_add__mono__thms__linordered__field_I3_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( ord_less_int @ I3 @ J )
% 4.98/5.23 & ( ord_less_eq_int @ K @ L ) )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(3)
% 4.98/5.23 thf(fact_1290_add__mono__thms__linordered__field_I4_J,axiom,
% 4.98/5.23 ! [I3: real,J: real,K: real,L: real] :
% 4.98/5.23 ( ( ( ord_less_eq_real @ I3 @ J )
% 4.98/5.23 & ( ord_less_real @ K @ L ) )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ I3 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(4)
% 4.98/5.23 thf(fact_1291_add__mono__thms__linordered__field_I4_J,axiom,
% 4.98/5.23 ! [I3: rat,J: rat,K: rat,L: rat] :
% 4.98/5.23 ( ( ( ord_less_eq_rat @ I3 @ J )
% 4.98/5.23 & ( ord_less_rat @ K @ L ) )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ I3 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(4)
% 4.98/5.23 thf(fact_1292_add__mono__thms__linordered__field_I4_J,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.23 ( ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 & ( ord_less_nat @ K @ L ) )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(4)
% 4.98/5.23 thf(fact_1293_add__mono__thms__linordered__field_I4_J,axiom,
% 4.98/5.23 ! [I3: int,J: int,K: int,L: int] :
% 4.98/5.23 ( ( ( ord_less_eq_int @ I3 @ J )
% 4.98/5.23 & ( ord_less_int @ K @ L ) )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ I3 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono_thms_linordered_field(4)
% 4.98/5.23 thf(fact_1294_not__one__less__zero,axiom,
% 4.98/5.23 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 4.98/5.23
% 4.98/5.23 % not_one_less_zero
% 4.98/5.23 thf(fact_1295_not__one__less__zero,axiom,
% 4.98/5.23 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 4.98/5.23
% 4.98/5.23 % not_one_less_zero
% 4.98/5.23 thf(fact_1296_not__one__less__zero,axiom,
% 4.98/5.23 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 4.98/5.23
% 4.98/5.23 % not_one_less_zero
% 4.98/5.23 thf(fact_1297_not__one__less__zero,axiom,
% 4.98/5.23 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 4.98/5.23
% 4.98/5.23 % not_one_less_zero
% 4.98/5.23 thf(fact_1298_zero__less__one,axiom,
% 4.98/5.23 ord_less_real @ zero_zero_real @ one_one_real ).
% 4.98/5.23
% 4.98/5.23 % zero_less_one
% 4.98/5.23 thf(fact_1299_zero__less__one,axiom,
% 4.98/5.23 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 4.98/5.23
% 4.98/5.23 % zero_less_one
% 4.98/5.23 thf(fact_1300_zero__less__one,axiom,
% 4.98/5.23 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 4.98/5.23
% 4.98/5.23 % zero_less_one
% 4.98/5.23 thf(fact_1301_zero__less__one,axiom,
% 4.98/5.23 ord_less_int @ zero_zero_int @ one_one_int ).
% 4.98/5.23
% 4.98/5.23 % zero_less_one
% 4.98/5.23 thf(fact_1302_pos__add__strict,axiom,
% 4.98/5.23 ! [A: real,B: real,C: real] :
% 4.98/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.23 => ( ( ord_less_real @ B @ C )
% 4.98/5.23 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % pos_add_strict
% 4.98/5.23 thf(fact_1303_pos__add__strict,axiom,
% 4.98/5.23 ! [A: rat,B: rat,C: rat] :
% 4.98/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.23 => ( ( ord_less_rat @ B @ C )
% 4.98/5.23 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % pos_add_strict
% 4.98/5.23 thf(fact_1304_pos__add__strict,axiom,
% 4.98/5.23 ! [A: nat,B: nat,C: nat] :
% 4.98/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.23 => ( ( ord_less_nat @ B @ C )
% 4.98/5.23 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % pos_add_strict
% 4.98/5.23 thf(fact_1305_pos__add__strict,axiom,
% 4.98/5.23 ! [A: int,B: int,C: int] :
% 4.98/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.23 => ( ( ord_less_int @ B @ C )
% 4.98/5.23 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % pos_add_strict
% 4.98/5.23 thf(fact_1306_canonically__ordered__monoid__add__class_OlessE,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ B )
% 4.98/5.23 => ~ ! [C3: nat] :
% 4.98/5.23 ( ( B
% 4.98/5.23 = ( plus_plus_nat @ A @ C3 ) )
% 4.98/5.23 => ( C3 = zero_zero_nat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % canonically_ordered_monoid_add_class.lessE
% 4.98/5.23 thf(fact_1307_add__pos__pos,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.23 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.98/5.23 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_pos_pos
% 4.98/5.23 thf(fact_1308_add__pos__pos,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.23 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.98/5.23 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_pos_pos
% 4.98/5.23 thf(fact_1309_add__pos__pos,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.23 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.23 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_pos_pos
% 4.98/5.23 thf(fact_1310_add__pos__pos,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.23 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.23 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_pos_pos
% 4.98/5.23 thf(fact_1311_add__neg__neg,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.23 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_neg_neg
% 4.98/5.23 thf(fact_1312_add__neg__neg,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.23 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_neg_neg
% 4.98/5.23 thf(fact_1313_add__neg__neg,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ zero_zero_nat )
% 4.98/5.23 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_neg_neg
% 4.98/5.23 thf(fact_1314_add__neg__neg,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.23 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_neg_neg
% 4.98/5.23 thf(fact_1315_add__less__zeroD,axiom,
% 4.98/5.23 ! [X2: real,Y: real] :
% 4.98/5.23 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y ) @ zero_zero_real )
% 4.98/5.23 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 4.98/5.23 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_zeroD
% 4.98/5.23 thf(fact_1316_add__less__zeroD,axiom,
% 4.98/5.23 ! [X2: rat,Y: rat] :
% 4.98/5.23 ( ( ord_less_rat @ ( plus_plus_rat @ X2 @ Y ) @ zero_zero_rat )
% 4.98/5.23 => ( ( ord_less_rat @ X2 @ zero_zero_rat )
% 4.98/5.23 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_zeroD
% 4.98/5.23 thf(fact_1317_add__less__zeroD,axiom,
% 4.98/5.23 ! [X2: int,Y: int] :
% 4.98/5.23 ( ( ord_less_int @ ( plus_plus_int @ X2 @ Y ) @ zero_zero_int )
% 4.98/5.23 => ( ( ord_less_int @ X2 @ zero_zero_int )
% 4.98/5.23 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_less_zeroD
% 4.98/5.23 thf(fact_1318_add__mono1,axiom,
% 4.98/5.23 ! [A: real,B: real] :
% 4.98/5.23 ( ( ord_less_real @ A @ B )
% 4.98/5.23 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono1
% 4.98/5.23 thf(fact_1319_add__mono1,axiom,
% 4.98/5.23 ! [A: rat,B: rat] :
% 4.98/5.23 ( ( ord_less_rat @ A @ B )
% 4.98/5.23 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono1
% 4.98/5.23 thf(fact_1320_add__mono1,axiom,
% 4.98/5.23 ! [A: nat,B: nat] :
% 4.98/5.23 ( ( ord_less_nat @ A @ B )
% 4.98/5.23 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono1
% 4.98/5.23 thf(fact_1321_add__mono1,axiom,
% 4.98/5.23 ! [A: int,B: int] :
% 4.98/5.23 ( ( ord_less_int @ A @ B )
% 4.98/5.23 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % add_mono1
% 4.98/5.23 thf(fact_1322_less__add__one,axiom,
% 4.98/5.23 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_one
% 4.98/5.23 thf(fact_1323_less__add__one,axiom,
% 4.98/5.23 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_one
% 4.98/5.23 thf(fact_1324_less__add__one,axiom,
% 4.98/5.23 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_one
% 4.98/5.23 thf(fact_1325_less__add__one,axiom,
% 4.98/5.23 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_add_one
% 4.98/5.23 thf(fact_1326_lift__Suc__mono__less__iff,axiom,
% 4.98/5.23 ! [F: nat > real,N2: nat,M: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 4.98/5.23 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less_iff
% 4.98/5.23 thf(fact_1327_lift__Suc__mono__less__iff,axiom,
% 4.98/5.23 ! [F: nat > rat,N2: nat,M: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 4.98/5.23 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less_iff
% 4.98/5.23 thf(fact_1328_lift__Suc__mono__less__iff,axiom,
% 4.98/5.23 ! [F: nat > num,N2: nat,M: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_num @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 4.98/5.23 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less_iff
% 4.98/5.23 thf(fact_1329_lift__Suc__mono__less__iff,axiom,
% 4.98/5.23 ! [F: nat > nat,N2: nat,M: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 4.98/5.23 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less_iff
% 4.98/5.23 thf(fact_1330_lift__Suc__mono__less__iff,axiom,
% 4.98/5.23 ! [F: nat > int,N2: nat,M: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 4.98/5.23 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less_iff
% 4.98/5.23 thf(fact_1331_lift__Suc__mono__less,axiom,
% 4.98/5.23 ! [F: nat > real,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_real @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less
% 4.98/5.23 thf(fact_1332_lift__Suc__mono__less,axiom,
% 4.98/5.23 ! [F: nat > rat,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less
% 4.98/5.23 thf(fact_1333_lift__Suc__mono__less,axiom,
% 4.98/5.23 ! [F: nat > num,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_num @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less
% 4.98/5.23 thf(fact_1334_lift__Suc__mono__less,axiom,
% 4.98/5.23 ! [F: nat > nat,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less
% 4.98/5.23 thf(fact_1335_lift__Suc__mono__less,axiom,
% 4.98/5.23 ! [F: nat > int,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_less
% 4.98/5.23 thf(fact_1336_lift__Suc__antimono__le,axiom,
% 4.98/5.23 ! [F: nat > set_nat,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_set_nat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_antimono_le
% 4.98/5.23 thf(fact_1337_lift__Suc__antimono__le,axiom,
% 4.98/5.23 ! [F: nat > rat,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_antimono_le
% 4.98/5.23 thf(fact_1338_lift__Suc__antimono__le,axiom,
% 4.98/5.23 ! [F: nat > num,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_antimono_le
% 4.98/5.23 thf(fact_1339_lift__Suc__antimono__le,axiom,
% 4.98/5.23 ! [F: nat > nat,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_antimono_le
% 4.98/5.23 thf(fact_1340_lift__Suc__antimono__le,axiom,
% 4.98/5.23 ! [F: nat > int,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_antimono_le
% 4.98/5.23 thf(fact_1341_lift__Suc__mono__le,axiom,
% 4.98/5.23 ! [F: nat > set_nat,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_set_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_le
% 4.98/5.23 thf(fact_1342_lift__Suc__mono__le,axiom,
% 4.98/5.23 ! [F: nat > rat,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_le
% 4.98/5.23 thf(fact_1343_lift__Suc__mono__le,axiom,
% 4.98/5.23 ! [F: nat > num,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_num @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_le
% 4.98/5.23 thf(fact_1344_lift__Suc__mono__le,axiom,
% 4.98/5.23 ! [F: nat > nat,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_le
% 4.98/5.23 thf(fact_1345_lift__Suc__mono__le,axiom,
% 4.98/5.23 ! [F: nat > int,N2: nat,N5: nat] :
% 4.98/5.23 ( ! [N: nat] : ( ord_less_eq_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 4.98/5.23 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 4.98/5.23 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % lift_Suc_mono_le
% 4.98/5.23 thf(fact_1346_less__Suc__eq__0__disj,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 4.98/5.23 = ( ( M = zero_zero_nat )
% 4.98/5.23 | ? [J3: nat] :
% 4.98/5.23 ( ( M
% 4.98/5.23 = ( suc @ J3 ) )
% 4.98/5.23 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_Suc_eq_0_disj
% 4.98/5.23 thf(fact_1347_gr0__implies__Suc,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.23 => ? [M3: nat] :
% 4.98/5.23 ( N2
% 4.98/5.23 = ( suc @ M3 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % gr0_implies_Suc
% 4.98/5.23 thf(fact_1348_All__less__Suc2,axiom,
% 4.98/5.23 ! [N2: nat,P: nat > $o] :
% 4.98/5.23 ( ( ! [I5: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 4.98/5.23 => ( P @ I5 ) ) )
% 4.98/5.23 = ( ( P @ zero_zero_nat )
% 4.98/5.23 & ! [I5: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I5 @ N2 )
% 4.98/5.23 => ( P @ ( suc @ I5 ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % All_less_Suc2
% 4.98/5.23 thf(fact_1349_gr0__conv__Suc,axiom,
% 4.98/5.23 ! [N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.23 = ( ? [M6: nat] :
% 4.98/5.23 ( N2
% 4.98/5.23 = ( suc @ M6 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % gr0_conv_Suc
% 4.98/5.23 thf(fact_1350_Ex__less__Suc2,axiom,
% 4.98/5.23 ! [N2: nat,P: nat > $o] :
% 4.98/5.23 ( ( ? [I5: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I5 @ ( suc @ N2 ) )
% 4.98/5.23 & ( P @ I5 ) ) )
% 4.98/5.23 = ( ( P @ zero_zero_nat )
% 4.98/5.23 | ? [I5: nat] :
% 4.98/5.23 ( ( ord_less_nat @ I5 @ N2 )
% 4.98/5.23 & ( P @ ( suc @ I5 ) ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % Ex_less_Suc2
% 4.98/5.23 thf(fact_1351_le__imp__less__Suc,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_imp_less_Suc
% 4.98/5.23 thf(fact_1352_less__eq__Suc__le,axiom,
% 4.98/5.23 ( ord_less_nat
% 4.98/5.23 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_eq_Suc_le
% 4.98/5.23 thf(fact_1353_less__Suc__eq__le,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 4.98/5.23 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % less_Suc_eq_le
% 4.98/5.23 thf(fact_1354_le__less__Suc__eq,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.23 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 4.98/5.23 = ( N2 = M ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % le_less_Suc_eq
% 4.98/5.23 thf(fact_1355_Suc__le__lessD,axiom,
% 4.98/5.23 ! [M: nat,N2: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 4.98/5.23 => ( ord_less_nat @ M @ N2 ) ) ).
% 4.98/5.23
% 4.98/5.23 % Suc_le_lessD
% 4.98/5.23 thf(fact_1356_inc__induct,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,P: nat > $o] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 => ( ( P @ J )
% 4.98/5.23 => ( ! [N: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ N )
% 4.98/5.23 => ( ( ord_less_nat @ N @ J )
% 4.98/5.23 => ( ( P @ ( suc @ N ) )
% 4.98/5.23 => ( P @ N ) ) ) )
% 4.98/5.23 => ( P @ I3 ) ) ) ) ).
% 4.98/5.23
% 4.98/5.23 % inc_induct
% 4.98/5.23 thf(fact_1357_dec__induct,axiom,
% 4.98/5.23 ! [I3: nat,J: nat,P: nat > $o] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.23 => ( ( P @ I3 )
% 4.98/5.23 => ( ! [N: nat] :
% 4.98/5.23 ( ( ord_less_eq_nat @ I3 @ N )
% 4.98/5.23 => ( ( ord_less_nat @ N @ J )
% 4.98/5.23 => ( ( P @ N )
% 4.98/5.23 => ( P @ ( suc @ N ) ) ) ) )
% 4.98/5.24 => ( P @ J ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % dec_induct
% 4.98/5.24 thf(fact_1358_Suc__le__eq,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 4.98/5.24 = ( ord_less_nat @ M @ N2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % Suc_le_eq
% 4.98/5.24 thf(fact_1359_Suc__leI,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.24 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % Suc_leI
% 4.98/5.24 thf(fact_1360_one__is__add,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ( suc @ zero_zero_nat )
% 4.98/5.24 = ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.24 = ( ( ( M
% 4.98/5.24 = ( suc @ zero_zero_nat ) )
% 4.98/5.24 & ( N2 = zero_zero_nat ) )
% 4.98/5.24 | ( ( M = zero_zero_nat )
% 4.98/5.24 & ( N2
% 4.98/5.24 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % one_is_add
% 4.98/5.24 thf(fact_1361_add__is__1,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ( plus_plus_nat @ M @ N2 )
% 4.98/5.24 = ( suc @ zero_zero_nat ) )
% 4.98/5.24 = ( ( ( M
% 4.98/5.24 = ( suc @ zero_zero_nat ) )
% 4.98/5.24 & ( N2 = zero_zero_nat ) )
% 4.98/5.24 | ( ( M = zero_zero_nat )
% 4.98/5.24 & ( N2
% 4.98/5.24 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_is_1
% 4.98/5.24 thf(fact_1362_ex__least__nat__le,axiom,
% 4.98/5.24 ! [P: nat > $o,N2: nat] :
% 4.98/5.24 ( ( P @ N2 )
% 4.98/5.24 => ( ~ ( P @ zero_zero_nat )
% 4.98/5.24 => ? [K2: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ K2 @ N2 )
% 4.98/5.24 & ! [I: nat] :
% 4.98/5.24 ( ( ord_less_nat @ I @ K2 )
% 4.98/5.24 => ~ ( P @ I ) )
% 4.98/5.24 & ( P @ K2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ex_least_nat_le
% 4.98/5.24 thf(fact_1363_less__imp__Suc__add,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.24 => ? [K2: nat] :
% 4.98/5.24 ( N2
% 4.98/5.24 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % less_imp_Suc_add
% 4.98/5.24 thf(fact_1364_less__iff__Suc__add,axiom,
% 4.98/5.24 ( ord_less_nat
% 4.98/5.24 = ( ^ [M6: nat,N3: nat] :
% 4.98/5.24 ? [K3: nat] :
% 4.98/5.24 ( N3
% 4.98/5.24 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % less_iff_Suc_add
% 4.98/5.24 thf(fact_1365_less__add__Suc2,axiom,
% 4.98/5.24 ! [I3: nat,M: nat] : ( ord_less_nat @ I3 @ ( suc @ ( plus_plus_nat @ M @ I3 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % less_add_Suc2
% 4.98/5.24 thf(fact_1366_less__add__Suc1,axiom,
% 4.98/5.24 ! [I3: nat,M: nat] : ( ord_less_nat @ I3 @ ( suc @ ( plus_plus_nat @ I3 @ M ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % less_add_Suc1
% 4.98/5.24 thf(fact_1367_less__natE,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.24 => ~ ! [Q3: nat] :
% 4.98/5.24 ( N2
% 4.98/5.24 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % less_natE
% 4.98/5.24 thf(fact_1368_less__imp__add__positive,axiom,
% 4.98/5.24 ! [I3: nat,J: nat] :
% 4.98/5.24 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.24 => ? [K2: nat] :
% 4.98/5.24 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 4.98/5.24 & ( ( plus_plus_nat @ I3 @ K2 )
% 4.98/5.24 = J ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % less_imp_add_positive
% 4.98/5.24 thf(fact_1369_mono__nat__linear__lb,axiom,
% 4.98/5.24 ! [F: nat > nat,M: nat,K: nat] :
% 4.98/5.24 ( ! [M3: nat,N: nat] :
% 4.98/5.24 ( ( ord_less_nat @ M3 @ N )
% 4.98/5.24 => ( ord_less_nat @ ( F @ M3 ) @ ( F @ N ) ) )
% 4.98/5.24 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mono_nat_linear_lb
% 4.98/5.24 thf(fact_1370_One__nat__def,axiom,
% 4.98/5.24 ( one_one_nat
% 4.98/5.24 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.24
% 4.98/5.24 % One_nat_def
% 4.98/5.24 thf(fact_1371_Suc__eq__plus1__left,axiom,
% 4.98/5.24 ( suc
% 4.98/5.24 = ( plus_plus_nat @ one_one_nat ) ) ).
% 4.98/5.24
% 4.98/5.24 % Suc_eq_plus1_left
% 4.98/5.24 thf(fact_1372_plus__1__eq__Suc,axiom,
% 4.98/5.24 ( ( plus_plus_nat @ one_one_nat )
% 4.98/5.24 = suc ) ).
% 4.98/5.24
% 4.98/5.24 % plus_1_eq_Suc
% 4.98/5.24 thf(fact_1373_Suc__eq__plus1,axiom,
% 4.98/5.24 ( suc
% 4.98/5.24 = ( ^ [N3: nat] : ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % Suc_eq_plus1
% 4.98/5.24 thf(fact_1374_add__strict__increasing2,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.24 => ( ( ord_less_real @ B @ C )
% 4.98/5.24 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_strict_increasing2
% 4.98/5.24 thf(fact_1375_add__strict__increasing2,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.24 => ( ( ord_less_rat @ B @ C )
% 4.98/5.24 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_strict_increasing2
% 4.98/5.24 thf(fact_1376_add__strict__increasing2,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.24 => ( ( ord_less_nat @ B @ C )
% 4.98/5.24 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_strict_increasing2
% 4.98/5.24 thf(fact_1377_add__strict__increasing2,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.24 => ( ( ord_less_int @ B @ C )
% 4.98/5.24 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_strict_increasing2
% 4.98/5.24 thf(fact_1378_add__strict__increasing,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.24 => ( ( ord_less_eq_real @ B @ C )
% 4.98/5.24 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_strict_increasing
% 4.98/5.24 thf(fact_1379_add__strict__increasing,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.24 => ( ( ord_less_eq_rat @ B @ C )
% 4.98/5.24 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_strict_increasing
% 4.98/5.24 thf(fact_1380_add__strict__increasing,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.24 => ( ( ord_less_eq_nat @ B @ C )
% 4.98/5.24 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_strict_increasing
% 4.98/5.24 thf(fact_1381_add__strict__increasing,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.24 => ( ( ord_less_eq_int @ B @ C )
% 4.98/5.24 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_strict_increasing
% 4.98/5.24 thf(fact_1382_add__pos__nonneg,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.24 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_pos_nonneg
% 4.98/5.24 thf(fact_1383_add__pos__nonneg,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.24 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_pos_nonneg
% 4.98/5.24 thf(fact_1384_add__pos__nonneg,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.24 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_pos_nonneg
% 4.98/5.24 thf(fact_1385_add__pos__nonneg,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.24 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_pos_nonneg
% 4.98/5.24 thf(fact_1386_add__nonpos__neg,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.24 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.98/5.24 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_nonpos_neg
% 4.98/5.24 thf(fact_1387_add__nonpos__neg,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.24 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.98/5.24 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_nonpos_neg
% 4.98/5.24 thf(fact_1388_add__nonpos__neg,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.98/5.24 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.98/5.24 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_nonpos_neg
% 4.98/5.24 thf(fact_1389_add__nonpos__neg,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.24 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.24 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_nonpos_neg
% 4.98/5.24 thf(fact_1390_add__nonneg__pos,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.24 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.98/5.24 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_nonneg_pos
% 4.98/5.24 thf(fact_1391_add__nonneg__pos,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.24 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.98/5.24 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_nonneg_pos
% 4.98/5.24 thf(fact_1392_add__nonneg__pos,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.24 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.24 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_nonneg_pos
% 4.98/5.24 thf(fact_1393_add__nonneg__pos,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.24 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.24 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_nonneg_pos
% 4.98/5.24 thf(fact_1394_add__neg__nonpos,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.24 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.98/5.24 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_neg_nonpos
% 4.98/5.24 thf(fact_1395_add__neg__nonpos,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.24 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.98/5.24 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_neg_nonpos
% 4.98/5.24 thf(fact_1396_add__neg__nonpos,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ord_less_nat @ A @ zero_zero_nat )
% 4.98/5.24 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.98/5.24 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_neg_nonpos
% 4.98/5.24 thf(fact_1397_add__neg__nonpos,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.24 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.98/5.24 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_neg_nonpos
% 4.98/5.24 thf(fact_1398_zero__less__two,axiom,
% 4.98/5.24 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 4.98/5.24
% 4.98/5.24 % zero_less_two
% 4.98/5.24 thf(fact_1399_zero__less__two,axiom,
% 4.98/5.24 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 4.98/5.24
% 4.98/5.24 % zero_less_two
% 4.98/5.24 thf(fact_1400_zero__less__two,axiom,
% 4.98/5.24 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 4.98/5.24
% 4.98/5.24 % zero_less_two
% 4.98/5.24 thf(fact_1401_zero__less__two,axiom,
% 4.98/5.24 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 4.98/5.24
% 4.98/5.24 % zero_less_two
% 4.98/5.24 thf(fact_1402_ex__least__nat__less,axiom,
% 4.98/5.24 ! [P: nat > $o,N2: nat] :
% 4.98/5.24 ( ( P @ N2 )
% 4.98/5.24 => ( ~ ( P @ zero_zero_nat )
% 4.98/5.24 => ? [K2: nat] :
% 4.98/5.24 ( ( ord_less_nat @ K2 @ N2 )
% 4.98/5.24 & ! [I: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ I @ K2 )
% 4.98/5.24 => ~ ( P @ I ) )
% 4.98/5.24 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ex_least_nat_less
% 4.98/5.24 thf(fact_1403_nat__induct__non__zero,axiom,
% 4.98/5.24 ! [N2: nat,P: nat > $o] :
% 4.98/5.24 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.24 => ( ( P @ one_one_nat )
% 4.98/5.24 => ( ! [N: nat] :
% 4.98/5.24 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.98/5.24 => ( ( P @ N )
% 4.98/5.24 => ( P @ ( suc @ N ) ) ) )
% 4.98/5.24 => ( P @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_induct_non_zero
% 4.98/5.24 thf(fact_1404_zdiv__numeral__Bit0,axiom,
% 4.98/5.24 ! [V: num,W: num] :
% 4.98/5.24 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 4.98/5.24 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % zdiv_numeral_Bit0
% 4.98/5.24 thf(fact_1405_nat__induct2,axiom,
% 4.98/5.24 ! [P: nat > $o,N2: nat] :
% 4.98/5.24 ( ( P @ zero_zero_nat )
% 4.98/5.24 => ( ( P @ one_one_nat )
% 4.98/5.24 => ( ! [N: nat] :
% 4.98/5.24 ( ( P @ N )
% 4.98/5.24 => ( P @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 4.98/5.24 => ( P @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_induct2
% 4.98/5.24 thf(fact_1406_field__less__half__sum,axiom,
% 4.98/5.24 ! [X2: real,Y: real] :
% 4.98/5.24 ( ( ord_less_real @ X2 @ Y )
% 4.98/5.24 => ( ord_less_real @ X2 @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % field_less_half_sum
% 4.98/5.24 thf(fact_1407_field__less__half__sum,axiom,
% 4.98/5.24 ! [X2: rat,Y: rat] :
% 4.98/5.24 ( ( ord_less_rat @ X2 @ Y )
% 4.98/5.24 => ( ord_less_rat @ X2 @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % field_less_half_sum
% 4.98/5.24 thf(fact_1408_bit__concat__def,axiom,
% 4.98/5.24 ( vEBT_VEBT_bit_concat
% 4.98/5.24 = ( ^ [H: nat,L2: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % bit_concat_def
% 4.98/5.24 thf(fact_1409_low__inv,axiom,
% 4.98/5.24 ! [X2: nat,N2: nat,Y: nat] :
% 4.98/5.24 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.24 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X2 ) @ N2 )
% 4.98/5.24 = X2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % low_inv
% 4.98/5.24 thf(fact_1410_high__inv,axiom,
% 4.98/5.24 ! [X2: nat,N2: nat,Y: nat] :
% 4.98/5.24 ( ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.24 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ X2 ) @ N2 )
% 4.98/5.24 = Y ) ) ).
% 4.98/5.24
% 4.98/5.24 % high_inv
% 4.98/5.24 thf(fact_1411_vebt__member_Osimps_I4_J,axiom,
% 4.98/5.24 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 4.98/5.24 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X2 ) ).
% 4.98/5.24
% 4.98/5.24 % vebt_member.simps(4)
% 4.98/5.24 thf(fact_1412_zle__add1__eq__le,axiom,
% 4.98/5.24 ! [W: int,Z: int] :
% 4.98/5.24 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 4.98/5.24 = ( ord_less_eq_int @ W @ Z ) ) ).
% 4.98/5.24
% 4.98/5.24 % zle_add1_eq_le
% 4.98/5.24 thf(fact_1413_max__less__iff__conj,axiom,
% 4.98/5.24 ! [X2: real,Y: real,Z: real] :
% 4.98/5.24 ( ( ord_less_real @ ( ord_max_real @ X2 @ Y ) @ Z )
% 4.98/5.24 = ( ( ord_less_real @ X2 @ Z )
% 4.98/5.24 & ( ord_less_real @ Y @ Z ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max_less_iff_conj
% 4.98/5.24 thf(fact_1414_max__less__iff__conj,axiom,
% 4.98/5.24 ! [X2: rat,Y: rat,Z: rat] :
% 4.98/5.24 ( ( ord_less_rat @ ( ord_max_rat @ X2 @ Y ) @ Z )
% 4.98/5.24 = ( ( ord_less_rat @ X2 @ Z )
% 4.98/5.24 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max_less_iff_conj
% 4.98/5.24 thf(fact_1415_max__less__iff__conj,axiom,
% 4.98/5.24 ! [X2: num,Y: num,Z: num] :
% 4.98/5.24 ( ( ord_less_num @ ( ord_max_num @ X2 @ Y ) @ Z )
% 4.98/5.24 = ( ( ord_less_num @ X2 @ Z )
% 4.98/5.24 & ( ord_less_num @ Y @ Z ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max_less_iff_conj
% 4.98/5.24 thf(fact_1416_max__less__iff__conj,axiom,
% 4.98/5.24 ! [X2: nat,Y: nat,Z: nat] :
% 4.98/5.24 ( ( ord_less_nat @ ( ord_max_nat @ X2 @ Y ) @ Z )
% 4.98/5.24 = ( ( ord_less_nat @ X2 @ Z )
% 4.98/5.24 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max_less_iff_conj
% 4.98/5.24 thf(fact_1417_max__less__iff__conj,axiom,
% 4.98/5.24 ! [X2: int,Y: int,Z: int] :
% 4.98/5.24 ( ( ord_less_int @ ( ord_max_int @ X2 @ Y ) @ Z )
% 4.98/5.24 = ( ( ord_less_int @ X2 @ Z )
% 4.98/5.24 & ( ord_less_int @ Y @ Z ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max_less_iff_conj
% 4.98/5.24 thf(fact_1418_max_Oabsorb4,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ord_less_real @ A @ B )
% 4.98/5.24 => ( ( ord_max_real @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb4
% 4.98/5.24 thf(fact_1419_max_Oabsorb4,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ord_less_rat @ A @ B )
% 4.98/5.24 => ( ( ord_max_rat @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb4
% 4.98/5.24 thf(fact_1420_max_Oabsorb4,axiom,
% 4.98/5.24 ! [A: num,B: num] :
% 4.98/5.24 ( ( ord_less_num @ A @ B )
% 4.98/5.24 => ( ( ord_max_num @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb4
% 4.98/5.24 thf(fact_1421_max_Oabsorb4,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ord_less_nat @ A @ B )
% 4.98/5.24 => ( ( ord_max_nat @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb4
% 4.98/5.24 thf(fact_1422_max_Oabsorb4,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_less_int @ A @ B )
% 4.98/5.24 => ( ( ord_max_int @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb4
% 4.98/5.24 thf(fact_1423_max_Oabsorb3,axiom,
% 4.98/5.24 ! [B: real,A: real] :
% 4.98/5.24 ( ( ord_less_real @ B @ A )
% 4.98/5.24 => ( ( ord_max_real @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb3
% 4.98/5.24 thf(fact_1424_max_Oabsorb3,axiom,
% 4.98/5.24 ! [B: rat,A: rat] :
% 4.98/5.24 ( ( ord_less_rat @ B @ A )
% 4.98/5.24 => ( ( ord_max_rat @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb3
% 4.98/5.24 thf(fact_1425_max_Oabsorb3,axiom,
% 4.98/5.24 ! [B: num,A: num] :
% 4.98/5.24 ( ( ord_less_num @ B @ A )
% 4.98/5.24 => ( ( ord_max_num @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb3
% 4.98/5.24 thf(fact_1426_max_Oabsorb3,axiom,
% 4.98/5.24 ! [B: nat,A: nat] :
% 4.98/5.24 ( ( ord_less_nat @ B @ A )
% 4.98/5.24 => ( ( ord_max_nat @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb3
% 4.98/5.24 thf(fact_1427_max_Oabsorb3,axiom,
% 4.98/5.24 ! [B: int,A: int] :
% 4.98/5.24 ( ( ord_less_int @ B @ A )
% 4.98/5.24 => ( ( ord_max_int @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb3
% 4.98/5.24 thf(fact_1428_max_Oidem,axiom,
% 4.98/5.24 ! [A: nat] :
% 4.98/5.24 ( ( ord_max_nat @ A @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % max.idem
% 4.98/5.24 thf(fact_1429_max_Oidem,axiom,
% 4.98/5.24 ! [A: int] :
% 4.98/5.24 ( ( ord_max_int @ A @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % max.idem
% 4.98/5.24 thf(fact_1430_max_Oleft__idem,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ord_max_nat @ A @ ( ord_max_nat @ A @ B ) )
% 4.98/5.24 = ( ord_max_nat @ A @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.left_idem
% 4.98/5.24 thf(fact_1431_max_Oleft__idem,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_max_int @ A @ ( ord_max_int @ A @ B ) )
% 4.98/5.24 = ( ord_max_int @ A @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.left_idem
% 4.98/5.24 thf(fact_1432_max_Oright__idem,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ord_max_nat @ ( ord_max_nat @ A @ B ) @ B )
% 4.98/5.24 = ( ord_max_nat @ A @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.right_idem
% 4.98/5.24 thf(fact_1433_max_Oright__idem,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_max_int @ ( ord_max_int @ A @ B ) @ B )
% 4.98/5.24 = ( ord_max_int @ A @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.right_idem
% 4.98/5.24 thf(fact_1434_mult__zero__left,axiom,
% 4.98/5.24 ! [A: complex] :
% 4.98/5.24 ( ( times_times_complex @ zero_zero_complex @ A )
% 4.98/5.24 = zero_zero_complex ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_left
% 4.98/5.24 thf(fact_1435_mult__zero__left,axiom,
% 4.98/5.24 ! [A: real] :
% 4.98/5.24 ( ( times_times_real @ zero_zero_real @ A )
% 4.98/5.24 = zero_zero_real ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_left
% 4.98/5.24 thf(fact_1436_mult__zero__left,axiom,
% 4.98/5.24 ! [A: rat] :
% 4.98/5.24 ( ( times_times_rat @ zero_zero_rat @ A )
% 4.98/5.24 = zero_zero_rat ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_left
% 4.98/5.24 thf(fact_1437_mult__zero__left,axiom,
% 4.98/5.24 ! [A: nat] :
% 4.98/5.24 ( ( times_times_nat @ zero_zero_nat @ A )
% 4.98/5.24 = zero_zero_nat ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_left
% 4.98/5.24 thf(fact_1438_mult__zero__left,axiom,
% 4.98/5.24 ! [A: int] :
% 4.98/5.24 ( ( times_times_int @ zero_zero_int @ A )
% 4.98/5.24 = zero_zero_int ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_left
% 4.98/5.24 thf(fact_1439_mult__zero__right,axiom,
% 4.98/5.24 ! [A: complex] :
% 4.98/5.24 ( ( times_times_complex @ A @ zero_zero_complex )
% 4.98/5.24 = zero_zero_complex ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_right
% 4.98/5.24 thf(fact_1440_mult__zero__right,axiom,
% 4.98/5.24 ! [A: real] :
% 4.98/5.24 ( ( times_times_real @ A @ zero_zero_real )
% 4.98/5.24 = zero_zero_real ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_right
% 4.98/5.24 thf(fact_1441_mult__zero__right,axiom,
% 4.98/5.24 ! [A: rat] :
% 4.98/5.24 ( ( times_times_rat @ A @ zero_zero_rat )
% 4.98/5.24 = zero_zero_rat ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_right
% 4.98/5.24 thf(fact_1442_mult__zero__right,axiom,
% 4.98/5.24 ! [A: nat] :
% 4.98/5.24 ( ( times_times_nat @ A @ zero_zero_nat )
% 4.98/5.24 = zero_zero_nat ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_right
% 4.98/5.24 thf(fact_1443_mult__zero__right,axiom,
% 4.98/5.24 ! [A: int] :
% 4.98/5.24 ( ( times_times_int @ A @ zero_zero_int )
% 4.98/5.24 = zero_zero_int ) ).
% 4.98/5.24
% 4.98/5.24 % mult_zero_right
% 4.98/5.24 thf(fact_1444_mult__eq__0__iff,axiom,
% 4.98/5.24 ! [A: complex,B: complex] :
% 4.98/5.24 ( ( ( times_times_complex @ A @ B )
% 4.98/5.24 = zero_zero_complex )
% 4.98/5.24 = ( ( A = zero_zero_complex )
% 4.98/5.24 | ( B = zero_zero_complex ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_eq_0_iff
% 4.98/5.24 thf(fact_1445_mult__eq__0__iff,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ( times_times_real @ A @ B )
% 4.98/5.24 = zero_zero_real )
% 4.98/5.24 = ( ( A = zero_zero_real )
% 4.98/5.24 | ( B = zero_zero_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_eq_0_iff
% 4.98/5.24 thf(fact_1446_mult__eq__0__iff,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ( times_times_rat @ A @ B )
% 4.98/5.24 = zero_zero_rat )
% 4.98/5.24 = ( ( A = zero_zero_rat )
% 4.98/5.24 | ( B = zero_zero_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_eq_0_iff
% 4.98/5.24 thf(fact_1447_mult__eq__0__iff,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ A @ B )
% 4.98/5.24 = zero_zero_nat )
% 4.98/5.24 = ( ( A = zero_zero_nat )
% 4.98/5.24 | ( B = zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_eq_0_iff
% 4.98/5.24 thf(fact_1448_mult__eq__0__iff,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ( times_times_int @ A @ B )
% 4.98/5.24 = zero_zero_int )
% 4.98/5.24 = ( ( A = zero_zero_int )
% 4.98/5.24 | ( B = zero_zero_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_eq_0_iff
% 4.98/5.24 thf(fact_1449_mult__cancel__left,axiom,
% 4.98/5.24 ! [C: complex,A: complex,B: complex] :
% 4.98/5.24 ( ( ( times_times_complex @ C @ A )
% 4.98/5.24 = ( times_times_complex @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_complex )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left
% 4.98/5.24 thf(fact_1450_mult__cancel__left,axiom,
% 4.98/5.24 ! [C: real,A: real,B: real] :
% 4.98/5.24 ( ( ( times_times_real @ C @ A )
% 4.98/5.24 = ( times_times_real @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_real )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left
% 4.98/5.24 thf(fact_1451_mult__cancel__left,axiom,
% 4.98/5.24 ! [C: rat,A: rat,B: rat] :
% 4.98/5.24 ( ( ( times_times_rat @ C @ A )
% 4.98/5.24 = ( times_times_rat @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_rat )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left
% 4.98/5.24 thf(fact_1452_mult__cancel__left,axiom,
% 4.98/5.24 ! [C: nat,A: nat,B: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ C @ A )
% 4.98/5.24 = ( times_times_nat @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_nat )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left
% 4.98/5.24 thf(fact_1453_mult__cancel__left,axiom,
% 4.98/5.24 ! [C: int,A: int,B: int] :
% 4.98/5.24 ( ( ( times_times_int @ C @ A )
% 4.98/5.24 = ( times_times_int @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_int )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left
% 4.98/5.24 thf(fact_1454_mult__cancel__right,axiom,
% 4.98/5.24 ! [A: complex,C: complex,B: complex] :
% 4.98/5.24 ( ( ( times_times_complex @ A @ C )
% 4.98/5.24 = ( times_times_complex @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_complex )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right
% 4.98/5.24 thf(fact_1455_mult__cancel__right,axiom,
% 4.98/5.24 ! [A: real,C: real,B: real] :
% 4.98/5.24 ( ( ( times_times_real @ A @ C )
% 4.98/5.24 = ( times_times_real @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_real )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right
% 4.98/5.24 thf(fact_1456_mult__cancel__right,axiom,
% 4.98/5.24 ! [A: rat,C: rat,B: rat] :
% 4.98/5.24 ( ( ( times_times_rat @ A @ C )
% 4.98/5.24 = ( times_times_rat @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_rat )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right
% 4.98/5.24 thf(fact_1457_mult__cancel__right,axiom,
% 4.98/5.24 ! [A: nat,C: nat,B: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ A @ C )
% 4.98/5.24 = ( times_times_nat @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_nat )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right
% 4.98/5.24 thf(fact_1458_mult__cancel__right,axiom,
% 4.98/5.24 ! [A: int,C: int,B: int] :
% 4.98/5.24 ( ( ( times_times_int @ A @ C )
% 4.98/5.24 = ( times_times_int @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_int )
% 4.98/5.24 | ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right
% 4.98/5.24 thf(fact_1459_double__eq__0__iff,axiom,
% 4.98/5.24 ! [A: real] :
% 4.98/5.24 ( ( ( plus_plus_real @ A @ A )
% 4.98/5.24 = zero_zero_real )
% 4.98/5.24 = ( A = zero_zero_real ) ) ).
% 4.98/5.24
% 4.98/5.24 % double_eq_0_iff
% 4.98/5.24 thf(fact_1460_double__eq__0__iff,axiom,
% 4.98/5.24 ! [A: rat] :
% 4.98/5.24 ( ( ( plus_plus_rat @ A @ A )
% 4.98/5.24 = zero_zero_rat )
% 4.98/5.24 = ( A = zero_zero_rat ) ) ).
% 4.98/5.24
% 4.98/5.24 % double_eq_0_iff
% 4.98/5.24 thf(fact_1461_double__eq__0__iff,axiom,
% 4.98/5.24 ! [A: int] :
% 4.98/5.24 ( ( ( plus_plus_int @ A @ A )
% 4.98/5.24 = zero_zero_int )
% 4.98/5.24 = ( A = zero_zero_int ) ) ).
% 4.98/5.24
% 4.98/5.24 % double_eq_0_iff
% 4.98/5.24 thf(fact_1462_mult__numeral__left__semiring__numeral,axiom,
% 4.98/5.24 ! [V: num,W: num,Z: complex] :
% 4.98/5.24 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 4.98/5.24 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_numeral_left_semiring_numeral
% 4.98/5.24 thf(fact_1463_mult__numeral__left__semiring__numeral,axiom,
% 4.98/5.24 ! [V: num,W: num,Z: real] :
% 4.98/5.24 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 4.98/5.24 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_numeral_left_semiring_numeral
% 4.98/5.24 thf(fact_1464_mult__numeral__left__semiring__numeral,axiom,
% 4.98/5.24 ! [V: num,W: num,Z: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 4.98/5.24 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_numeral_left_semiring_numeral
% 4.98/5.24 thf(fact_1465_mult__numeral__left__semiring__numeral,axiom,
% 4.98/5.24 ! [V: num,W: num,Z: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 4.98/5.24 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_numeral_left_semiring_numeral
% 4.98/5.24 thf(fact_1466_mult__numeral__left__semiring__numeral,axiom,
% 4.98/5.24 ! [V: num,W: num,Z: int] :
% 4.98/5.24 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 4.98/5.24 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_numeral_left_semiring_numeral
% 4.98/5.24 thf(fact_1467_numeral__times__numeral,axiom,
% 4.98/5.24 ! [M: num,N2: num] :
% 4.98/5.24 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 4.98/5.24 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % numeral_times_numeral
% 4.98/5.24 thf(fact_1468_numeral__times__numeral,axiom,
% 4.98/5.24 ! [M: num,N2: num] :
% 4.98/5.24 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 4.98/5.24 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % numeral_times_numeral
% 4.98/5.24 thf(fact_1469_numeral__times__numeral,axiom,
% 4.98/5.24 ! [M: num,N2: num] :
% 4.98/5.24 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 4.98/5.24 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % numeral_times_numeral
% 4.98/5.24 thf(fact_1470_numeral__times__numeral,axiom,
% 4.98/5.24 ! [M: num,N2: num] :
% 4.98/5.24 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.24 = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % numeral_times_numeral
% 4.98/5.24 thf(fact_1471_numeral__times__numeral,axiom,
% 4.98/5.24 ! [M: num,N2: num] :
% 4.98/5.24 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 4.98/5.24 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % numeral_times_numeral
% 4.98/5.24 thf(fact_1472_mult_Oright__neutral,axiom,
% 4.98/5.24 ! [A: complex] :
% 4.98/5.24 ( ( times_times_complex @ A @ one_one_complex )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.right_neutral
% 4.98/5.24 thf(fact_1473_mult_Oright__neutral,axiom,
% 4.98/5.24 ! [A: real] :
% 4.98/5.24 ( ( times_times_real @ A @ one_one_real )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.right_neutral
% 4.98/5.24 thf(fact_1474_mult_Oright__neutral,axiom,
% 4.98/5.24 ! [A: rat] :
% 4.98/5.24 ( ( times_times_rat @ A @ one_one_rat )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.right_neutral
% 4.98/5.24 thf(fact_1475_mult_Oright__neutral,axiom,
% 4.98/5.24 ! [A: nat] :
% 4.98/5.24 ( ( times_times_nat @ A @ one_one_nat )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.right_neutral
% 4.98/5.24 thf(fact_1476_mult_Oright__neutral,axiom,
% 4.98/5.24 ! [A: int] :
% 4.98/5.24 ( ( times_times_int @ A @ one_one_int )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.right_neutral
% 4.98/5.24 thf(fact_1477_mult__1,axiom,
% 4.98/5.24 ! [A: complex] :
% 4.98/5.24 ( ( times_times_complex @ one_one_complex @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult_1
% 4.98/5.24 thf(fact_1478_mult__1,axiom,
% 4.98/5.24 ! [A: real] :
% 4.98/5.24 ( ( times_times_real @ one_one_real @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult_1
% 4.98/5.24 thf(fact_1479_mult__1,axiom,
% 4.98/5.24 ! [A: rat] :
% 4.98/5.24 ( ( times_times_rat @ one_one_rat @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult_1
% 4.98/5.24 thf(fact_1480_mult__1,axiom,
% 4.98/5.24 ! [A: nat] :
% 4.98/5.24 ( ( times_times_nat @ one_one_nat @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult_1
% 4.98/5.24 thf(fact_1481_mult__1,axiom,
% 4.98/5.24 ! [A: int] :
% 4.98/5.24 ( ( times_times_int @ one_one_int @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult_1
% 4.98/5.24 thf(fact_1482_times__divide__eq__left,axiom,
% 4.98/5.24 ! [B: complex,C: complex,A: complex] :
% 4.98/5.24 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 4.98/5.24 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_eq_left
% 4.98/5.24 thf(fact_1483_times__divide__eq__left,axiom,
% 4.98/5.24 ! [B: real,C: real,A: real] :
% 4.98/5.24 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.98/5.24 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_eq_left
% 4.98/5.24 thf(fact_1484_times__divide__eq__left,axiom,
% 4.98/5.24 ! [B: rat,C: rat,A: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.98/5.24 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_eq_left
% 4.98/5.24 thf(fact_1485_divide__divide__eq__left,axiom,
% 4.98/5.24 ! [A: complex,B: complex,C: complex] :
% 4.98/5.24 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 4.98/5.24 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_left
% 4.98/5.24 thf(fact_1486_divide__divide__eq__left,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 4.98/5.24 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_left
% 4.98/5.24 thf(fact_1487_divide__divide__eq__left,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 4.98/5.24 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_left
% 4.98/5.24 thf(fact_1488_divide__divide__eq__right,axiom,
% 4.98/5.24 ! [A: complex,B: complex,C: complex] :
% 4.98/5.24 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_right
% 4.98/5.24 thf(fact_1489_divide__divide__eq__right,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.98/5.24 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_right
% 4.98/5.24 thf(fact_1490_divide__divide__eq__right,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.24 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_right
% 4.98/5.24 thf(fact_1491_times__divide__eq__right,axiom,
% 4.98/5.24 ! [A: complex,B: complex,C: complex] :
% 4.98/5.24 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_eq_right
% 4.98/5.24 thf(fact_1492_times__divide__eq__right,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.98/5.24 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_eq_right
% 4.98/5.24 thf(fact_1493_times__divide__eq__right,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.24 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_eq_right
% 4.98/5.24 thf(fact_1494_max_Oabsorb1,axiom,
% 4.98/5.24 ! [B: rat,A: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.24 => ( ( ord_max_rat @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb1
% 4.98/5.24 thf(fact_1495_max_Oabsorb1,axiom,
% 4.98/5.24 ! [B: num,A: num] :
% 4.98/5.24 ( ( ord_less_eq_num @ B @ A )
% 4.98/5.24 => ( ( ord_max_num @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb1
% 4.98/5.24 thf(fact_1496_max_Oabsorb1,axiom,
% 4.98/5.24 ! [B: nat,A: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.24 => ( ( ord_max_nat @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb1
% 4.98/5.24 thf(fact_1497_max_Oabsorb1,axiom,
% 4.98/5.24 ! [B: int,A: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ B @ A )
% 4.98/5.24 => ( ( ord_max_int @ A @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb1
% 4.98/5.24 thf(fact_1498_max_Oabsorb2,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.24 => ( ( ord_max_rat @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb2
% 4.98/5.24 thf(fact_1499_max_Oabsorb2,axiom,
% 4.98/5.24 ! [A: num,B: num] :
% 4.98/5.24 ( ( ord_less_eq_num @ A @ B )
% 4.98/5.24 => ( ( ord_max_num @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb2
% 4.98/5.24 thf(fact_1500_max_Oabsorb2,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.24 => ( ( ord_max_nat @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb2
% 4.98/5.24 thf(fact_1501_max_Oabsorb2,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.24 => ( ( ord_max_int @ A @ B )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.absorb2
% 4.98/5.24 thf(fact_1502_max_Obounded__iff,axiom,
% 4.98/5.24 ! [B: rat,C: rat,A: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 4.98/5.24 = ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.24 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.bounded_iff
% 4.98/5.24 thf(fact_1503_max_Obounded__iff,axiom,
% 4.98/5.24 ! [B: num,C: num,A: num] :
% 4.98/5.24 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 4.98/5.24 = ( ( ord_less_eq_num @ B @ A )
% 4.98/5.24 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.bounded_iff
% 4.98/5.24 thf(fact_1504_max_Obounded__iff,axiom,
% 4.98/5.24 ! [B: nat,C: nat,A: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 4.98/5.24 = ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.24 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.bounded_iff
% 4.98/5.24 thf(fact_1505_max_Obounded__iff,axiom,
% 4.98/5.24 ! [B: int,C: int,A: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 4.98/5.24 = ( ( ord_less_eq_int @ B @ A )
% 4.98/5.24 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % max.bounded_iff
% 4.98/5.24 thf(fact_1506_mult__is__0,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ M @ N2 )
% 4.98/5.24 = zero_zero_nat )
% 4.98/5.24 = ( ( M = zero_zero_nat )
% 4.98/5.24 | ( N2 = zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_is_0
% 4.98/5.24 thf(fact_1507_mult__0__right,axiom,
% 4.98/5.24 ! [M: nat] :
% 4.98/5.24 ( ( times_times_nat @ M @ zero_zero_nat )
% 4.98/5.24 = zero_zero_nat ) ).
% 4.98/5.24
% 4.98/5.24 % mult_0_right
% 4.98/5.24 thf(fact_1508_mult__cancel1,axiom,
% 4.98/5.24 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ K @ M )
% 4.98/5.24 = ( times_times_nat @ K @ N2 ) )
% 4.98/5.24 = ( ( M = N2 )
% 4.98/5.24 | ( K = zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel1
% 4.98/5.24 thf(fact_1509_mult__cancel2,axiom,
% 4.98/5.24 ! [M: nat,K: nat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ M @ K )
% 4.98/5.24 = ( times_times_nat @ N2 @ K ) )
% 4.98/5.24 = ( ( M = N2 )
% 4.98/5.24 | ( K = zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel2
% 4.98/5.24 thf(fact_1510_nat__1__eq__mult__iff,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( one_one_nat
% 4.98/5.24 = ( times_times_nat @ M @ N2 ) )
% 4.98/5.24 = ( ( M = one_one_nat )
% 4.98/5.24 & ( N2 = one_one_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_1_eq_mult_iff
% 4.98/5.24 thf(fact_1511_nat__mult__eq__1__iff,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ M @ N2 )
% 4.98/5.24 = one_one_nat )
% 4.98/5.24 = ( ( M = one_one_nat )
% 4.98/5.24 & ( N2 = one_one_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_eq_1_iff
% 4.98/5.24 thf(fact_1512_mult__cancel__left1,axiom,
% 4.98/5.24 ! [C: complex,B: complex] :
% 4.98/5.24 ( ( C
% 4.98/5.24 = ( times_times_complex @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_complex )
% 4.98/5.24 | ( B = one_one_complex ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left1
% 4.98/5.24 thf(fact_1513_mult__cancel__left1,axiom,
% 4.98/5.24 ! [C: real,B: real] :
% 4.98/5.24 ( ( C
% 4.98/5.24 = ( times_times_real @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_real )
% 4.98/5.24 | ( B = one_one_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left1
% 4.98/5.24 thf(fact_1514_mult__cancel__left1,axiom,
% 4.98/5.24 ! [C: rat,B: rat] :
% 4.98/5.24 ( ( C
% 4.98/5.24 = ( times_times_rat @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_rat )
% 4.98/5.24 | ( B = one_one_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left1
% 4.98/5.24 thf(fact_1515_mult__cancel__left1,axiom,
% 4.98/5.24 ! [C: int,B: int] :
% 4.98/5.24 ( ( C
% 4.98/5.24 = ( times_times_int @ C @ B ) )
% 4.98/5.24 = ( ( C = zero_zero_int )
% 4.98/5.24 | ( B = one_one_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left1
% 4.98/5.24 thf(fact_1516_mult__cancel__left2,axiom,
% 4.98/5.24 ! [C: complex,A: complex] :
% 4.98/5.24 ( ( ( times_times_complex @ C @ A )
% 4.98/5.24 = C )
% 4.98/5.24 = ( ( C = zero_zero_complex )
% 4.98/5.24 | ( A = one_one_complex ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left2
% 4.98/5.24 thf(fact_1517_mult__cancel__left2,axiom,
% 4.98/5.24 ! [C: real,A: real] :
% 4.98/5.24 ( ( ( times_times_real @ C @ A )
% 4.98/5.24 = C )
% 4.98/5.24 = ( ( C = zero_zero_real )
% 4.98/5.24 | ( A = one_one_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left2
% 4.98/5.24 thf(fact_1518_mult__cancel__left2,axiom,
% 4.98/5.24 ! [C: rat,A: rat] :
% 4.98/5.24 ( ( ( times_times_rat @ C @ A )
% 4.98/5.24 = C )
% 4.98/5.24 = ( ( C = zero_zero_rat )
% 4.98/5.24 | ( A = one_one_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left2
% 4.98/5.24 thf(fact_1519_mult__cancel__left2,axiom,
% 4.98/5.24 ! [C: int,A: int] :
% 4.98/5.24 ( ( ( times_times_int @ C @ A )
% 4.98/5.24 = C )
% 4.98/5.24 = ( ( C = zero_zero_int )
% 4.98/5.24 | ( A = one_one_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_left2
% 4.98/5.24 thf(fact_1520_mult__cancel__right1,axiom,
% 4.98/5.24 ! [C: complex,B: complex] :
% 4.98/5.24 ( ( C
% 4.98/5.24 = ( times_times_complex @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_complex )
% 4.98/5.24 | ( B = one_one_complex ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right1
% 4.98/5.24 thf(fact_1521_mult__cancel__right1,axiom,
% 4.98/5.24 ! [C: real,B: real] :
% 4.98/5.24 ( ( C
% 4.98/5.24 = ( times_times_real @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_real )
% 4.98/5.24 | ( B = one_one_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right1
% 4.98/5.24 thf(fact_1522_mult__cancel__right1,axiom,
% 4.98/5.24 ! [C: rat,B: rat] :
% 4.98/5.24 ( ( C
% 4.98/5.24 = ( times_times_rat @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_rat )
% 4.98/5.24 | ( B = one_one_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right1
% 4.98/5.24 thf(fact_1523_mult__cancel__right1,axiom,
% 4.98/5.24 ! [C: int,B: int] :
% 4.98/5.24 ( ( C
% 4.98/5.24 = ( times_times_int @ B @ C ) )
% 4.98/5.24 = ( ( C = zero_zero_int )
% 4.98/5.24 | ( B = one_one_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right1
% 4.98/5.24 thf(fact_1524_mult__cancel__right2,axiom,
% 4.98/5.24 ! [A: complex,C: complex] :
% 4.98/5.24 ( ( ( times_times_complex @ A @ C )
% 4.98/5.24 = C )
% 4.98/5.24 = ( ( C = zero_zero_complex )
% 4.98/5.24 | ( A = one_one_complex ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right2
% 4.98/5.24 thf(fact_1525_mult__cancel__right2,axiom,
% 4.98/5.24 ! [A: real,C: real] :
% 4.98/5.24 ( ( ( times_times_real @ A @ C )
% 4.98/5.24 = C )
% 4.98/5.24 = ( ( C = zero_zero_real )
% 4.98/5.24 | ( A = one_one_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right2
% 4.98/5.24 thf(fact_1526_mult__cancel__right2,axiom,
% 4.98/5.24 ! [A: rat,C: rat] :
% 4.98/5.24 ( ( ( times_times_rat @ A @ C )
% 4.98/5.24 = C )
% 4.98/5.24 = ( ( C = zero_zero_rat )
% 4.98/5.24 | ( A = one_one_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right2
% 4.98/5.24 thf(fact_1527_mult__cancel__right2,axiom,
% 4.98/5.24 ! [A: int,C: int] :
% 4.98/5.24 ( ( ( times_times_int @ A @ C )
% 4.98/5.24 = C )
% 4.98/5.24 = ( ( C = zero_zero_int )
% 4.98/5.24 | ( A = one_one_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_cancel_right2
% 4.98/5.24 thf(fact_1528_sum__squares__eq__zero__iff,axiom,
% 4.98/5.24 ! [X2: real,Y: real] :
% 4.98/5.24 ( ( ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) )
% 4.98/5.24 = zero_zero_real )
% 4.98/5.24 = ( ( X2 = zero_zero_real )
% 4.98/5.24 & ( Y = zero_zero_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % sum_squares_eq_zero_iff
% 4.98/5.24 thf(fact_1529_sum__squares__eq__zero__iff,axiom,
% 4.98/5.24 ! [X2: rat,Y: rat] :
% 4.98/5.24 ( ( ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) )
% 4.98/5.24 = zero_zero_rat )
% 4.98/5.24 = ( ( X2 = zero_zero_rat )
% 4.98/5.24 & ( Y = zero_zero_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % sum_squares_eq_zero_iff
% 4.98/5.24 thf(fact_1530_sum__squares__eq__zero__iff,axiom,
% 4.98/5.24 ! [X2: int,Y: int] :
% 4.98/5.24 ( ( ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) )
% 4.98/5.24 = zero_zero_int )
% 4.98/5.24 = ( ( X2 = zero_zero_int )
% 4.98/5.24 & ( Y = zero_zero_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % sum_squares_eq_zero_iff
% 4.98/5.24 thf(fact_1531_div__mult__mult1__if,axiom,
% 4.98/5.24 ! [C: nat,A: nat,B: nat] :
% 4.98/5.24 ( ( ( C = zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.98/5.24 = zero_zero_nat ) )
% 4.98/5.24 & ( ( C != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.98/5.24 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_mult1_if
% 4.98/5.24 thf(fact_1532_div__mult__mult1__if,axiom,
% 4.98/5.24 ! [C: int,A: int,B: int] :
% 4.98/5.24 ( ( ( C = zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.24 = zero_zero_int ) )
% 4.98/5.24 & ( ( C != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.24 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_mult1_if
% 4.98/5.24 thf(fact_1533_div__mult__mult2,axiom,
% 4.98/5.24 ! [C: nat,A: nat,B: nat] :
% 4.98/5.24 ( ( C != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 4.98/5.24 = ( divide_divide_nat @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_mult2
% 4.98/5.24 thf(fact_1534_div__mult__mult2,axiom,
% 4.98/5.24 ! [C: int,A: int,B: int] :
% 4.98/5.24 ( ( C != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.98/5.24 = ( divide_divide_int @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_mult2
% 4.98/5.24 thf(fact_1535_div__mult__mult1,axiom,
% 4.98/5.24 ! [C: nat,A: nat,B: nat] :
% 4.98/5.24 ( ( C != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.98/5.24 = ( divide_divide_nat @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_mult1
% 4.98/5.24 thf(fact_1536_div__mult__mult1,axiom,
% 4.98/5.24 ! [C: int,A: int,B: int] :
% 4.98/5.24 ( ( C != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.24 = ( divide_divide_int @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_mult1
% 4.98/5.24 thf(fact_1537_nonzero__mult__divide__mult__cancel__right2,axiom,
% 4.98/5.24 ! [C: complex,A: complex,B: complex] :
% 4.98/5.24 ( ( C != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_right2
% 4.98/5.24 thf(fact_1538_nonzero__mult__divide__mult__cancel__right2,axiom,
% 4.98/5.24 ! [C: real,A: real,B: real] :
% 4.98/5.24 ( ( C != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 4.98/5.24 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_right2
% 4.98/5.24 thf(fact_1539_nonzero__mult__divide__mult__cancel__right2,axiom,
% 4.98/5.24 ! [C: rat,A: rat,B: rat] :
% 4.98/5.24 ( ( C != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.24 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_right2
% 4.98/5.24 thf(fact_1540_nonzero__mult__divide__mult__cancel__right,axiom,
% 4.98/5.24 ! [C: complex,A: complex,B: complex] :
% 4.98/5.24 ( ( C != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_right
% 4.98/5.24 thf(fact_1541_nonzero__mult__divide__mult__cancel__right,axiom,
% 4.98/5.24 ! [C: real,A: real,B: real] :
% 4.98/5.24 ( ( C != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.98/5.24 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_right
% 4.98/5.24 thf(fact_1542_nonzero__mult__divide__mult__cancel__right,axiom,
% 4.98/5.24 ! [C: rat,A: rat,B: rat] :
% 4.98/5.24 ( ( C != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.98/5.24 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_right
% 4.98/5.24 thf(fact_1543_nonzero__mult__divide__mult__cancel__left2,axiom,
% 4.98/5.24 ! [C: complex,A: complex,B: complex] :
% 4.98/5.24 ( ( C != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_left2
% 4.98/5.24 thf(fact_1544_nonzero__mult__divide__mult__cancel__left2,axiom,
% 4.98/5.24 ! [C: real,A: real,B: real] :
% 4.98/5.24 ( ( C != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 4.98/5.24 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_left2
% 4.98/5.24 thf(fact_1545_nonzero__mult__divide__mult__cancel__left2,axiom,
% 4.98/5.24 ! [C: rat,A: rat,B: rat] :
% 4.98/5.24 ( ( C != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 4.98/5.24 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_left2
% 4.98/5.24 thf(fact_1546_nonzero__mult__divide__mult__cancel__left,axiom,
% 4.98/5.24 ! [C: complex,A: complex,B: complex] :
% 4.98/5.24 ( ( C != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_left
% 4.98/5.24 thf(fact_1547_nonzero__mult__divide__mult__cancel__left,axiom,
% 4.98/5.24 ! [C: real,A: real,B: real] :
% 4.98/5.24 ( ( C != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.24 = ( divide_divide_real @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_left
% 4.98/5.24 thf(fact_1548_nonzero__mult__divide__mult__cancel__left,axiom,
% 4.98/5.24 ! [C: rat,A: rat,B: rat] :
% 4.98/5.24 ( ( C != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.24 = ( divide_divide_rat @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_divide_mult_cancel_left
% 4.98/5.24 thf(fact_1549_mult__divide__mult__cancel__left__if,axiom,
% 4.98/5.24 ! [C: complex,A: complex,B: complex] :
% 4.98/5.24 ( ( ( C = zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 4.98/5.24 = zero_zero_complex ) )
% 4.98/5.24 & ( ( C != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_divide_mult_cancel_left_if
% 4.98/5.24 thf(fact_1550_mult__divide__mult__cancel__left__if,axiom,
% 4.98/5.24 ! [C: real,A: real,B: real] :
% 4.98/5.24 ( ( ( C = zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.24 = zero_zero_real ) )
% 4.98/5.24 & ( ( C != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.24 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_divide_mult_cancel_left_if
% 4.98/5.24 thf(fact_1551_mult__divide__mult__cancel__left__if,axiom,
% 4.98/5.24 ! [C: rat,A: rat,B: rat] :
% 4.98/5.24 ( ( ( C = zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.24 = zero_zero_rat ) )
% 4.98/5.24 & ( ( C != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.24 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_divide_mult_cancel_left_if
% 4.98/5.24 thf(fact_1552_nonzero__mult__div__cancel__right,axiom,
% 4.98/5.24 ! [B: complex,A: complex] :
% 4.98/5.24 ( ( B != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_right
% 4.98/5.24 thf(fact_1553_nonzero__mult__div__cancel__right,axiom,
% 4.98/5.24 ! [B: real,A: real] :
% 4.98/5.24 ( ( B != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_right
% 4.98/5.24 thf(fact_1554_nonzero__mult__div__cancel__right,axiom,
% 4.98/5.24 ! [B: rat,A: rat] :
% 4.98/5.24 ( ( B != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_right
% 4.98/5.24 thf(fact_1555_nonzero__mult__div__cancel__right,axiom,
% 4.98/5.24 ! [B: nat,A: nat] :
% 4.98/5.24 ( ( B != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_right
% 4.98/5.24 thf(fact_1556_nonzero__mult__div__cancel__right,axiom,
% 4.98/5.24 ! [B: int,A: int] :
% 4.98/5.24 ( ( B != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 4.98/5.24 = A ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_right
% 4.98/5.24 thf(fact_1557_nonzero__mult__div__cancel__left,axiom,
% 4.98/5.24 ! [A: complex,B: complex] :
% 4.98/5.24 ( ( A != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_left
% 4.98/5.24 thf(fact_1558_nonzero__mult__div__cancel__left,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( A != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_left
% 4.98/5.24 thf(fact_1559_nonzero__mult__div__cancel__left,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( A != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_left
% 4.98/5.24 thf(fact_1560_nonzero__mult__div__cancel__left,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( A != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_left
% 4.98/5.24 thf(fact_1561_nonzero__mult__div__cancel__left,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( A != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 4.98/5.24 = B ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_mult_div_cancel_left
% 4.98/5.24 thf(fact_1562_distrib__left__numeral,axiom,
% 4.98/5.24 ! [V: num,B: complex,C: complex] :
% 4.98/5.24 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 4.98/5.24 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left_numeral
% 4.98/5.24 thf(fact_1563_distrib__left__numeral,axiom,
% 4.98/5.24 ! [V: num,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 4.98/5.24 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left_numeral
% 4.98/5.24 thf(fact_1564_distrib__left__numeral,axiom,
% 4.98/5.24 ! [V: num,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.24 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left_numeral
% 4.98/5.24 thf(fact_1565_distrib__left__numeral,axiom,
% 4.98/5.24 ! [V: num,B: nat,C: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left_numeral
% 4.98/5.24 thf(fact_1566_distrib__left__numeral,axiom,
% 4.98/5.24 ! [V: num,B: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 4.98/5.24 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left_numeral
% 4.98/5.24 thf(fact_1567_distrib__right__numeral,axiom,
% 4.98/5.24 ! [A: complex,B: complex,V: num] :
% 4.98/5.24 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 4.98/5.24 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right_numeral
% 4.98/5.24 thf(fact_1568_distrib__right__numeral,axiom,
% 4.98/5.24 ! [A: real,B: real,V: num] :
% 4.98/5.24 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 4.98/5.24 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right_numeral
% 4.98/5.24 thf(fact_1569_distrib__right__numeral,axiom,
% 4.98/5.24 ! [A: rat,B: rat,V: num] :
% 4.98/5.24 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 4.98/5.24 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right_numeral
% 4.98/5.24 thf(fact_1570_distrib__right__numeral,axiom,
% 4.98/5.24 ! [A: nat,B: nat,V: num] :
% 4.98/5.24 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right_numeral
% 4.98/5.24 thf(fact_1571_distrib__right__numeral,axiom,
% 4.98/5.24 ! [A: int,B: int,V: num] :
% 4.98/5.24 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 4.98/5.24 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right_numeral
% 4.98/5.24 thf(fact_1572_mult__eq__1__iff,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ M @ N2 )
% 4.98/5.24 = ( suc @ zero_zero_nat ) )
% 4.98/5.24 = ( ( M
% 4.98/5.24 = ( suc @ zero_zero_nat ) )
% 4.98/5.24 & ( N2
% 4.98/5.24 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_eq_1_iff
% 4.98/5.24 thf(fact_1573_one__eq__mult__iff,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ( suc @ zero_zero_nat )
% 4.98/5.24 = ( times_times_nat @ M @ N2 ) )
% 4.98/5.24 = ( ( M
% 4.98/5.24 = ( suc @ zero_zero_nat ) )
% 4.98/5.24 & ( N2
% 4.98/5.24 = ( suc @ zero_zero_nat ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % one_eq_mult_iff
% 4.98/5.24 thf(fact_1574_mult__less__cancel2,axiom,
% 4.98/5.24 ! [M: nat,K: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 4.98/5.24 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.24 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_less_cancel2
% 4.98/5.24 thf(fact_1575_nat__0__less__mult__iff,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 4.98/5.24 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.98/5.24 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_0_less_mult_iff
% 4.98/5.24 thf(fact_1576_nat__mult__less__cancel__disj,axiom,
% 4.98/5.24 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 4.98/5.24 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.24 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_less_cancel_disj
% 4.98/5.24 thf(fact_1577_mult__Suc__right,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 4.98/5.24 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_Suc_right
% 4.98/5.24 thf(fact_1578_nat__mult__div__cancel__disj,axiom,
% 4.98/5.24 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.24 ( ( ( K = zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 4.98/5.24 = zero_zero_nat ) )
% 4.98/5.24 & ( ( K != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 4.98/5.24 = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_div_cancel_disj
% 4.98/5.24 thf(fact_1579_divide__le__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [B: real,W: num,A: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 4.98/5.24 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_le_eq_numeral1(1)
% 4.98/5.24 thf(fact_1580_divide__le__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [B: rat,W: num,A: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 4.98/5.24 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_le_eq_numeral1(1)
% 4.98/5.24 thf(fact_1581_le__divide__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [A: real,B: real,W: num] :
% 4.98/5.24 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 4.98/5.24 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % le_divide_eq_numeral1(1)
% 4.98/5.24 thf(fact_1582_le__divide__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [A: rat,B: rat,W: num] :
% 4.98/5.24 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 4.98/5.24 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % le_divide_eq_numeral1(1)
% 4.98/5.24 thf(fact_1583_divide__eq__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [B: complex,W: num,A: complex] :
% 4.98/5.24 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 4.98/5.24 = A )
% 4.98/5.24 = ( ( ( ( numera6690914467698888265omplex @ W )
% 4.98/5.24 != zero_zero_complex )
% 4.98/5.24 => ( B
% 4.98/5.24 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 4.98/5.24 & ( ( ( numera6690914467698888265omplex @ W )
% 4.98/5.24 = zero_zero_complex )
% 4.98/5.24 => ( A = zero_zero_complex ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_eq_eq_numeral1(1)
% 4.98/5.24 thf(fact_1584_divide__eq__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [B: real,W: num,A: real] :
% 4.98/5.24 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 4.98/5.24 = A )
% 4.98/5.24 = ( ( ( ( numeral_numeral_real @ W )
% 4.98/5.24 != zero_zero_real )
% 4.98/5.24 => ( B
% 4.98/5.24 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 4.98/5.24 & ( ( ( numeral_numeral_real @ W )
% 4.98/5.24 = zero_zero_real )
% 4.98/5.24 => ( A = zero_zero_real ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_eq_eq_numeral1(1)
% 4.98/5.24 thf(fact_1585_divide__eq__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [B: rat,W: num,A: rat] :
% 4.98/5.24 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 4.98/5.24 = A )
% 4.98/5.24 = ( ( ( ( numeral_numeral_rat @ W )
% 4.98/5.24 != zero_zero_rat )
% 4.98/5.24 => ( B
% 4.98/5.24 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 4.98/5.24 & ( ( ( numeral_numeral_rat @ W )
% 4.98/5.24 = zero_zero_rat )
% 4.98/5.24 => ( A = zero_zero_rat ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_eq_eq_numeral1(1)
% 4.98/5.24 thf(fact_1586_eq__divide__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [A: complex,B: complex,W: num] :
% 4.98/5.24 ( ( A
% 4.98/5.24 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 4.98/5.24 = ( ( ( ( numera6690914467698888265omplex @ W )
% 4.98/5.24 != zero_zero_complex )
% 4.98/5.24 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 4.98/5.24 = B ) )
% 4.98/5.24 & ( ( ( numera6690914467698888265omplex @ W )
% 4.98/5.24 = zero_zero_complex )
% 4.98/5.24 => ( A = zero_zero_complex ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % eq_divide_eq_numeral1(1)
% 4.98/5.24 thf(fact_1587_eq__divide__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [A: real,B: real,W: num] :
% 4.98/5.24 ( ( A
% 4.98/5.24 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 4.98/5.24 = ( ( ( ( numeral_numeral_real @ W )
% 4.98/5.24 != zero_zero_real )
% 4.98/5.24 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 4.98/5.24 = B ) )
% 4.98/5.24 & ( ( ( numeral_numeral_real @ W )
% 4.98/5.24 = zero_zero_real )
% 4.98/5.24 => ( A = zero_zero_real ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % eq_divide_eq_numeral1(1)
% 4.98/5.24 thf(fact_1588_eq__divide__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [A: rat,B: rat,W: num] :
% 4.98/5.24 ( ( A
% 4.98/5.24 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 4.98/5.24 = ( ( ( ( numeral_numeral_rat @ W )
% 4.98/5.24 != zero_zero_rat )
% 4.98/5.24 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 4.98/5.24 = B ) )
% 4.98/5.24 & ( ( ( numeral_numeral_rat @ W )
% 4.98/5.24 = zero_zero_rat )
% 4.98/5.24 => ( A = zero_zero_rat ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % eq_divide_eq_numeral1(1)
% 4.98/5.24 thf(fact_1589_divide__less__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [B: real,W: num,A: real] :
% 4.98/5.24 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 4.98/5.24 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_less_eq_numeral1(1)
% 4.98/5.24 thf(fact_1590_divide__less__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [B: rat,W: num,A: rat] :
% 4.98/5.24 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 4.98/5.24 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_less_eq_numeral1(1)
% 4.98/5.24 thf(fact_1591_less__divide__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [A: real,B: real,W: num] :
% 4.98/5.24 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 4.98/5.24 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % less_divide_eq_numeral1(1)
% 4.98/5.24 thf(fact_1592_less__divide__eq__numeral1_I1_J,axiom,
% 4.98/5.24 ! [A: rat,B: rat,W: num] :
% 4.98/5.24 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 4.98/5.24 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % less_divide_eq_numeral1(1)
% 4.98/5.24 thf(fact_1593_nonzero__divide__mult__cancel__right,axiom,
% 4.98/5.24 ! [B: complex,A: complex] :
% 4.98/5.24 ( ( B != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_divide_mult_cancel_right
% 4.98/5.24 thf(fact_1594_nonzero__divide__mult__cancel__right,axiom,
% 4.98/5.24 ! [B: real,A: real] :
% 4.98/5.24 ( ( B != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 4.98/5.24 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_divide_mult_cancel_right
% 4.98/5.24 thf(fact_1595_nonzero__divide__mult__cancel__right,axiom,
% 4.98/5.24 ! [B: rat,A: rat] :
% 4.98/5.24 ( ( B != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 4.98/5.24 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_divide_mult_cancel_right
% 4.98/5.24 thf(fact_1596_nonzero__divide__mult__cancel__left,axiom,
% 4.98/5.24 ! [A: complex,B: complex] :
% 4.98/5.24 ( ( A != zero_zero_complex )
% 4.98/5.24 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_divide_mult_cancel_left
% 4.98/5.24 thf(fact_1597_nonzero__divide__mult__cancel__left,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( A != zero_zero_real )
% 4.98/5.24 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 4.98/5.24 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_divide_mult_cancel_left
% 4.98/5.24 thf(fact_1598_nonzero__divide__mult__cancel__left,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( A != zero_zero_rat )
% 4.98/5.24 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 4.98/5.24 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nonzero_divide_mult_cancel_left
% 4.98/5.24 thf(fact_1599_div__mult__self1,axiom,
% 4.98/5.24 ! [B: nat,A: nat,C: nat] :
% 4.98/5.24 ( ( B != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 4.98/5.24 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self1
% 4.98/5.24 thf(fact_1600_div__mult__self1,axiom,
% 4.98/5.24 ! [B: int,A: int,C: int] :
% 4.98/5.24 ( ( B != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 4.98/5.24 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self1
% 4.98/5.24 thf(fact_1601_div__mult__self2,axiom,
% 4.98/5.24 ! [B: nat,A: nat,C: nat] :
% 4.98/5.24 ( ( B != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 4.98/5.24 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self2
% 4.98/5.24 thf(fact_1602_div__mult__self2,axiom,
% 4.98/5.24 ! [B: int,A: int,C: int] :
% 4.98/5.24 ( ( B != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 4.98/5.24 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self2
% 4.98/5.24 thf(fact_1603_div__mult__self3,axiom,
% 4.98/5.24 ! [B: nat,C: nat,A: nat] :
% 4.98/5.24 ( ( B != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 4.98/5.24 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self3
% 4.98/5.24 thf(fact_1604_div__mult__self3,axiom,
% 4.98/5.24 ! [B: int,C: int,A: int] :
% 4.98/5.24 ( ( B != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 4.98/5.24 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self3
% 4.98/5.24 thf(fact_1605_div__mult__self4,axiom,
% 4.98/5.24 ! [B: nat,C: nat,A: nat] :
% 4.98/5.24 ( ( B != zero_zero_nat )
% 4.98/5.24 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 4.98/5.24 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self4
% 4.98/5.24 thf(fact_1606_div__mult__self4,axiom,
% 4.98/5.24 ! [B: int,C: int,A: int] :
% 4.98/5.24 ( ( B != zero_zero_int )
% 4.98/5.24 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 4.98/5.24 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self4
% 4.98/5.24 thf(fact_1607_one__le__mult__iff,axiom,
% 4.98/5.24 ! [M: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 4.98/5.24 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 4.98/5.24 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % one_le_mult_iff
% 4.98/5.24 thf(fact_1608_mult__le__cancel2,axiom,
% 4.98/5.24 ! [M: nat,K: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 4.98/5.24 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.24 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_le_cancel2
% 4.98/5.24 thf(fact_1609_nat__mult__le__cancel__disj,axiom,
% 4.98/5.24 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 4.98/5.24 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.24 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_le_cancel_disj
% 4.98/5.24 thf(fact_1610_div__mult__self__is__m,axiom,
% 4.98/5.24 ! [N2: nat,M: nat] :
% 4.98/5.24 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 4.98/5.24 = M ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self_is_m
% 4.98/5.24 thf(fact_1611_div__mult__self1__is__m,axiom,
% 4.98/5.24 ! [N2: nat,M: nat] :
% 4.98/5.24 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.24 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 4.98/5.24 = M ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult_self1_is_m
% 4.98/5.24 thf(fact_1612_power__add__numeral,axiom,
% 4.98/5.24 ! [A: complex,M: num,N2: num] :
% 4.98/5.24 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 4.98/5.24 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral
% 4.98/5.24 thf(fact_1613_power__add__numeral,axiom,
% 4.98/5.24 ! [A: real,M: num,N2: num] :
% 4.98/5.24 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 4.98/5.24 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral
% 4.98/5.24 thf(fact_1614_power__add__numeral,axiom,
% 4.98/5.24 ! [A: rat,M: num,N2: num] :
% 4.98/5.24 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 4.98/5.24 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral
% 4.98/5.24 thf(fact_1615_power__add__numeral,axiom,
% 4.98/5.24 ! [A: nat,M: num,N2: num] :
% 4.98/5.24 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 4.98/5.24 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral
% 4.98/5.24 thf(fact_1616_power__add__numeral,axiom,
% 4.98/5.24 ! [A: int,M: num,N2: num] :
% 4.98/5.24 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 4.98/5.24 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral
% 4.98/5.24 thf(fact_1617_power__add__numeral2,axiom,
% 4.98/5.24 ! [A: complex,M: num,N2: num,B: complex] :
% 4.98/5.24 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 4.98/5.24 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral2
% 4.98/5.24 thf(fact_1618_power__add__numeral2,axiom,
% 4.98/5.24 ! [A: real,M: num,N2: num,B: real] :
% 4.98/5.24 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 4.98/5.24 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral2
% 4.98/5.24 thf(fact_1619_power__add__numeral2,axiom,
% 4.98/5.24 ! [A: rat,M: num,N2: num,B: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 4.98/5.24 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral2
% 4.98/5.24 thf(fact_1620_power__add__numeral2,axiom,
% 4.98/5.24 ! [A: nat,M: num,N2: num,B: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 4.98/5.24 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral2
% 4.98/5.24 thf(fact_1621_power__add__numeral2,axiom,
% 4.98/5.24 ! [A: int,M: num,N2: num,B: int] :
% 4.98/5.24 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 4.98/5.24 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_add_numeral2
% 4.98/5.24 thf(fact_1622_mult_Oleft__commute,axiom,
% 4.98/5.24 ! [B: real,A: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 4.98/5.24 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.left_commute
% 4.98/5.24 thf(fact_1623_mult_Oleft__commute,axiom,
% 4.98/5.24 ! [B: rat,A: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 4.98/5.24 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.left_commute
% 4.98/5.24 thf(fact_1624_mult_Oleft__commute,axiom,
% 4.98/5.24 ! [B: nat,A: nat,C: nat] :
% 4.98/5.24 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 4.98/5.24 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.left_commute
% 4.98/5.24 thf(fact_1625_mult_Oleft__commute,axiom,
% 4.98/5.24 ! [B: int,A: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 4.98/5.24 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.left_commute
% 4.98/5.24 thf(fact_1626_mult_Ocommute,axiom,
% 4.98/5.24 ( times_times_real
% 4.98/5.24 = ( ^ [A5: real,B5: real] : ( times_times_real @ B5 @ A5 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.commute
% 4.98/5.24 thf(fact_1627_mult_Ocommute,axiom,
% 4.98/5.24 ( times_times_rat
% 4.98/5.24 = ( ^ [A5: rat,B5: rat] : ( times_times_rat @ B5 @ A5 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.commute
% 4.98/5.24 thf(fact_1628_mult_Ocommute,axiom,
% 4.98/5.24 ( times_times_nat
% 4.98/5.24 = ( ^ [A5: nat,B5: nat] : ( times_times_nat @ B5 @ A5 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.commute
% 4.98/5.24 thf(fact_1629_mult_Ocommute,axiom,
% 4.98/5.24 ( times_times_int
% 4.98/5.24 = ( ^ [A5: int,B5: int] : ( times_times_int @ B5 @ A5 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.commute
% 4.98/5.24 thf(fact_1630_mult_Oassoc,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 4.98/5.24 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.assoc
% 4.98/5.24 thf(fact_1631_mult_Oassoc,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 4.98/5.24 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.assoc
% 4.98/5.24 thf(fact_1632_mult_Oassoc,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.98/5.24 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.assoc
% 4.98/5.24 thf(fact_1633_mult_Oassoc,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 4.98/5.24 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult.assoc
% 4.98/5.24 thf(fact_1634_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 4.98/5.24 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ab_semigroup_mult_class.mult_ac(1)
% 4.98/5.24 thf(fact_1635_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 4.98/5.24 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ab_semigroup_mult_class.mult_ac(1)
% 4.98/5.24 thf(fact_1636_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.98/5.24 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ab_semigroup_mult_class.mult_ac(1)
% 4.98/5.24 thf(fact_1637_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 4.98/5.24 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ab_semigroup_mult_class.mult_ac(1)
% 4.98/5.24 thf(fact_1638_mult__not__zero,axiom,
% 4.98/5.24 ! [A: complex,B: complex] :
% 4.98/5.24 ( ( ( times_times_complex @ A @ B )
% 4.98/5.24 != zero_zero_complex )
% 4.98/5.24 => ( ( A != zero_zero_complex )
% 4.98/5.24 & ( B != zero_zero_complex ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_not_zero
% 4.98/5.24 thf(fact_1639_mult__not__zero,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ( times_times_real @ A @ B )
% 4.98/5.24 != zero_zero_real )
% 4.98/5.24 => ( ( A != zero_zero_real )
% 4.98/5.24 & ( B != zero_zero_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_not_zero
% 4.98/5.24 thf(fact_1640_mult__not__zero,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ( times_times_rat @ A @ B )
% 4.98/5.24 != zero_zero_rat )
% 4.98/5.24 => ( ( A != zero_zero_rat )
% 4.98/5.24 & ( B != zero_zero_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_not_zero
% 4.98/5.24 thf(fact_1641_mult__not__zero,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ A @ B )
% 4.98/5.24 != zero_zero_nat )
% 4.98/5.24 => ( ( A != zero_zero_nat )
% 4.98/5.24 & ( B != zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_not_zero
% 4.98/5.24 thf(fact_1642_mult__not__zero,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ( times_times_int @ A @ B )
% 4.98/5.24 != zero_zero_int )
% 4.98/5.24 => ( ( A != zero_zero_int )
% 4.98/5.24 & ( B != zero_zero_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_not_zero
% 4.98/5.24 thf(fact_1643_divisors__zero,axiom,
% 4.98/5.24 ! [A: complex,B: complex] :
% 4.98/5.24 ( ( ( times_times_complex @ A @ B )
% 4.98/5.24 = zero_zero_complex )
% 4.98/5.24 => ( ( A = zero_zero_complex )
% 4.98/5.24 | ( B = zero_zero_complex ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divisors_zero
% 4.98/5.24 thf(fact_1644_divisors__zero,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ( times_times_real @ A @ B )
% 4.98/5.24 = zero_zero_real )
% 4.98/5.24 => ( ( A = zero_zero_real )
% 4.98/5.24 | ( B = zero_zero_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divisors_zero
% 4.98/5.24 thf(fact_1645_divisors__zero,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ( times_times_rat @ A @ B )
% 4.98/5.24 = zero_zero_rat )
% 4.98/5.24 => ( ( A = zero_zero_rat )
% 4.98/5.24 | ( B = zero_zero_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divisors_zero
% 4.98/5.24 thf(fact_1646_divisors__zero,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ A @ B )
% 4.98/5.24 = zero_zero_nat )
% 4.98/5.24 => ( ( A = zero_zero_nat )
% 4.98/5.24 | ( B = zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divisors_zero
% 4.98/5.24 thf(fact_1647_divisors__zero,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ( times_times_int @ A @ B )
% 4.98/5.24 = zero_zero_int )
% 4.98/5.24 => ( ( A = zero_zero_int )
% 4.98/5.24 | ( B = zero_zero_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divisors_zero
% 4.98/5.24 thf(fact_1648_no__zero__divisors,axiom,
% 4.98/5.24 ! [A: complex,B: complex] :
% 4.98/5.24 ( ( A != zero_zero_complex )
% 4.98/5.24 => ( ( B != zero_zero_complex )
% 4.98/5.24 => ( ( times_times_complex @ A @ B )
% 4.98/5.24 != zero_zero_complex ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % no_zero_divisors
% 4.98/5.24 thf(fact_1649_no__zero__divisors,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( A != zero_zero_real )
% 4.98/5.24 => ( ( B != zero_zero_real )
% 4.98/5.24 => ( ( times_times_real @ A @ B )
% 4.98/5.24 != zero_zero_real ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % no_zero_divisors
% 4.98/5.24 thf(fact_1650_no__zero__divisors,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( A != zero_zero_rat )
% 4.98/5.24 => ( ( B != zero_zero_rat )
% 4.98/5.24 => ( ( times_times_rat @ A @ B )
% 4.98/5.24 != zero_zero_rat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % no_zero_divisors
% 4.98/5.24 thf(fact_1651_no__zero__divisors,axiom,
% 4.98/5.24 ! [A: nat,B: nat] :
% 4.98/5.24 ( ( A != zero_zero_nat )
% 4.98/5.24 => ( ( B != zero_zero_nat )
% 4.98/5.24 => ( ( times_times_nat @ A @ B )
% 4.98/5.24 != zero_zero_nat ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % no_zero_divisors
% 4.98/5.24 thf(fact_1652_no__zero__divisors,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( A != zero_zero_int )
% 4.98/5.24 => ( ( B != zero_zero_int )
% 4.98/5.24 => ( ( times_times_int @ A @ B )
% 4.98/5.24 != zero_zero_int ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % no_zero_divisors
% 4.98/5.24 thf(fact_1653_mult__left__cancel,axiom,
% 4.98/5.24 ! [C: complex,A: complex,B: complex] :
% 4.98/5.24 ( ( C != zero_zero_complex )
% 4.98/5.24 => ( ( ( times_times_complex @ C @ A )
% 4.98/5.24 = ( times_times_complex @ C @ B ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_cancel
% 4.98/5.24 thf(fact_1654_mult__left__cancel,axiom,
% 4.98/5.24 ! [C: real,A: real,B: real] :
% 4.98/5.24 ( ( C != zero_zero_real )
% 4.98/5.24 => ( ( ( times_times_real @ C @ A )
% 4.98/5.24 = ( times_times_real @ C @ B ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_cancel
% 4.98/5.24 thf(fact_1655_mult__left__cancel,axiom,
% 4.98/5.24 ! [C: rat,A: rat,B: rat] :
% 4.98/5.24 ( ( C != zero_zero_rat )
% 4.98/5.24 => ( ( ( times_times_rat @ C @ A )
% 4.98/5.24 = ( times_times_rat @ C @ B ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_cancel
% 4.98/5.24 thf(fact_1656_mult__left__cancel,axiom,
% 4.98/5.24 ! [C: nat,A: nat,B: nat] :
% 4.98/5.24 ( ( C != zero_zero_nat )
% 4.98/5.24 => ( ( ( times_times_nat @ C @ A )
% 4.98/5.24 = ( times_times_nat @ C @ B ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_cancel
% 4.98/5.24 thf(fact_1657_mult__left__cancel,axiom,
% 4.98/5.24 ! [C: int,A: int,B: int] :
% 4.98/5.24 ( ( C != zero_zero_int )
% 4.98/5.24 => ( ( ( times_times_int @ C @ A )
% 4.98/5.24 = ( times_times_int @ C @ B ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_cancel
% 4.98/5.24 thf(fact_1658_mult__right__cancel,axiom,
% 4.98/5.24 ! [C: complex,A: complex,B: complex] :
% 4.98/5.24 ( ( C != zero_zero_complex )
% 4.98/5.24 => ( ( ( times_times_complex @ A @ C )
% 4.98/5.24 = ( times_times_complex @ B @ C ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_cancel
% 4.98/5.24 thf(fact_1659_mult__right__cancel,axiom,
% 4.98/5.24 ! [C: real,A: real,B: real] :
% 4.98/5.24 ( ( C != zero_zero_real )
% 4.98/5.24 => ( ( ( times_times_real @ A @ C )
% 4.98/5.24 = ( times_times_real @ B @ C ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_cancel
% 4.98/5.24 thf(fact_1660_mult__right__cancel,axiom,
% 4.98/5.24 ! [C: rat,A: rat,B: rat] :
% 4.98/5.24 ( ( C != zero_zero_rat )
% 4.98/5.24 => ( ( ( times_times_rat @ A @ C )
% 4.98/5.24 = ( times_times_rat @ B @ C ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_cancel
% 4.98/5.24 thf(fact_1661_mult__right__cancel,axiom,
% 4.98/5.24 ! [C: nat,A: nat,B: nat] :
% 4.98/5.24 ( ( C != zero_zero_nat )
% 4.98/5.24 => ( ( ( times_times_nat @ A @ C )
% 4.98/5.24 = ( times_times_nat @ B @ C ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_cancel
% 4.98/5.24 thf(fact_1662_mult__right__cancel,axiom,
% 4.98/5.24 ! [C: int,A: int,B: int] :
% 4.98/5.24 ( ( C != zero_zero_int )
% 4.98/5.24 => ( ( ( times_times_int @ A @ C )
% 4.98/5.24 = ( times_times_int @ B @ C ) )
% 4.98/5.24 = ( A = B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_cancel
% 4.98/5.24 thf(fact_1663_comm__monoid__mult__class_Omult__1,axiom,
% 4.98/5.24 ! [A: complex] :
% 4.98/5.24 ( ( times_times_complex @ one_one_complex @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % comm_monoid_mult_class.mult_1
% 4.98/5.24 thf(fact_1664_comm__monoid__mult__class_Omult__1,axiom,
% 4.98/5.24 ! [A: real] :
% 4.98/5.24 ( ( times_times_real @ one_one_real @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % comm_monoid_mult_class.mult_1
% 4.98/5.24 thf(fact_1665_comm__monoid__mult__class_Omult__1,axiom,
% 4.98/5.24 ! [A: rat] :
% 4.98/5.24 ( ( times_times_rat @ one_one_rat @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % comm_monoid_mult_class.mult_1
% 4.98/5.24 thf(fact_1666_comm__monoid__mult__class_Omult__1,axiom,
% 4.98/5.24 ! [A: nat] :
% 4.98/5.24 ( ( times_times_nat @ one_one_nat @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % comm_monoid_mult_class.mult_1
% 4.98/5.24 thf(fact_1667_comm__monoid__mult__class_Omult__1,axiom,
% 4.98/5.24 ! [A: int] :
% 4.98/5.24 ( ( times_times_int @ one_one_int @ A )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % comm_monoid_mult_class.mult_1
% 4.98/5.24 thf(fact_1668_mult_Ocomm__neutral,axiom,
% 4.98/5.24 ! [A: complex] :
% 4.98/5.24 ( ( times_times_complex @ A @ one_one_complex )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.comm_neutral
% 4.98/5.24 thf(fact_1669_mult_Ocomm__neutral,axiom,
% 4.98/5.24 ! [A: real] :
% 4.98/5.24 ( ( times_times_real @ A @ one_one_real )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.comm_neutral
% 4.98/5.24 thf(fact_1670_mult_Ocomm__neutral,axiom,
% 4.98/5.24 ! [A: rat] :
% 4.98/5.24 ( ( times_times_rat @ A @ one_one_rat )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.comm_neutral
% 4.98/5.24 thf(fact_1671_mult_Ocomm__neutral,axiom,
% 4.98/5.24 ! [A: nat] :
% 4.98/5.24 ( ( times_times_nat @ A @ one_one_nat )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.comm_neutral
% 4.98/5.24 thf(fact_1672_mult_Ocomm__neutral,axiom,
% 4.98/5.24 ! [A: int] :
% 4.98/5.24 ( ( times_times_int @ A @ one_one_int )
% 4.98/5.24 = A ) ).
% 4.98/5.24
% 4.98/5.24 % mult.comm_neutral
% 4.98/5.24 thf(fact_1673_ring__class_Oring__distribs_I2_J,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ring_class.ring_distribs(2)
% 4.98/5.24 thf(fact_1674_ring__class_Oring__distribs_I2_J,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ring_class.ring_distribs(2)
% 4.98/5.24 thf(fact_1675_ring__class_Oring__distribs_I2_J,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ring_class.ring_distribs(2)
% 4.98/5.24 thf(fact_1676_ring__class_Oring__distribs_I1_J,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.98/5.24 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ring_class.ring_distribs(1)
% 4.98/5.24 thf(fact_1677_ring__class_Oring__distribs_I1_J,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.24 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ring_class.ring_distribs(1)
% 4.98/5.24 thf(fact_1678_ring__class_Oring__distribs_I1_J,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.98/5.24 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % ring_class.ring_distribs(1)
% 4.98/5.24 thf(fact_1679_comm__semiring__class_Odistrib,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % comm_semiring_class.distrib
% 4.98/5.24 thf(fact_1680_comm__semiring__class_Odistrib,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % comm_semiring_class.distrib
% 4.98/5.24 thf(fact_1681_comm__semiring__class_Odistrib,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % comm_semiring_class.distrib
% 4.98/5.24 thf(fact_1682_comm__semiring__class_Odistrib,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % comm_semiring_class.distrib
% 4.98/5.24 thf(fact_1683_distrib__left,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.98/5.24 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left
% 4.98/5.24 thf(fact_1684_distrib__left,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.24 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left
% 4.98/5.24 thf(fact_1685_distrib__left,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left
% 4.98/5.24 thf(fact_1686_distrib__left,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.98/5.24 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_left
% 4.98/5.24 thf(fact_1687_distrib__right,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right
% 4.98/5.24 thf(fact_1688_distrib__right,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right
% 4.98/5.24 thf(fact_1689_distrib__right,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right
% 4.98/5.24 thf(fact_1690_distrib__right,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.24 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % distrib_right
% 4.98/5.24 thf(fact_1691_combine__common__factor,axiom,
% 4.98/5.24 ! [A: real,E2: real,B: real,C: real] :
% 4.98/5.24 ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 4.98/5.24 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % combine_common_factor
% 4.98/5.24 thf(fact_1692_combine__common__factor,axiom,
% 4.98/5.24 ! [A: rat,E2: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 4.98/5.24 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % combine_common_factor
% 4.98/5.24 thf(fact_1693_combine__common__factor,axiom,
% 4.98/5.24 ! [A: nat,E2: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % combine_common_factor
% 4.98/5.24 thf(fact_1694_combine__common__factor,axiom,
% 4.98/5.24 ! [A: int,E2: int,B: int,C: int] :
% 4.98/5.24 ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 4.98/5.24 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 4.98/5.24
% 4.98/5.24 % combine_common_factor
% 4.98/5.24 thf(fact_1695_times__divide__times__eq,axiom,
% 4.98/5.24 ! [X2: complex,Y: complex,Z: complex,W: complex] :
% 4.98/5.24 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_times_eq
% 4.98/5.24 thf(fact_1696_times__divide__times__eq,axiom,
% 4.98/5.24 ! [X2: real,Y: real,Z: real,W: real] :
% 4.98/5.24 ( ( times_times_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 4.98/5.24 = ( divide_divide_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_times_eq
% 4.98/5.24 thf(fact_1697_times__divide__times__eq,axiom,
% 4.98/5.24 ! [X2: rat,Y: rat,Z: rat,W: rat] :
% 4.98/5.24 ( ( times_times_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 4.98/5.24 = ( divide_divide_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % times_divide_times_eq
% 4.98/5.24 thf(fact_1698_divide__divide__times__eq,axiom,
% 4.98/5.24 ! [X2: complex,Y: complex,Z: complex,W: complex] :
% 4.98/5.24 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 4.98/5.24 = ( divide1717551699836669952omplex @ ( times_times_complex @ X2 @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_times_eq
% 4.98/5.24 thf(fact_1699_divide__divide__times__eq,axiom,
% 4.98/5.24 ! [X2: real,Y: real,Z: real,W: real] :
% 4.98/5.24 ( ( divide_divide_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 4.98/5.24 = ( divide_divide_real @ ( times_times_real @ X2 @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_times_eq
% 4.98/5.24 thf(fact_1700_divide__divide__times__eq,axiom,
% 4.98/5.24 ! [X2: rat,Y: rat,Z: rat,W: rat] :
% 4.98/5.24 ( ( divide_divide_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 4.98/5.24 = ( divide_divide_rat @ ( times_times_rat @ X2 @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_times_eq
% 4.98/5.24 thf(fact_1701_divide__divide__eq__left_H,axiom,
% 4.98/5.24 ! [A: complex,B: complex,C: complex] :
% 4.98/5.24 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 4.98/5.24 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_left'
% 4.98/5.24 thf(fact_1702_divide__divide__eq__left_H,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 4.98/5.24 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_left'
% 4.98/5.24 thf(fact_1703_divide__divide__eq__left_H,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 4.98/5.24 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % divide_divide_eq_left'
% 4.98/5.24 thf(fact_1704_power__commutes,axiom,
% 4.98/5.24 ! [A: complex,N2: nat] :
% 4.98/5.24 ( ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A )
% 4.98/5.24 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commutes
% 4.98/5.24 thf(fact_1705_power__commutes,axiom,
% 4.98/5.24 ! [A: real,N2: nat] :
% 4.98/5.24 ( ( times_times_real @ ( power_power_real @ A @ N2 ) @ A )
% 4.98/5.24 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commutes
% 4.98/5.24 thf(fact_1706_power__commutes,axiom,
% 4.98/5.24 ! [A: rat,N2: nat] :
% 4.98/5.24 ( ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ A )
% 4.98/5.24 = ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commutes
% 4.98/5.24 thf(fact_1707_power__commutes,axiom,
% 4.98/5.24 ! [A: nat,N2: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
% 4.98/5.24 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commutes
% 4.98/5.24 thf(fact_1708_power__commutes,axiom,
% 4.98/5.24 ! [A: int,N2: nat] :
% 4.98/5.24 ( ( times_times_int @ ( power_power_int @ A @ N2 ) @ A )
% 4.98/5.24 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commutes
% 4.98/5.24 thf(fact_1709_power__mult__distrib,axiom,
% 4.98/5.24 ! [A: complex,B: complex,N2: nat] :
% 4.98/5.24 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N2 )
% 4.98/5.24 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult_distrib
% 4.98/5.24 thf(fact_1710_power__mult__distrib,axiom,
% 4.98/5.24 ! [A: real,B: real,N2: nat] :
% 4.98/5.24 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N2 )
% 4.98/5.24 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult_distrib
% 4.98/5.24 thf(fact_1711_power__mult__distrib,axiom,
% 4.98/5.24 ! [A: rat,B: rat,N2: nat] :
% 4.98/5.24 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N2 )
% 4.98/5.24 = ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult_distrib
% 4.98/5.24 thf(fact_1712_power__mult__distrib,axiom,
% 4.98/5.24 ! [A: nat,B: nat,N2: nat] :
% 4.98/5.24 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
% 4.98/5.24 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult_distrib
% 4.98/5.24 thf(fact_1713_power__mult__distrib,axiom,
% 4.98/5.24 ! [A: int,B: int,N2: nat] :
% 4.98/5.24 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N2 )
% 4.98/5.24 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult_distrib
% 4.98/5.24 thf(fact_1714_power__commuting__commutes,axiom,
% 4.98/5.24 ! [X2: complex,Y: complex,N2: nat] :
% 4.98/5.24 ( ( ( times_times_complex @ X2 @ Y )
% 4.98/5.24 = ( times_times_complex @ Y @ X2 ) )
% 4.98/5.24 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N2 ) @ Y )
% 4.98/5.24 = ( times_times_complex @ Y @ ( power_power_complex @ X2 @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commuting_commutes
% 4.98/5.24 thf(fact_1715_power__commuting__commutes,axiom,
% 4.98/5.24 ! [X2: real,Y: real,N2: nat] :
% 4.98/5.24 ( ( ( times_times_real @ X2 @ Y )
% 4.98/5.24 = ( times_times_real @ Y @ X2 ) )
% 4.98/5.24 => ( ( times_times_real @ ( power_power_real @ X2 @ N2 ) @ Y )
% 4.98/5.24 = ( times_times_real @ Y @ ( power_power_real @ X2 @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commuting_commutes
% 4.98/5.24 thf(fact_1716_power__commuting__commutes,axiom,
% 4.98/5.24 ! [X2: rat,Y: rat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_rat @ X2 @ Y )
% 4.98/5.24 = ( times_times_rat @ Y @ X2 ) )
% 4.98/5.24 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N2 ) @ Y )
% 4.98/5.24 = ( times_times_rat @ Y @ ( power_power_rat @ X2 @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commuting_commutes
% 4.98/5.24 thf(fact_1717_power__commuting__commutes,axiom,
% 4.98/5.24 ! [X2: nat,Y: nat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ X2 @ Y )
% 4.98/5.24 = ( times_times_nat @ Y @ X2 ) )
% 4.98/5.24 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N2 ) @ Y )
% 4.98/5.24 = ( times_times_nat @ Y @ ( power_power_nat @ X2 @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commuting_commutes
% 4.98/5.24 thf(fact_1718_power__commuting__commutes,axiom,
% 4.98/5.24 ! [X2: int,Y: int,N2: nat] :
% 4.98/5.24 ( ( ( times_times_int @ X2 @ Y )
% 4.98/5.24 = ( times_times_int @ Y @ X2 ) )
% 4.98/5.24 => ( ( times_times_int @ ( power_power_int @ X2 @ N2 ) @ Y )
% 4.98/5.24 = ( times_times_int @ Y @ ( power_power_int @ X2 @ N2 ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_commuting_commutes
% 4.98/5.24 thf(fact_1719_Suc__mult__cancel1,axiom,
% 4.98/5.24 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 4.98/5.24 = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 4.98/5.24 = ( M = N2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % Suc_mult_cancel1
% 4.98/5.24 thf(fact_1720_power__mult,axiom,
% 4.98/5.24 ! [A: nat,M: nat,N2: nat] :
% 4.98/5.24 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
% 4.98/5.24 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult
% 4.98/5.24 thf(fact_1721_power__mult,axiom,
% 4.98/5.24 ! [A: int,M: nat,N2: nat] :
% 4.98/5.24 ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
% 4.98/5.24 = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult
% 4.98/5.24 thf(fact_1722_power__mult,axiom,
% 4.98/5.24 ! [A: real,M: nat,N2: nat] :
% 4.98/5.24 ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
% 4.98/5.24 = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult
% 4.98/5.24 thf(fact_1723_power__mult,axiom,
% 4.98/5.24 ! [A: complex,M: nat,N2: nat] :
% 4.98/5.24 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
% 4.98/5.24 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % power_mult
% 4.98/5.24 thf(fact_1724_mult__0,axiom,
% 4.98/5.24 ! [N2: nat] :
% 4.98/5.24 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 4.98/5.24 = zero_zero_nat ) ).
% 4.98/5.24
% 4.98/5.24 % mult_0
% 4.98/5.24 thf(fact_1725_nat__mult__eq__cancel__disj,axiom,
% 4.98/5.24 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.24 ( ( ( times_times_nat @ K @ M )
% 4.98/5.24 = ( times_times_nat @ K @ N2 ) )
% 4.98/5.24 = ( ( K = zero_zero_nat )
% 4.98/5.24 | ( M = N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_eq_cancel_disj
% 4.98/5.24 thf(fact_1726_le__cube,axiom,
% 4.98/5.24 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % le_cube
% 4.98/5.24 thf(fact_1727_le__square,axiom,
% 4.98/5.24 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 4.98/5.24
% 4.98/5.24 % le_square
% 4.98/5.24 thf(fact_1728_mult__le__mono,axiom,
% 4.98/5.24 ! [I3: nat,J: nat,K: nat,L: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.24 => ( ( ord_less_eq_nat @ K @ L )
% 4.98/5.24 => ( ord_less_eq_nat @ ( times_times_nat @ I3 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_le_mono
% 4.98/5.24 thf(fact_1729_mult__le__mono1,axiom,
% 4.98/5.24 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.24 => ( ord_less_eq_nat @ ( times_times_nat @ I3 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_le_mono1
% 4.98/5.24 thf(fact_1730_mult__le__mono2,axiom,
% 4.98/5.24 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ I3 @ J )
% 4.98/5.24 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I3 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_le_mono2
% 4.98/5.24 thf(fact_1731_add__mult__distrib,axiom,
% 4.98/5.24 ! [M: nat,N2: nat,K: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_mult_distrib
% 4.98/5.24 thf(fact_1732_add__mult__distrib2,axiom,
% 4.98/5.24 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.24 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % add_mult_distrib2
% 4.98/5.24 thf(fact_1733_left__add__mult__distrib,axiom,
% 4.98/5.24 ! [I3: nat,U: nat,J: nat,K: nat] :
% 4.98/5.24 ( ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 4.98/5.24 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I3 @ J ) @ U ) @ K ) ) ).
% 4.98/5.24
% 4.98/5.24 % left_add_mult_distrib
% 4.98/5.24 thf(fact_1734_nat__mult__1,axiom,
% 4.98/5.24 ! [N2: nat] :
% 4.98/5.24 ( ( times_times_nat @ one_one_nat @ N2 )
% 4.98/5.24 = N2 ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_1
% 4.98/5.24 thf(fact_1735_nat__mult__1__right,axiom,
% 4.98/5.24 ! [N2: nat] :
% 4.98/5.24 ( ( times_times_nat @ N2 @ one_one_nat )
% 4.98/5.24 = N2 ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_1_right
% 4.98/5.24 thf(fact_1736_div__mult2__eq,axiom,
% 4.98/5.24 ! [M: nat,N2: nat,Q2: nat] :
% 4.98/5.24 ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
% 4.98/5.24 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) ).
% 4.98/5.24
% 4.98/5.24 % div_mult2_eq
% 4.98/5.24 thf(fact_1737_nat__mult__max__left,axiom,
% 4.98/5.24 ! [M: nat,N2: nat,Q2: nat] :
% 4.98/5.24 ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q2 )
% 4.98/5.24 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N2 @ Q2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_max_left
% 4.98/5.24 thf(fact_1738_nat__mult__max__right,axiom,
% 4.98/5.24 ! [M: nat,N2: nat,Q2: nat] :
% 4.98/5.24 ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q2 ) )
% 4.98/5.24 = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % nat_mult_max_right
% 4.98/5.24 thf(fact_1739_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 4.98/5.24 ! [C: nat,A: nat,B: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.24 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 4.98/5.24 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 4.98/5.24 thf(fact_1740_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 4.98/5.24 ! [C: int,A: int,B: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.24 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 4.98/5.24 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 4.98/5.24 thf(fact_1741_mult__mono,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_real @ C @ D )
% 4.98/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.24 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_mono
% 4.98/5.24 thf(fact_1742_mult__mono,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_rat @ C @ D )
% 4.98/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_mono
% 4.98/5.24 thf(fact_1743_mult__mono,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_nat @ C @ D )
% 4.98/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.24 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_mono
% 4.98/5.24 thf(fact_1744_mult__mono,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_int @ C @ D )
% 4.98/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.24 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_mono
% 4.98/5.24 thf(fact_1745_mult__mono_H,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_real @ C @ D )
% 4.98/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.24 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_mono'
% 4.98/5.24 thf(fact_1746_mult__mono_H,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_rat @ C @ D )
% 4.98/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_mono'
% 4.98/5.24 thf(fact_1747_mult__mono_H,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_nat @ C @ D )
% 4.98/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.24 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_mono'
% 4.98/5.24 thf(fact_1748_mult__mono_H,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_int @ C @ D )
% 4.98/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.24 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_mono'
% 4.98/5.24 thf(fact_1749_zero__le__square,axiom,
% 4.98/5.24 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 4.98/5.24
% 4.98/5.24 % zero_le_square
% 4.98/5.24 thf(fact_1750_zero__le__square,axiom,
% 4.98/5.24 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 4.98/5.24
% 4.98/5.24 % zero_le_square
% 4.98/5.24 thf(fact_1751_zero__le__square,axiom,
% 4.98/5.24 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 4.98/5.24
% 4.98/5.24 % zero_le_square
% 4.98/5.24 thf(fact_1752_split__mult__pos__le,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.24 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 4.98/5.24 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.24 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 4.98/5.24 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % split_mult_pos_le
% 4.98/5.24 thf(fact_1753_split__mult__pos__le,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.24 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 4.98/5.24 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.24 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 4.98/5.24 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % split_mult_pos_le
% 4.98/5.24 thf(fact_1754_split__mult__pos__le,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.24 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 4.98/5.24 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.24 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 4.98/5.24 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % split_mult_pos_le
% 4.98/5.24 thf(fact_1755_mult__left__mono__neg,axiom,
% 4.98/5.24 ! [B: real,A: real,C: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ B @ A )
% 4.98/5.24 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.24 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_mono_neg
% 4.98/5.24 thf(fact_1756_mult__left__mono__neg,axiom,
% 4.98/5.24 ! [B: rat,A: rat,C: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.24 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_mono_neg
% 4.98/5.24 thf(fact_1757_mult__left__mono__neg,axiom,
% 4.98/5.24 ! [B: int,A: int,C: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ B @ A )
% 4.98/5.24 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.24 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_mono_neg
% 4.98/5.24 thf(fact_1758_mult__nonpos__nonpos,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.24 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.98/5.24 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_nonpos_nonpos
% 4.98/5.24 thf(fact_1759_mult__nonpos__nonpos,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.24 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.98/5.24 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_nonpos_nonpos
% 4.98/5.24 thf(fact_1760_mult__nonpos__nonpos,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.24 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.98/5.24 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_nonpos_nonpos
% 4.98/5.24 thf(fact_1761_mult__left__mono,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.24 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_mono
% 4.98/5.24 thf(fact_1762_mult__left__mono,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_mono
% 4.98/5.24 thf(fact_1763_mult__left__mono,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.24 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_mono
% 4.98/5.24 thf(fact_1764_mult__left__mono,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.24 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_left_mono
% 4.98/5.24 thf(fact_1765_mult__right__mono__neg,axiom,
% 4.98/5.24 ! [B: real,A: real,C: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ B @ A )
% 4.98/5.24 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.24 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_mono_neg
% 4.98/5.24 thf(fact_1766_mult__right__mono__neg,axiom,
% 4.98/5.24 ! [B: rat,A: rat,C: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.24 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_mono_neg
% 4.98/5.24 thf(fact_1767_mult__right__mono__neg,axiom,
% 4.98/5.24 ! [B: int,A: int,C: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ B @ A )
% 4.98/5.24 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.24 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_mono_neg
% 4.98/5.24 thf(fact_1768_mult__right__mono,axiom,
% 4.98/5.24 ! [A: real,B: real,C: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.24 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_mono
% 4.98/5.24 thf(fact_1769_mult__right__mono,axiom,
% 4.98/5.24 ! [A: rat,B: rat,C: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.24 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_mono
% 4.98/5.24 thf(fact_1770_mult__right__mono,axiom,
% 4.98/5.24 ! [A: nat,B: nat,C: nat] :
% 4.98/5.24 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.24 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_mono
% 4.98/5.24 thf(fact_1771_mult__right__mono,axiom,
% 4.98/5.24 ! [A: int,B: int,C: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.24 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.24 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_right_mono
% 4.98/5.24 thf(fact_1772_mult__le__0__iff,axiom,
% 4.98/5.24 ! [A: real,B: real] :
% 4.98/5.24 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 4.98/5.24 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.24 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 4.98/5.24 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.24 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_le_0_iff
% 4.98/5.24 thf(fact_1773_mult__le__0__iff,axiom,
% 4.98/5.24 ! [A: rat,B: rat] :
% 4.98/5.24 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 4.98/5.24 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.24 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 4.98/5.24 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.24 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.98/5.24
% 4.98/5.24 % mult_le_0_iff
% 4.98/5.24 thf(fact_1774_mult__le__0__iff,axiom,
% 4.98/5.24 ! [A: int,B: int] :
% 4.98/5.24 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 4.98/5.24 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.24 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 4.98/5.24 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.24 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_0_iff
% 4.98/5.25 thf(fact_1775_split__mult__neg__le,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.25 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 4.98/5.25 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.25 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 4.98/5.25
% 4.98/5.25 % split_mult_neg_le
% 4.98/5.25 thf(fact_1776_split__mult__neg__le,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.25 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 4.98/5.25 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.25 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 4.98/5.25
% 4.98/5.25 % split_mult_neg_le
% 4.98/5.25 thf(fact_1777_split__mult__neg__le,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.25 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 4.98/5.25 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.98/5.25 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 4.98/5.25 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 4.98/5.25
% 4.98/5.25 % split_mult_neg_le
% 4.98/5.25 thf(fact_1778_split__mult__neg__le,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.25 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 4.98/5.25 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.25 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 4.98/5.25
% 4.98/5.25 % split_mult_neg_le
% 4.98/5.25 thf(fact_1779_mult__nonneg__nonneg,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.25 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonneg
% 4.98/5.25 thf(fact_1780_mult__nonneg__nonneg,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.25 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonneg
% 4.98/5.25 thf(fact_1781_mult__nonneg__nonneg,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.25 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonneg
% 4.98/5.25 thf(fact_1782_mult__nonneg__nonneg,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.25 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonneg
% 4.98/5.25 thf(fact_1783_mult__nonneg__nonpos,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonpos
% 4.98/5.25 thf(fact_1784_mult__nonneg__nonpos,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonpos
% 4.98/5.25 thf(fact_1785_mult__nonneg__nonpos,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.98/5.25 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonpos
% 4.98/5.25 thf(fact_1786_mult__nonneg__nonpos,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonpos
% 4.98/5.25 thf(fact_1787_mult__nonpos__nonneg,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonpos_nonneg
% 4.98/5.25 thf(fact_1788_mult__nonpos__nonneg,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonpos_nonneg
% 4.98/5.25 thf(fact_1789_mult__nonpos__nonneg,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.25 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonpos_nonneg
% 4.98/5.25 thf(fact_1790_mult__nonpos__nonneg,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonpos_nonneg
% 4.98/5.25 thf(fact_1791_mult__nonneg__nonpos2,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonpos2
% 4.98/5.25 thf(fact_1792_mult__nonneg__nonpos2,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonpos2
% 4.98/5.25 thf(fact_1793_mult__nonneg__nonpos2,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 4.98/5.25 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonpos2
% 4.98/5.25 thf(fact_1794_mult__nonneg__nonpos2,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_nonneg_nonpos2
% 4.98/5.25 thf(fact_1795_zero__le__mult__iff,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.25 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 4.98/5.25 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 4.98/5.25 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_le_mult_iff
% 4.98/5.25 thf(fact_1796_zero__le__mult__iff,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.25 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 4.98/5.25 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 4.98/5.25 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_le_mult_iff
% 4.98/5.25 thf(fact_1797_zero__le__mult__iff,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.25 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 4.98/5.25 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.25 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_le_mult_iff
% 4.98/5.25 thf(fact_1798_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.98/5.25 thf(fact_1799_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.98/5.25 thf(fact_1800_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.98/5.25 thf(fact_1801_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % ordered_comm_semiring_class.comm_mult_left_mono
% 4.98/5.25 thf(fact_1802_mult__neg__neg,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_neg_neg
% 4.98/5.25 thf(fact_1803_mult__neg__neg,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_neg_neg
% 4.98/5.25 thf(fact_1804_mult__neg__neg,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.25 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_neg_neg
% 4.98/5.25 thf(fact_1805_not__square__less__zero,axiom,
% 4.98/5.25 ! [A: real] :
% 4.98/5.25 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 4.98/5.25
% 4.98/5.25 % not_square_less_zero
% 4.98/5.25 thf(fact_1806_not__square__less__zero,axiom,
% 4.98/5.25 ! [A: rat] :
% 4.98/5.25 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 4.98/5.25
% 4.98/5.25 % not_square_less_zero
% 4.98/5.25 thf(fact_1807_not__square__less__zero,axiom,
% 4.98/5.25 ! [A: int] :
% 4.98/5.25 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 4.98/5.25
% 4.98/5.25 % not_square_less_zero
% 4.98/5.25 thf(fact_1808_mult__less__0__iff,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 & ( ord_less_real @ B @ zero_zero_real ) )
% 4.98/5.25 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.25 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_0_iff
% 4.98/5.25 thf(fact_1809_mult__less__0__iff,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 4.98/5.25 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.25 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_0_iff
% 4.98/5.25 thf(fact_1810_mult__less__0__iff,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 & ( ord_less_int @ B @ zero_zero_int ) )
% 4.98/5.25 | ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.25 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_0_iff
% 4.98/5.25 thf(fact_1811_mult__neg__pos,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_neg_pos
% 4.98/5.25 thf(fact_1812_mult__neg__pos,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_neg_pos
% 4.98/5.25 thf(fact_1813_mult__neg__pos,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_nat @ A @ zero_zero_nat )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_neg_pos
% 4.98/5.25 thf(fact_1814_mult__neg__pos,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_neg_pos
% 4.98/5.25 thf(fact_1815_mult__pos__neg,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_neg
% 4.98/5.25 thf(fact_1816_mult__pos__neg,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_neg
% 4.98/5.25 thf(fact_1817_mult__pos__neg,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_neg
% 4.98/5.25 thf(fact_1818_mult__pos__neg,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_neg
% 4.98/5.25 thf(fact_1819_mult__pos__pos,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.98/5.25 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_pos
% 4.98/5.25 thf(fact_1820_mult__pos__pos,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.98/5.25 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_pos
% 4.98/5.25 thf(fact_1821_mult__pos__pos,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.25 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_pos
% 4.98/5.25 thf(fact_1822_mult__pos__pos,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.25 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_pos
% 4.98/5.25 thf(fact_1823_mult__pos__neg2,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_real @ B @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_neg2
% 4.98/5.25 thf(fact_1824_mult__pos__neg2,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_neg2
% 4.98/5.25 thf(fact_1825_mult__pos__neg2,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_neg2
% 4.98/5.25 thf(fact_1826_mult__pos__neg2,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_pos_neg2
% 4.98/5.25 thf(fact_1827_zero__less__mult__iff,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 & ( ord_less_real @ zero_zero_real @ B ) )
% 4.98/5.25 | ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.25 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_iff
% 4.98/5.25 thf(fact_1828_zero__less__mult__iff,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 4.98/5.25 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.25 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_iff
% 4.98/5.25 thf(fact_1829_zero__less__mult__iff,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 & ( ord_less_int @ zero_zero_int @ B ) )
% 4.98/5.25 | ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.25 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_iff
% 4.98/5.25 thf(fact_1830_zero__less__mult__pos,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_pos
% 4.98/5.25 thf(fact_1831_zero__less__mult__pos,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_pos
% 4.98/5.25 thf(fact_1832_zero__less__mult__pos,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_pos
% 4.98/5.25 thf(fact_1833_zero__less__mult__pos,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_pos
% 4.98/5.25 thf(fact_1834_zero__less__mult__pos2,axiom,
% 4.98/5.25 ! [B: real,A: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_pos2
% 4.98/5.25 thf(fact_1835_zero__less__mult__pos2,axiom,
% 4.98/5.25 ! [B: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_pos2
% 4.98/5.25 thf(fact_1836_zero__less__mult__pos2,axiom,
% 4.98/5.25 ! [B: nat,A: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_pos2
% 4.98/5.25 thf(fact_1837_zero__less__mult__pos2,axiom,
% 4.98/5.25 ! [B: int,A: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zero_less_mult_pos2
% 4.98/5.25 thf(fact_1838_mult__less__cancel__left__neg,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ord_less_real @ B @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_neg
% 4.98/5.25 thf(fact_1839_mult__less__cancel__left__neg,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ord_less_rat @ B @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_neg
% 4.98/5.25 thf(fact_1840_mult__less__cancel__left__neg,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ord_less_int @ B @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_neg
% 4.98/5.25 thf(fact_1841_mult__less__cancel__left__pos,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ord_less_real @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_pos
% 4.98/5.25 thf(fact_1842_mult__less__cancel__left__pos,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ord_less_rat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_pos
% 4.98/5.25 thf(fact_1843_mult__less__cancel__left__pos,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ord_less_int @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_pos
% 4.98/5.25 thf(fact_1844_mult__strict__left__mono__neg,axiom,
% 4.98/5.25 ! [B: real,A: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ B @ A )
% 4.98/5.25 => ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_left_mono_neg
% 4.98/5.25 thf(fact_1845_mult__strict__left__mono__neg,axiom,
% 4.98/5.25 ! [B: rat,A: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ B @ A )
% 4.98/5.25 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_left_mono_neg
% 4.98/5.25 thf(fact_1846_mult__strict__left__mono__neg,axiom,
% 4.98/5.25 ! [B: int,A: int,C: int] :
% 4.98/5.25 ( ( ord_less_int @ B @ A )
% 4.98/5.25 => ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_left_mono_neg
% 4.98/5.25 thf(fact_1847_mult__strict__left__mono,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_left_mono
% 4.98/5.25 thf(fact_1848_mult__strict__left__mono,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_left_mono
% 4.98/5.25 thf(fact_1849_mult__strict__left__mono,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat] :
% 4.98/5.25 ( ( ord_less_nat @ A @ B )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_left_mono
% 4.98/5.25 thf(fact_1850_mult__strict__left__mono,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int] :
% 4.98/5.25 ( ( ord_less_int @ A @ B )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_left_mono
% 4.98/5.25 thf(fact_1851_mult__less__cancel__left__disj,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 & ( ord_less_real @ A @ B ) )
% 4.98/5.25 | ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 & ( ord_less_real @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_disj
% 4.98/5.25 thf(fact_1852_mult__less__cancel__left__disj,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 & ( ord_less_rat @ A @ B ) )
% 4.98/5.25 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_disj
% 4.98/5.25 thf(fact_1853_mult__less__cancel__left__disj,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 & ( ord_less_int @ A @ B ) )
% 4.98/5.25 | ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 & ( ord_less_int @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left_disj
% 4.98/5.25 thf(fact_1854_mult__strict__right__mono__neg,axiom,
% 4.98/5.25 ! [B: real,A: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ B @ A )
% 4.98/5.25 => ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_right_mono_neg
% 4.98/5.25 thf(fact_1855_mult__strict__right__mono__neg,axiom,
% 4.98/5.25 ! [B: rat,A: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ B @ A )
% 4.98/5.25 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_right_mono_neg
% 4.98/5.25 thf(fact_1856_mult__strict__right__mono__neg,axiom,
% 4.98/5.25 ! [B: int,A: int,C: int] :
% 4.98/5.25 ( ( ord_less_int @ B @ A )
% 4.98/5.25 => ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_right_mono_neg
% 4.98/5.25 thf(fact_1857_mult__strict__right__mono,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_right_mono
% 4.98/5.25 thf(fact_1858_mult__strict__right__mono,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_right_mono
% 4.98/5.25 thf(fact_1859_mult__strict__right__mono,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat] :
% 4.98/5.25 ( ( ord_less_nat @ A @ B )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_right_mono
% 4.98/5.25 thf(fact_1860_mult__strict__right__mono,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int] :
% 4.98/5.25 ( ( ord_less_int @ A @ B )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_right_mono
% 4.98/5.25 thf(fact_1861_mult__less__cancel__right__disj,axiom,
% 4.98/5.25 ! [A: real,C: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 & ( ord_less_real @ A @ B ) )
% 4.98/5.25 | ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 & ( ord_less_real @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right_disj
% 4.98/5.25 thf(fact_1862_mult__less__cancel__right__disj,axiom,
% 4.98/5.25 ! [A: rat,C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 & ( ord_less_rat @ A @ B ) )
% 4.98/5.25 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right_disj
% 4.98/5.25 thf(fact_1863_mult__less__cancel__right__disj,axiom,
% 4.98/5.25 ! [A: int,C: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 & ( ord_less_int @ A @ B ) )
% 4.98/5.25 | ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 & ( ord_less_int @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right_disj
% 4.98/5.25 thf(fact_1864_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.98/5.25 thf(fact_1865_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.98/5.25 thf(fact_1866_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat] :
% 4.98/5.25 ( ( ord_less_nat @ A @ B )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.98/5.25 thf(fact_1867_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int] :
% 4.98/5.25 ( ( ord_less_int @ A @ B )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 4.98/5.25 thf(fact_1868_less__1__mult,axiom,
% 4.98/5.25 ! [M: real,N2: real] :
% 4.98/5.25 ( ( ord_less_real @ one_one_real @ M )
% 4.98/5.25 => ( ( ord_less_real @ one_one_real @ N2 )
% 4.98/5.25 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_1_mult
% 4.98/5.25 thf(fact_1869_less__1__mult,axiom,
% 4.98/5.25 ! [M: rat,N2: rat] :
% 4.98/5.25 ( ( ord_less_rat @ one_one_rat @ M )
% 4.98/5.25 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 4.98/5.25 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_1_mult
% 4.98/5.25 thf(fact_1870_less__1__mult,axiom,
% 4.98/5.25 ! [M: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ one_one_nat @ M )
% 4.98/5.25 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 4.98/5.25 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_1_mult
% 4.98/5.25 thf(fact_1871_less__1__mult,axiom,
% 4.98/5.25 ! [M: int,N2: int] :
% 4.98/5.25 ( ( ord_less_int @ one_one_int @ M )
% 4.98/5.25 => ( ( ord_less_int @ one_one_int @ N2 )
% 4.98/5.25 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_1_mult
% 4.98/5.25 thf(fact_1872_nonzero__eq__divide__eq,axiom,
% 4.98/5.25 ! [C: complex,A: complex,B: complex] :
% 4.98/5.25 ( ( C != zero_zero_complex )
% 4.98/5.25 => ( ( A
% 4.98/5.25 = ( divide1717551699836669952omplex @ B @ C ) )
% 4.98/5.25 = ( ( times_times_complex @ A @ C )
% 4.98/5.25 = B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nonzero_eq_divide_eq
% 4.98/5.25 thf(fact_1873_nonzero__eq__divide__eq,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( C != zero_zero_real )
% 4.98/5.25 => ( ( A
% 4.98/5.25 = ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ( times_times_real @ A @ C )
% 4.98/5.25 = B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nonzero_eq_divide_eq
% 4.98/5.25 thf(fact_1874_nonzero__eq__divide__eq,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( C != zero_zero_rat )
% 4.98/5.25 => ( ( A
% 4.98/5.25 = ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ( times_times_rat @ A @ C )
% 4.98/5.25 = B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nonzero_eq_divide_eq
% 4.98/5.25 thf(fact_1875_nonzero__divide__eq__eq,axiom,
% 4.98/5.25 ! [C: complex,B: complex,A: complex] :
% 4.98/5.25 ( ( C != zero_zero_complex )
% 4.98/5.25 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 4.98/5.25 = A )
% 4.98/5.25 = ( B
% 4.98/5.25 = ( times_times_complex @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nonzero_divide_eq_eq
% 4.98/5.25 thf(fact_1876_nonzero__divide__eq__eq,axiom,
% 4.98/5.25 ! [C: real,B: real,A: real] :
% 4.98/5.25 ( ( C != zero_zero_real )
% 4.98/5.25 => ( ( ( divide_divide_real @ B @ C )
% 4.98/5.25 = A )
% 4.98/5.25 = ( B
% 4.98/5.25 = ( times_times_real @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nonzero_divide_eq_eq
% 4.98/5.25 thf(fact_1877_nonzero__divide__eq__eq,axiom,
% 4.98/5.25 ! [C: rat,B: rat,A: rat] :
% 4.98/5.25 ( ( C != zero_zero_rat )
% 4.98/5.25 => ( ( ( divide_divide_rat @ B @ C )
% 4.98/5.25 = A )
% 4.98/5.25 = ( B
% 4.98/5.25 = ( times_times_rat @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nonzero_divide_eq_eq
% 4.98/5.25 thf(fact_1878_eq__divide__imp,axiom,
% 4.98/5.25 ! [C: complex,A: complex,B: complex] :
% 4.98/5.25 ( ( C != zero_zero_complex )
% 4.98/5.25 => ( ( ( times_times_complex @ A @ C )
% 4.98/5.25 = B )
% 4.98/5.25 => ( A
% 4.98/5.25 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_imp
% 4.98/5.25 thf(fact_1879_eq__divide__imp,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( C != zero_zero_real )
% 4.98/5.25 => ( ( ( times_times_real @ A @ C )
% 4.98/5.25 = B )
% 4.98/5.25 => ( A
% 4.98/5.25 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_imp
% 4.98/5.25 thf(fact_1880_eq__divide__imp,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( C != zero_zero_rat )
% 4.98/5.25 => ( ( ( times_times_rat @ A @ C )
% 4.98/5.25 = B )
% 4.98/5.25 => ( A
% 4.98/5.25 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_imp
% 4.98/5.25 thf(fact_1881_divide__eq__imp,axiom,
% 4.98/5.25 ! [C: complex,B: complex,A: complex] :
% 4.98/5.25 ( ( C != zero_zero_complex )
% 4.98/5.25 => ( ( B
% 4.98/5.25 = ( times_times_complex @ A @ C ) )
% 4.98/5.25 => ( ( divide1717551699836669952omplex @ B @ C )
% 4.98/5.25 = A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_imp
% 4.98/5.25 thf(fact_1882_divide__eq__imp,axiom,
% 4.98/5.25 ! [C: real,B: real,A: real] :
% 4.98/5.25 ( ( C != zero_zero_real )
% 4.98/5.25 => ( ( B
% 4.98/5.25 = ( times_times_real @ A @ C ) )
% 4.98/5.25 => ( ( divide_divide_real @ B @ C )
% 4.98/5.25 = A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_imp
% 4.98/5.25 thf(fact_1883_divide__eq__imp,axiom,
% 4.98/5.25 ! [C: rat,B: rat,A: rat] :
% 4.98/5.25 ( ( C != zero_zero_rat )
% 4.98/5.25 => ( ( B
% 4.98/5.25 = ( times_times_rat @ A @ C ) )
% 4.98/5.25 => ( ( divide_divide_rat @ B @ C )
% 4.98/5.25 = A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_imp
% 4.98/5.25 thf(fact_1884_eq__divide__eq,axiom,
% 4.98/5.25 ! [A: complex,B: complex,C: complex] :
% 4.98/5.25 ( ( A
% 4.98/5.25 = ( divide1717551699836669952omplex @ B @ C ) )
% 4.98/5.25 = ( ( ( C != zero_zero_complex )
% 4.98/5.25 => ( ( times_times_complex @ A @ C )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( C = zero_zero_complex )
% 4.98/5.25 => ( A = zero_zero_complex ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_eq
% 4.98/5.25 thf(fact_1885_eq__divide__eq,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( A
% 4.98/5.25 = ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ( ( C != zero_zero_real )
% 4.98/5.25 => ( ( times_times_real @ A @ C )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( C = zero_zero_real )
% 4.98/5.25 => ( A = zero_zero_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_eq
% 4.98/5.25 thf(fact_1886_eq__divide__eq,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( A
% 4.98/5.25 = ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( C != zero_zero_rat )
% 4.98/5.25 => ( ( times_times_rat @ A @ C )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( C = zero_zero_rat )
% 4.98/5.25 => ( A = zero_zero_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_eq
% 4.98/5.25 thf(fact_1887_divide__eq__eq,axiom,
% 4.98/5.25 ! [B: complex,C: complex,A: complex] :
% 4.98/5.25 ( ( ( divide1717551699836669952omplex @ B @ C )
% 4.98/5.25 = A )
% 4.98/5.25 = ( ( ( C != zero_zero_complex )
% 4.98/5.25 => ( B
% 4.98/5.25 = ( times_times_complex @ A @ C ) ) )
% 4.98/5.25 & ( ( C = zero_zero_complex )
% 4.98/5.25 => ( A = zero_zero_complex ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_eq
% 4.98/5.25 thf(fact_1888_divide__eq__eq,axiom,
% 4.98/5.25 ! [B: real,C: real,A: real] :
% 4.98/5.25 ( ( ( divide_divide_real @ B @ C )
% 4.98/5.25 = A )
% 4.98/5.25 = ( ( ( C != zero_zero_real )
% 4.98/5.25 => ( B
% 4.98/5.25 = ( times_times_real @ A @ C ) ) )
% 4.98/5.25 & ( ( C = zero_zero_real )
% 4.98/5.25 => ( A = zero_zero_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_eq
% 4.98/5.25 thf(fact_1889_divide__eq__eq,axiom,
% 4.98/5.25 ! [B: rat,C: rat,A: rat] :
% 4.98/5.25 ( ( ( divide_divide_rat @ B @ C )
% 4.98/5.25 = A )
% 4.98/5.25 = ( ( ( C != zero_zero_rat )
% 4.98/5.25 => ( B
% 4.98/5.25 = ( times_times_rat @ A @ C ) ) )
% 4.98/5.25 & ( ( C = zero_zero_rat )
% 4.98/5.25 => ( A = zero_zero_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_eq
% 4.98/5.25 thf(fact_1890_frac__eq__eq,axiom,
% 4.98/5.25 ! [Y: complex,Z: complex,X2: complex,W: complex] :
% 4.98/5.25 ( ( Y != zero_zero_complex )
% 4.98/5.25 => ( ( Z != zero_zero_complex )
% 4.98/5.25 => ( ( ( divide1717551699836669952omplex @ X2 @ Y )
% 4.98/5.25 = ( divide1717551699836669952omplex @ W @ Z ) )
% 4.98/5.25 = ( ( times_times_complex @ X2 @ Z )
% 4.98/5.25 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % frac_eq_eq
% 4.98/5.25 thf(fact_1891_frac__eq__eq,axiom,
% 4.98/5.25 ! [Y: real,Z: real,X2: real,W: real] :
% 4.98/5.25 ( ( Y != zero_zero_real )
% 4.98/5.25 => ( ( Z != zero_zero_real )
% 4.98/5.25 => ( ( ( divide_divide_real @ X2 @ Y )
% 4.98/5.25 = ( divide_divide_real @ W @ Z ) )
% 4.98/5.25 = ( ( times_times_real @ X2 @ Z )
% 4.98/5.25 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % frac_eq_eq
% 4.98/5.25 thf(fact_1892_frac__eq__eq,axiom,
% 4.98/5.25 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 4.98/5.25 ( ( Y != zero_zero_rat )
% 4.98/5.25 => ( ( Z != zero_zero_rat )
% 4.98/5.25 => ( ( ( divide_divide_rat @ X2 @ Y )
% 4.98/5.25 = ( divide_divide_rat @ W @ Z ) )
% 4.98/5.25 = ( ( times_times_rat @ X2 @ Z )
% 4.98/5.25 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % frac_eq_eq
% 4.98/5.25 thf(fact_1893_mult__numeral__1,axiom,
% 4.98/5.25 ! [A: complex] :
% 4.98/5.25 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1
% 4.98/5.25 thf(fact_1894_mult__numeral__1,axiom,
% 4.98/5.25 ! [A: real] :
% 4.98/5.25 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1
% 4.98/5.25 thf(fact_1895_mult__numeral__1,axiom,
% 4.98/5.25 ! [A: rat] :
% 4.98/5.25 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1
% 4.98/5.25 thf(fact_1896_mult__numeral__1,axiom,
% 4.98/5.25 ! [A: nat] :
% 4.98/5.25 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1
% 4.98/5.25 thf(fact_1897_mult__numeral__1,axiom,
% 4.98/5.25 ! [A: int] :
% 4.98/5.25 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1
% 4.98/5.25 thf(fact_1898_mult__numeral__1__right,axiom,
% 4.98/5.25 ! [A: complex] :
% 4.98/5.25 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1_right
% 4.98/5.25 thf(fact_1899_mult__numeral__1__right,axiom,
% 4.98/5.25 ! [A: real] :
% 4.98/5.25 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1_right
% 4.98/5.25 thf(fact_1900_mult__numeral__1__right,axiom,
% 4.98/5.25 ! [A: rat] :
% 4.98/5.25 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1_right
% 4.98/5.25 thf(fact_1901_mult__numeral__1__right,axiom,
% 4.98/5.25 ! [A: nat] :
% 4.98/5.25 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1_right
% 4.98/5.25 thf(fact_1902_mult__numeral__1__right,axiom,
% 4.98/5.25 ! [A: int] :
% 4.98/5.25 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 4.98/5.25 = A ) ).
% 4.98/5.25
% 4.98/5.25 % mult_numeral_1_right
% 4.98/5.25 thf(fact_1903_left__right__inverse__power,axiom,
% 4.98/5.25 ! [X2: complex,Y: complex,N2: nat] :
% 4.98/5.25 ( ( ( times_times_complex @ X2 @ Y )
% 4.98/5.25 = one_one_complex )
% 4.98/5.25 => ( ( times_times_complex @ ( power_power_complex @ X2 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 4.98/5.25 = one_one_complex ) ) ).
% 4.98/5.25
% 4.98/5.25 % left_right_inverse_power
% 4.98/5.25 thf(fact_1904_left__right__inverse__power,axiom,
% 4.98/5.25 ! [X2: real,Y: real,N2: nat] :
% 4.98/5.25 ( ( ( times_times_real @ X2 @ Y )
% 4.98/5.25 = one_one_real )
% 4.98/5.25 => ( ( times_times_real @ ( power_power_real @ X2 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 4.98/5.25 = one_one_real ) ) ).
% 4.98/5.25
% 4.98/5.25 % left_right_inverse_power
% 4.98/5.25 thf(fact_1905_left__right__inverse__power,axiom,
% 4.98/5.25 ! [X2: rat,Y: rat,N2: nat] :
% 4.98/5.25 ( ( ( times_times_rat @ X2 @ Y )
% 4.98/5.25 = one_one_rat )
% 4.98/5.25 => ( ( times_times_rat @ ( power_power_rat @ X2 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 4.98/5.25 = one_one_rat ) ) ).
% 4.98/5.25
% 4.98/5.25 % left_right_inverse_power
% 4.98/5.25 thf(fact_1906_left__right__inverse__power,axiom,
% 4.98/5.25 ! [X2: nat,Y: nat,N2: nat] :
% 4.98/5.25 ( ( ( times_times_nat @ X2 @ Y )
% 4.98/5.25 = one_one_nat )
% 4.98/5.25 => ( ( times_times_nat @ ( power_power_nat @ X2 @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 4.98/5.25 = one_one_nat ) ) ).
% 4.98/5.25
% 4.98/5.25 % left_right_inverse_power
% 4.98/5.25 thf(fact_1907_left__right__inverse__power,axiom,
% 4.98/5.25 ! [X2: int,Y: int,N2: nat] :
% 4.98/5.25 ( ( ( times_times_int @ X2 @ Y )
% 4.98/5.25 = one_one_int )
% 4.98/5.25 => ( ( times_times_int @ ( power_power_int @ X2 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 4.98/5.25 = one_one_int ) ) ).
% 4.98/5.25
% 4.98/5.25 % left_right_inverse_power
% 4.98/5.25 thf(fact_1908_power__Suc,axiom,
% 4.98/5.25 ! [A: complex,N2: nat] :
% 4.98/5.25 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc
% 4.98/5.25 thf(fact_1909_power__Suc,axiom,
% 4.98/5.25 ! [A: real,N2: nat] :
% 4.98/5.25 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc
% 4.98/5.25 thf(fact_1910_power__Suc,axiom,
% 4.98/5.25 ! [A: rat,N2: nat] :
% 4.98/5.25 ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc
% 4.98/5.25 thf(fact_1911_power__Suc,axiom,
% 4.98/5.25 ! [A: nat,N2: nat] :
% 4.98/5.25 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc
% 4.98/5.25 thf(fact_1912_power__Suc,axiom,
% 4.98/5.25 ! [A: int,N2: nat] :
% 4.98/5.25 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc
% 4.98/5.25 thf(fact_1913_power__Suc2,axiom,
% 4.98/5.25 ! [A: complex,N2: nat] :
% 4.98/5.25 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc2
% 4.98/5.25 thf(fact_1914_power__Suc2,axiom,
% 4.98/5.25 ! [A: real,N2: nat] :
% 4.98/5.25 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ A ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc2
% 4.98/5.25 thf(fact_1915_power__Suc2,axiom,
% 4.98/5.25 ! [A: rat,N2: nat] :
% 4.98/5.25 ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ A ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc2
% 4.98/5.25 thf(fact_1916_power__Suc2,axiom,
% 4.98/5.25 ! [A: nat,N2: nat] :
% 4.98/5.25 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc2
% 4.98/5.25 thf(fact_1917_power__Suc2,axiom,
% 4.98/5.25 ! [A: int,N2: nat] :
% 4.98/5.25 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 4.98/5.25 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc2
% 4.98/5.25 thf(fact_1918_Suc__mult__less__cancel1,axiom,
% 4.98/5.25 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 4.98/5.25 = ( ord_less_nat @ M @ N2 ) ) ).
% 4.98/5.25
% 4.98/5.25 % Suc_mult_less_cancel1
% 4.98/5.25 thf(fact_1919_power__add,axiom,
% 4.98/5.25 ! [A: complex,M: nat,N2: nat] :
% 4.98/5.25 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.25 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_add
% 4.98/5.25 thf(fact_1920_power__add,axiom,
% 4.98/5.25 ! [A: real,M: nat,N2: nat] :
% 4.98/5.25 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.25 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_add
% 4.98/5.25 thf(fact_1921_power__add,axiom,
% 4.98/5.25 ! [A: rat,M: nat,N2: nat] :
% 4.98/5.25 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.25 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_add
% 4.98/5.25 thf(fact_1922_power__add,axiom,
% 4.98/5.25 ! [A: nat,M: nat,N2: nat] :
% 4.98/5.25 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.25 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_add
% 4.98/5.25 thf(fact_1923_power__add,axiom,
% 4.98/5.25 ! [A: int,M: nat,N2: nat] :
% 4.98/5.25 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 4.98/5.25 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_add
% 4.98/5.25 thf(fact_1924_mult__less__mono1,axiom,
% 4.98/5.25 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.25 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ I3 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_mono1
% 4.98/5.25 thf(fact_1925_mult__less__mono2,axiom,
% 4.98/5.25 ! [I3: nat,J: nat,K: nat] :
% 4.98/5.25 ( ( ord_less_nat @ I3 @ J )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ K @ I3 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_mono2
% 4.98/5.25 thf(fact_1926_nat__mult__eq__cancel1,axiom,
% 4.98/5.25 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.25 => ( ( ( times_times_nat @ K @ M )
% 4.98/5.25 = ( times_times_nat @ K @ N2 ) )
% 4.98/5.25 = ( M = N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nat_mult_eq_cancel1
% 4.98/5.25 thf(fact_1927_nat__mult__less__cancel1,axiom,
% 4.98/5.25 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.25 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 4.98/5.25 = ( ord_less_nat @ M @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nat_mult_less_cancel1
% 4.98/5.25 thf(fact_1928_Suc__mult__le__cancel1,axiom,
% 4.98/5.25 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 4.98/5.25 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 4.98/5.25
% 4.98/5.25 % Suc_mult_le_cancel1
% 4.98/5.25 thf(fact_1929_mult__Suc,axiom,
% 4.98/5.25 ! [M: nat,N2: nat] :
% 4.98/5.25 ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 4.98/5.25 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_Suc
% 4.98/5.25 thf(fact_1930_mult__eq__self__implies__10,axiom,
% 4.98/5.25 ! [M: nat,N2: nat] :
% 4.98/5.25 ( ( M
% 4.98/5.25 = ( times_times_nat @ M @ N2 ) )
% 4.98/5.25 => ( ( N2 = one_one_nat )
% 4.98/5.25 | ( M = zero_zero_nat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_eq_self_implies_10
% 4.98/5.25 thf(fact_1931_less__mult__imp__div__less,axiom,
% 4.98/5.25 ! [M: nat,I3: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ M @ ( times_times_nat @ I3 @ N2 ) )
% 4.98/5.25 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I3 ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_mult_imp_div_less
% 4.98/5.25 thf(fact_1932_times__div__less__eq__dividend,axiom,
% 4.98/5.25 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 4.98/5.25
% 4.98/5.25 % times_div_less_eq_dividend
% 4.98/5.25 thf(fact_1933_div__times__less__eq__dividend,axiom,
% 4.98/5.25 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 4.98/5.25
% 4.98/5.25 % div_times_less_eq_dividend
% 4.98/5.25 thf(fact_1934_power__odd__eq,axiom,
% 4.98/5.25 ! [A: complex,N2: nat] :
% 4.98/5.25 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 4.98/5.25 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_odd_eq
% 4.98/5.25 thf(fact_1935_power__odd__eq,axiom,
% 4.98/5.25 ! [A: real,N2: nat] :
% 4.98/5.25 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 4.98/5.25 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_odd_eq
% 4.98/5.25 thf(fact_1936_power__odd__eq,axiom,
% 4.98/5.25 ! [A: rat,N2: nat] :
% 4.98/5.25 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 4.98/5.25 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_odd_eq
% 4.98/5.25 thf(fact_1937_power__odd__eq,axiom,
% 4.98/5.25 ! [A: nat,N2: nat] :
% 4.98/5.25 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 4.98/5.25 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_odd_eq
% 4.98/5.25 thf(fact_1938_power__odd__eq,axiom,
% 4.98/5.25 ! [A: int,N2: nat] :
% 4.98/5.25 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 4.98/5.25 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_odd_eq
% 4.98/5.25 thf(fact_1939_Suc__double__not__eq__double,axiom,
% 4.98/5.25 ! [M: nat,N2: nat] :
% 4.98/5.25 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.25 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 4.98/5.25
% 4.98/5.25 % Suc_double_not_eq_double
% 4.98/5.25 thf(fact_1940_double__not__eq__Suc__double,axiom,
% 4.98/5.25 ! [M: nat,N2: nat] :
% 4.98/5.25 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 4.98/5.25 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % double_not_eq_Suc_double
% 4.98/5.25 thf(fact_1941_mult__le__cancel__left,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left
% 4.98/5.25 thf(fact_1942_mult__le__cancel__left,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left
% 4.98/5.25 thf(fact_1943_mult__le__cancel__left,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left
% 4.98/5.25 thf(fact_1944_mult__le__cancel__right,axiom,
% 4.98/5.25 ! [A: real,C: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right
% 4.98/5.25 thf(fact_1945_mult__le__cancel__right,axiom,
% 4.98/5.25 ! [A: rat,C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right
% 4.98/5.25 thf(fact_1946_mult__le__cancel__right,axiom,
% 4.98/5.25 ! [A: int,C: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right
% 4.98/5.25 thf(fact_1947_mult__left__less__imp__less,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_less_imp_less
% 4.98/5.25 thf(fact_1948_mult__left__less__imp__less,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_less_imp_less
% 4.98/5.25 thf(fact_1949_mult__left__less__imp__less,axiom,
% 4.98/5.25 ! [C: nat,A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_less_imp_less
% 4.98/5.25 thf(fact_1950_mult__left__less__imp__less,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_less_imp_less
% 4.98/5.25 thf(fact_1951_mult__strict__mono,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_real @ C @ D )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ B )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_mono
% 4.98/5.25 thf(fact_1952_mult__strict__mono,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_rat @ C @ D )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_mono
% 4.98/5.25 thf(fact_1953_mult__strict__mono,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.25 ( ( ord_less_nat @ A @ B )
% 4.98/5.25 => ( ( ord_less_nat @ C @ D )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_mono
% 4.98/5.25 thf(fact_1954_mult__strict__mono,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.25 ( ( ord_less_int @ A @ B )
% 4.98/5.25 => ( ( ord_less_int @ C @ D )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_mono
% 4.98/5.25 thf(fact_1955_mult__less__cancel__left,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left
% 4.98/5.25 thf(fact_1956_mult__less__cancel__left,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left
% 4.98/5.25 thf(fact_1957_mult__less__cancel__left,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left
% 4.98/5.25 thf(fact_1958_mult__right__less__imp__less,axiom,
% 4.98/5.25 ! [A: real,C: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_less_imp_less
% 4.98/5.25 thf(fact_1959_mult__right__less__imp__less,axiom,
% 4.98/5.25 ! [A: rat,C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_less_imp_less
% 4.98/5.25 thf(fact_1960_mult__right__less__imp__less,axiom,
% 4.98/5.25 ! [A: nat,C: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_less_imp_less
% 4.98/5.25 thf(fact_1961_mult__right__less__imp__less,axiom,
% 4.98/5.25 ! [A: int,C: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_less_imp_less
% 4.98/5.25 thf(fact_1962_mult__strict__mono_H,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_real @ C @ D )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_mono'
% 4.98/5.25 thf(fact_1963_mult__strict__mono_H,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_rat @ C @ D )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_mono'
% 4.98/5.25 thf(fact_1964_mult__strict__mono_H,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.25 ( ( ord_less_nat @ A @ B )
% 4.98/5.25 => ( ( ord_less_nat @ C @ D )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_mono'
% 4.98/5.25 thf(fact_1965_mult__strict__mono_H,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.25 ( ( ord_less_int @ A @ B )
% 4.98/5.25 => ( ( ord_less_int @ C @ D )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_strict_mono'
% 4.98/5.25 thf(fact_1966_mult__less__cancel__right,axiom,
% 4.98/5.25 ! [A: real,C: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right
% 4.98/5.25 thf(fact_1967_mult__less__cancel__right,axiom,
% 4.98/5.25 ! [A: rat,C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right
% 4.98/5.25 thf(fact_1968_mult__less__cancel__right,axiom,
% 4.98/5.25 ! [A: int,C: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ A @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ B @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right
% 4.98/5.25 thf(fact_1969_mult__le__cancel__left__neg,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left_neg
% 4.98/5.25 thf(fact_1970_mult__le__cancel__left__neg,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left_neg
% 4.98/5.25 thf(fact_1971_mult__le__cancel__left__neg,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left_neg
% 4.98/5.25 thf(fact_1972_mult__le__cancel__left__pos,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left_pos
% 4.98/5.25 thf(fact_1973_mult__le__cancel__left__pos,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left_pos
% 4.98/5.25 thf(fact_1974_mult__le__cancel__left__pos,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left_pos
% 4.98/5.25 thf(fact_1975_mult__left__le__imp__le,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le_imp_le
% 4.98/5.25 thf(fact_1976_mult__left__le__imp__le,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le_imp_le
% 4.98/5.25 thf(fact_1977_mult__left__le__imp__le,axiom,
% 4.98/5.25 ! [C: nat,A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le_imp_le
% 4.98/5.25 thf(fact_1978_mult__left__le__imp__le,axiom,
% 4.98/5.25 ! [C: int,A: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le_imp_le
% 4.98/5.25 thf(fact_1979_mult__right__le__imp__le,axiom,
% 4.98/5.25 ! [A: real,C: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_le_imp_le
% 4.98/5.25 thf(fact_1980_mult__right__le__imp__le,axiom,
% 4.98/5.25 ! [A: rat,C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_le_imp_le
% 4.98/5.25 thf(fact_1981_mult__right__le__imp__le,axiom,
% 4.98/5.25 ! [A: nat,C: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_le_imp_le
% 4.98/5.25 thf(fact_1982_mult__right__le__imp__le,axiom,
% 4.98/5.25 ! [A: int,C: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_le_imp_le
% 4.98/5.25 thf(fact_1983_mult__le__less__imp__less,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_real @ C @ D )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_less_imp_less
% 4.98/5.25 thf(fact_1984_mult__le__less__imp__less,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_rat @ C @ D )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_less_imp_less
% 4.98/5.25 thf(fact_1985_mult__le__less__imp__less,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.25 => ( ( ord_less_nat @ C @ D )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_less_imp_less
% 4.98/5.25 thf(fact_1986_mult__le__less__imp__less,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.25 => ( ( ord_less_int @ C @ D )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_less_imp_less
% 4.98/5.25 thf(fact_1987_mult__less__le__imp__less,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_real @ C @ D )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_le_imp_less
% 4.98/5.25 thf(fact_1988_mult__less__le__imp__less,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_rat @ C @ D )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_le_imp_less
% 4.98/5.25 thf(fact_1989_mult__less__le__imp__less,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.25 ( ( ord_less_nat @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_nat @ C @ D )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_le_imp_less
% 4.98/5.25 thf(fact_1990_mult__less__le__imp__less,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.25 ( ( ord_less_int @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_int @ C @ D )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_le_imp_less
% 4.98/5.25 thf(fact_1991_mult__left__le__one__le,axiom,
% 4.98/5.25 ! [X2: real,Y: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.25 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ Y @ X2 ) @ X2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le_one_le
% 4.98/5.25 thf(fact_1992_mult__left__le__one__le,axiom,
% 4.98/5.25 ! [X2: rat,Y: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.25 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X2 ) @ X2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le_one_le
% 4.98/5.25 thf(fact_1993_mult__left__le__one__le,axiom,
% 4.98/5.25 ! [X2: int,Y: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.98/5.25 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ Y @ X2 ) @ X2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le_one_le
% 4.98/5.25 thf(fact_1994_mult__right__le__one__le,axiom,
% 4.98/5.25 ! [X2: real,Y: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.25 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ X2 @ Y ) @ X2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_le_one_le
% 4.98/5.25 thf(fact_1995_mult__right__le__one__le,axiom,
% 4.98/5.25 ! [X2: rat,Y: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.25 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Y ) @ X2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_le_one_le
% 4.98/5.25 thf(fact_1996_mult__right__le__one__le,axiom,
% 4.98/5.25 ! [X2: int,Y: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 4.98/5.25 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ X2 @ Y ) @ X2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_right_le_one_le
% 4.98/5.25 thf(fact_1997_mult__le__one,axiom,
% 4.98/5.25 ! [A: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ A @ one_one_real )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 4.98/5.25 => ( ( ord_less_eq_real @ B @ one_one_real )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_one
% 4.98/5.25 thf(fact_1998_mult__le__one,axiom,
% 4.98/5.25 ! [A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 4.98/5.25 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_one
% 4.98/5.25 thf(fact_1999_mult__le__one,axiom,
% 4.98/5.25 ! [A: nat,B: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 4.98/5.25 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 4.98/5.25 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_one
% 4.98/5.25 thf(fact_2000_mult__le__one,axiom,
% 4.98/5.25 ! [A: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ A @ one_one_int )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.25 => ( ( ord_less_eq_int @ B @ one_one_int )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_one
% 4.98/5.25 thf(fact_2001_mult__left__le,axiom,
% 4.98/5.25 ! [C: real,A: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ C @ one_one_real )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le
% 4.98/5.25 thf(fact_2002_mult__left__le,axiom,
% 4.98/5.25 ! [C: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le
% 4.98/5.25 thf(fact_2003_mult__left__le,axiom,
% 4.98/5.25 ! [C: nat,A: nat] :
% 4.98/5.25 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 4.98/5.25 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le
% 4.98/5.25 thf(fact_2004_mult__left__le,axiom,
% 4.98/5.25 ! [C: int,A: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ C @ one_one_int )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_left_le
% 4.98/5.25 thf(fact_2005_sum__squares__le__zero__iff,axiom,
% 4.98/5.25 ! [X2: real,Y: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 4.98/5.25 = ( ( X2 = zero_zero_real )
% 4.98/5.25 & ( Y = zero_zero_real ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_le_zero_iff
% 4.98/5.25 thf(fact_2006_sum__squares__le__zero__iff,axiom,
% 4.98/5.25 ! [X2: rat,Y: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 4.98/5.25 = ( ( X2 = zero_zero_rat )
% 4.98/5.25 & ( Y = zero_zero_rat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_le_zero_iff
% 4.98/5.25 thf(fact_2007_sum__squares__le__zero__iff,axiom,
% 4.98/5.25 ! [X2: int,Y: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 4.98/5.25 = ( ( X2 = zero_zero_int )
% 4.98/5.25 & ( Y = zero_zero_int ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_le_zero_iff
% 4.98/5.25 thf(fact_2008_sum__squares__ge__zero,axiom,
% 4.98/5.25 ! [X2: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_ge_zero
% 4.98/5.25 thf(fact_2009_sum__squares__ge__zero,axiom,
% 4.98/5.25 ! [X2: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_ge_zero
% 4.98/5.25 thf(fact_2010_sum__squares__ge__zero,axiom,
% 4.98/5.25 ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_ge_zero
% 4.98/5.25 thf(fact_2011_sum__squares__gt__zero__iff,axiom,
% 4.98/5.25 ! [X2: real,Y: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) )
% 4.98/5.25 = ( ( X2 != zero_zero_real )
% 4.98/5.25 | ( Y != zero_zero_real ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_gt_zero_iff
% 4.98/5.25 thf(fact_2012_sum__squares__gt__zero__iff,axiom,
% 4.98/5.25 ! [X2: rat,Y: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) )
% 4.98/5.25 = ( ( X2 != zero_zero_rat )
% 4.98/5.25 | ( Y != zero_zero_rat ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_gt_zero_iff
% 4.98/5.25 thf(fact_2013_sum__squares__gt__zero__iff,axiom,
% 4.98/5.25 ! [X2: int,Y: int] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) )
% 4.98/5.25 = ( ( X2 != zero_zero_int )
% 4.98/5.25 | ( Y != zero_zero_int ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % sum_squares_gt_zero_iff
% 4.98/5.25 thf(fact_2014_not__sum__squares__lt__zero,axiom,
% 4.98/5.25 ! [X2: real,Y: real] :
% 4.98/5.25 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 4.98/5.25
% 4.98/5.25 % not_sum_squares_lt_zero
% 4.98/5.25 thf(fact_2015_not__sum__squares__lt__zero,axiom,
% 4.98/5.25 ! [X2: rat,Y: rat] :
% 4.98/5.25 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 4.98/5.25
% 4.98/5.25 % not_sum_squares_lt_zero
% 4.98/5.25 thf(fact_2016_not__sum__squares__lt__zero,axiom,
% 4.98/5.25 ! [X2: int,Y: int] :
% 4.98/5.25 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 4.98/5.25
% 4.98/5.25 % not_sum_squares_lt_zero
% 4.98/5.25 thf(fact_2017_divide__less__eq,axiom,
% 4.98/5.25 ! [B: real,C: real,A: real] :
% 4.98/5.25 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_less_eq
% 4.98/5.25 thf(fact_2018_divide__less__eq,axiom,
% 4.98/5.25 ! [B: rat,C: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_less_eq
% 4.98/5.25 thf(fact_2019_less__divide__eq,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_divide_eq
% 4.98/5.25 thf(fact_2020_less__divide__eq,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_divide_eq
% 4.98/5.25 thf(fact_2021_neg__divide__less__eq,axiom,
% 4.98/5.25 ! [C: real,B: real,A: real] :
% 4.98/5.25 ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.98/5.25 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % neg_divide_less_eq
% 4.98/5.25 thf(fact_2022_neg__divide__less__eq,axiom,
% 4.98/5.25 ! [C: rat,B: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.98/5.25 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % neg_divide_less_eq
% 4.98/5.25 thf(fact_2023_neg__less__divide__eq,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % neg_less_divide_eq
% 4.98/5.25 thf(fact_2024_neg__less__divide__eq,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % neg_less_divide_eq
% 4.98/5.25 thf(fact_2025_pos__divide__less__eq,axiom,
% 4.98/5.25 ! [C: real,B: real,A: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.98/5.25 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % pos_divide_less_eq
% 4.98/5.25 thf(fact_2026_pos__divide__less__eq,axiom,
% 4.98/5.25 ! [C: rat,B: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.98/5.25 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % pos_divide_less_eq
% 4.98/5.25 thf(fact_2027_pos__less__divide__eq,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % pos_less_divide_eq
% 4.98/5.25 thf(fact_2028_pos__less__divide__eq,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % pos_less_divide_eq
% 4.98/5.25 thf(fact_2029_mult__imp__div__pos__less,axiom,
% 4.98/5.25 ! [Y: real,X2: real,Z: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.25 => ( ( ord_less_real @ X2 @ ( times_times_real @ Z @ Y ) )
% 4.98/5.25 => ( ord_less_real @ ( divide_divide_real @ X2 @ Y ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_imp_div_pos_less
% 4.98/5.25 thf(fact_2030_mult__imp__div__pos__less,axiom,
% 4.98/5.25 ! [Y: rat,X2: rat,Z: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.98/5.25 => ( ( ord_less_rat @ X2 @ ( times_times_rat @ Z @ Y ) )
% 4.98/5.25 => ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_imp_div_pos_less
% 4.98/5.25 thf(fact_2031_mult__imp__less__div__pos,axiom,
% 4.98/5.25 ! [Y: real,Z: real,X2: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.25 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X2 )
% 4.98/5.25 => ( ord_less_real @ Z @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_imp_less_div_pos
% 4.98/5.25 thf(fact_2032_mult__imp__less__div__pos,axiom,
% 4.98/5.25 ! [Y: rat,Z: rat,X2: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.98/5.25 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X2 )
% 4.98/5.25 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_imp_less_div_pos
% 4.98/5.25 thf(fact_2033_divide__strict__left__mono,axiom,
% 4.98/5.25 ! [B: real,A: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ B @ A )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.98/5.25 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_strict_left_mono
% 4.98/5.25 thf(fact_2034_divide__strict__left__mono,axiom,
% 4.98/5.25 ! [B: rat,A: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ B @ A )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.98/5.25 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_strict_left_mono
% 4.98/5.25 thf(fact_2035_divide__strict__left__mono__neg,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.98/5.25 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_strict_left_mono_neg
% 4.98/5.25 thf(fact_2036_divide__strict__left__mono__neg,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.98/5.25 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_strict_left_mono_neg
% 4.98/5.25 thf(fact_2037_divide__eq__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [B: complex,C: complex,W: num] :
% 4.98/5.25 ( ( ( divide1717551699836669952omplex @ B @ C )
% 4.98/5.25 = ( numera6690914467698888265omplex @ W ) )
% 4.98/5.25 = ( ( ( C != zero_zero_complex )
% 4.98/5.25 => ( B
% 4.98/5.25 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 4.98/5.25 & ( ( C = zero_zero_complex )
% 4.98/5.25 => ( ( numera6690914467698888265omplex @ W )
% 4.98/5.25 = zero_zero_complex ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_eq_numeral(1)
% 4.98/5.25 thf(fact_2038_divide__eq__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [B: real,C: real,W: num] :
% 4.98/5.25 ( ( ( divide_divide_real @ B @ C )
% 4.98/5.25 = ( numeral_numeral_real @ W ) )
% 4.98/5.25 = ( ( ( C != zero_zero_real )
% 4.98/5.25 => ( B
% 4.98/5.25 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 4.98/5.25 & ( ( C = zero_zero_real )
% 4.98/5.25 => ( ( numeral_numeral_real @ W )
% 4.98/5.25 = zero_zero_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_eq_numeral(1)
% 4.98/5.25 thf(fact_2039_divide__eq__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [B: rat,C: rat,W: num] :
% 4.98/5.25 ( ( ( divide_divide_rat @ B @ C )
% 4.98/5.25 = ( numeral_numeral_rat @ W ) )
% 4.98/5.25 = ( ( ( C != zero_zero_rat )
% 4.98/5.25 => ( B
% 4.98/5.25 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 4.98/5.25 & ( ( C = zero_zero_rat )
% 4.98/5.25 => ( ( numeral_numeral_rat @ W )
% 4.98/5.25 = zero_zero_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_eq_eq_numeral(1)
% 4.98/5.25 thf(fact_2040_eq__divide__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [W: num,B: complex,C: complex] :
% 4.98/5.25 ( ( ( numera6690914467698888265omplex @ W )
% 4.98/5.25 = ( divide1717551699836669952omplex @ B @ C ) )
% 4.98/5.25 = ( ( ( C != zero_zero_complex )
% 4.98/5.25 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( C = zero_zero_complex )
% 4.98/5.25 => ( ( numera6690914467698888265omplex @ W )
% 4.98/5.25 = zero_zero_complex ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_eq_numeral(1)
% 4.98/5.25 thf(fact_2041_eq__divide__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [W: num,B: real,C: real] :
% 4.98/5.25 ( ( ( numeral_numeral_real @ W )
% 4.98/5.25 = ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ( ( C != zero_zero_real )
% 4.98/5.25 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( C = zero_zero_real )
% 4.98/5.25 => ( ( numeral_numeral_real @ W )
% 4.98/5.25 = zero_zero_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_eq_numeral(1)
% 4.98/5.25 thf(fact_2042_eq__divide__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [W: num,B: rat,C: rat] :
% 4.98/5.25 ( ( ( numeral_numeral_rat @ W )
% 4.98/5.25 = ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( C != zero_zero_rat )
% 4.98/5.25 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( C = zero_zero_rat )
% 4.98/5.25 => ( ( numeral_numeral_rat @ W )
% 4.98/5.25 = zero_zero_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % eq_divide_eq_numeral(1)
% 4.98/5.25 thf(fact_2043_add__divide__eq__if__simps_I2_J,axiom,
% 4.98/5.25 ! [Z: complex,A: complex,B: complex] :
% 4.98/5.25 ( ( ( Z = zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( Z != zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 4.98/5.25 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_if_simps(2)
% 4.98/5.25 thf(fact_2044_add__divide__eq__if__simps_I2_J,axiom,
% 4.98/5.25 ! [Z: real,A: real,B: real] :
% 4.98/5.25 ( ( ( Z = zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( Z != zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 4.98/5.25 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_if_simps(2)
% 4.98/5.25 thf(fact_2045_add__divide__eq__if__simps_I2_J,axiom,
% 4.98/5.25 ! [Z: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ( Z = zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 4.98/5.25 = B ) )
% 4.98/5.25 & ( ( Z != zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 4.98/5.25 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_if_simps(2)
% 4.98/5.25 thf(fact_2046_add__divide__eq__if__simps_I1_J,axiom,
% 4.98/5.25 ! [Z: complex,A: complex,B: complex] :
% 4.98/5.25 ( ( ( Z = zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 4.98/5.25 = A ) )
% 4.98/5.25 & ( ( Z != zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 4.98/5.25 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_if_simps(1)
% 4.98/5.25 thf(fact_2047_add__divide__eq__if__simps_I1_J,axiom,
% 4.98/5.25 ! [Z: real,A: real,B: real] :
% 4.98/5.25 ( ( ( Z = zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 4.98/5.25 = A ) )
% 4.98/5.25 & ( ( Z != zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 4.98/5.25 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_if_simps(1)
% 4.98/5.25 thf(fact_2048_add__divide__eq__if__simps_I1_J,axiom,
% 4.98/5.25 ! [Z: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ( Z = zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 4.98/5.25 = A ) )
% 4.98/5.25 & ( ( Z != zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 4.98/5.25 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_if_simps(1)
% 4.98/5.25 thf(fact_2049_add__frac__eq,axiom,
% 4.98/5.25 ! [Y: complex,Z: complex,X2: complex,W: complex] :
% 4.98/5.25 ( ( Y != zero_zero_complex )
% 4.98/5.25 => ( ( Z != zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 4.98/5.25 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_frac_eq
% 4.98/5.25 thf(fact_2050_add__frac__eq,axiom,
% 4.98/5.25 ! [Y: real,Z: real,X2: real,W: real] :
% 4.98/5.25 ( ( Y != zero_zero_real )
% 4.98/5.25 => ( ( Z != zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 4.98/5.25 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_frac_eq
% 4.98/5.25 thf(fact_2051_add__frac__eq,axiom,
% 4.98/5.25 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 4.98/5.25 ( ( Y != zero_zero_rat )
% 4.98/5.25 => ( ( Z != zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 4.98/5.25 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_frac_eq
% 4.98/5.25 thf(fact_2052_add__frac__num,axiom,
% 4.98/5.25 ! [Y: complex,X2: complex,Z: complex] :
% 4.98/5.25 ( ( Y != zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ Z )
% 4.98/5.25 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_frac_num
% 4.98/5.25 thf(fact_2053_add__frac__num,axiom,
% 4.98/5.25 ! [Y: real,X2: real,Z: real] :
% 4.98/5.25 ( ( Y != zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Y ) @ Z )
% 4.98/5.25 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_frac_num
% 4.98/5.25 thf(fact_2054_add__frac__num,axiom,
% 4.98/5.25 ! [Y: rat,X2: rat,Z: rat] :
% 4.98/5.25 ( ( Y != zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z )
% 4.98/5.25 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_frac_num
% 4.98/5.25 thf(fact_2055_add__num__frac,axiom,
% 4.98/5.25 ! [Y: complex,Z: complex,X2: complex] :
% 4.98/5.25 ( ( Y != zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X2 @ Y ) )
% 4.98/5.25 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_num_frac
% 4.98/5.25 thf(fact_2056_add__num__frac,axiom,
% 4.98/5.25 ! [Y: real,Z: real,X2: real] :
% 4.98/5.25 ( ( Y != zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X2 @ Y ) )
% 4.98/5.25 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_num_frac
% 4.98/5.25 thf(fact_2057_add__num__frac,axiom,
% 4.98/5.25 ! [Y: rat,Z: rat,X2: rat] :
% 4.98/5.25 ( ( Y != zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X2 @ Y ) )
% 4.98/5.25 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_num_frac
% 4.98/5.25 thf(fact_2058_add__divide__eq__iff,axiom,
% 4.98/5.25 ! [Z: complex,X2: complex,Y: complex] :
% 4.98/5.25 ( ( Z != zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ X2 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 4.98/5.25 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_iff
% 4.98/5.25 thf(fact_2059_add__divide__eq__iff,axiom,
% 4.98/5.25 ! [Z: real,X2: real,Y: real] :
% 4.98/5.25 ( ( Z != zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ X2 @ ( divide_divide_real @ Y @ Z ) )
% 4.98/5.25 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_iff
% 4.98/5.25 thf(fact_2060_add__divide__eq__iff,axiom,
% 4.98/5.25 ! [Z: rat,X2: rat,Y: rat] :
% 4.98/5.25 ( ( Z != zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ X2 @ ( divide_divide_rat @ Y @ Z ) )
% 4.98/5.25 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % add_divide_eq_iff
% 4.98/5.25 thf(fact_2061_divide__add__eq__iff,axiom,
% 4.98/5.25 ! [Z: complex,X2: complex,Y: complex] :
% 4.98/5.25 ( ( Z != zero_zero_complex )
% 4.98/5.25 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y )
% 4.98/5.25 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X2 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_add_eq_iff
% 4.98/5.25 thf(fact_2062_divide__add__eq__iff,axiom,
% 4.98/5.25 ! [Z: real,X2: real,Y: real] :
% 4.98/5.25 ( ( Z != zero_zero_real )
% 4.98/5.25 => ( ( plus_plus_real @ ( divide_divide_real @ X2 @ Z ) @ Y )
% 4.98/5.25 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_add_eq_iff
% 4.98/5.25 thf(fact_2063_divide__add__eq__iff,axiom,
% 4.98/5.25 ! [Z: rat,X2: rat,Y: rat] :
% 4.98/5.25 ( ( Z != zero_zero_rat )
% 4.98/5.25 => ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y )
% 4.98/5.25 = ( divide_divide_rat @ ( plus_plus_rat @ X2 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_add_eq_iff
% 4.98/5.25 thf(fact_2064_power__gt1__lemma,axiom,
% 4.98/5.25 ! [A: real,N2: nat] :
% 4.98/5.25 ( ( ord_less_real @ one_one_real @ A )
% 4.98/5.25 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_gt1_lemma
% 4.98/5.25 thf(fact_2065_power__gt1__lemma,axiom,
% 4.98/5.25 ! [A: rat,N2: nat] :
% 4.98/5.25 ( ( ord_less_rat @ one_one_rat @ A )
% 4.98/5.25 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_gt1_lemma
% 4.98/5.25 thf(fact_2066_power__gt1__lemma,axiom,
% 4.98/5.25 ! [A: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ one_one_nat @ A )
% 4.98/5.25 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_gt1_lemma
% 4.98/5.25 thf(fact_2067_power__gt1__lemma,axiom,
% 4.98/5.25 ! [A: int,N2: nat] :
% 4.98/5.25 ( ( ord_less_int @ one_one_int @ A )
% 4.98/5.25 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_gt1_lemma
% 4.98/5.25 thf(fact_2068_power__less__power__Suc,axiom,
% 4.98/5.25 ! [A: real,N2: nat] :
% 4.98/5.25 ( ( ord_less_real @ one_one_real @ A )
% 4.98/5.25 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_less_power_Suc
% 4.98/5.25 thf(fact_2069_power__less__power__Suc,axiom,
% 4.98/5.25 ! [A: rat,N2: nat] :
% 4.98/5.25 ( ( ord_less_rat @ one_one_rat @ A )
% 4.98/5.25 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_less_power_Suc
% 4.98/5.25 thf(fact_2070_power__less__power__Suc,axiom,
% 4.98/5.25 ! [A: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ one_one_nat @ A )
% 4.98/5.25 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_less_power_Suc
% 4.98/5.25 thf(fact_2071_power__less__power__Suc,axiom,
% 4.98/5.25 ! [A: int,N2: nat] :
% 4.98/5.25 ( ( ord_less_int @ one_one_int @ A )
% 4.98/5.25 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_less_power_Suc
% 4.98/5.25 thf(fact_2072_one__less__mult,axiom,
% 4.98/5.25 ! [N2: nat,M: nat] :
% 4.98/5.25 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 4.98/5.25 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 4.98/5.25 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % one_less_mult
% 4.98/5.25 thf(fact_2073_n__less__m__mult__n,axiom,
% 4.98/5.25 ! [N2: nat,M: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.25 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 4.98/5.25 => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % n_less_m_mult_n
% 4.98/5.25 thf(fact_2074_n__less__n__mult__m,axiom,
% 4.98/5.25 ! [N2: nat,M: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.25 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 4.98/5.25 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % n_less_n_mult_m
% 4.98/5.25 thf(fact_2075_nat__mult__le__cancel1,axiom,
% 4.98/5.25 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.25 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 4.98/5.25 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nat_mult_le_cancel1
% 4.98/5.25 thf(fact_2076_div__less__iff__less__mult,axiom,
% 4.98/5.25 ! [Q2: nat,M: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 4.98/5.25 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N2 )
% 4.98/5.25 = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % div_less_iff_less_mult
% 4.98/5.25 thf(fact_2077_nat__mult__div__cancel1,axiom,
% 4.98/5.25 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ K )
% 4.98/5.25 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 4.98/5.25 = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % nat_mult_div_cancel1
% 4.98/5.25 thf(fact_2078_odd__nonzero,axiom,
% 4.98/5.25 ! [Z: int] :
% 4.98/5.25 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 4.98/5.25 != zero_zero_int ) ).
% 4.98/5.25
% 4.98/5.25 % odd_nonzero
% 4.98/5.25 thf(fact_2079_plus__int__code_I1_J,axiom,
% 4.98/5.25 ! [K: int] :
% 4.98/5.25 ( ( plus_plus_int @ K @ zero_zero_int )
% 4.98/5.25 = K ) ).
% 4.98/5.25
% 4.98/5.25 % plus_int_code(1)
% 4.98/5.25 thf(fact_2080_plus__int__code_I2_J,axiom,
% 4.98/5.25 ! [L: int] :
% 4.98/5.25 ( ( plus_plus_int @ zero_zero_int @ L )
% 4.98/5.25 = L ) ).
% 4.98/5.25
% 4.98/5.25 % plus_int_code(2)
% 4.98/5.25 thf(fact_2081_int__ge__induct,axiom,
% 4.98/5.25 ! [K: int,I3: int,P: int > $o] :
% 4.98/5.25 ( ( ord_less_eq_int @ K @ I3 )
% 4.98/5.25 => ( ( P @ K )
% 4.98/5.25 => ( ! [I2: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ K @ I2 )
% 4.98/5.25 => ( ( P @ I2 )
% 4.98/5.25 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 4.98/5.25 => ( P @ I3 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % int_ge_induct
% 4.98/5.25 thf(fact_2082_zless__add1__eq,axiom,
% 4.98/5.25 ! [W: int,Z: int] :
% 4.98/5.25 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 4.98/5.25 = ( ( ord_less_int @ W @ Z )
% 4.98/5.25 | ( W = Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % zless_add1_eq
% 4.98/5.25 thf(fact_2083_int__gr__induct,axiom,
% 4.98/5.25 ! [K: int,I3: int,P: int > $o] :
% 4.98/5.25 ( ( ord_less_int @ K @ I3 )
% 4.98/5.25 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 4.98/5.25 => ( ! [I2: int] :
% 4.98/5.25 ( ( ord_less_int @ K @ I2 )
% 4.98/5.25 => ( ( P @ I2 )
% 4.98/5.25 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 4.98/5.25 => ( P @ I3 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % int_gr_induct
% 4.98/5.25 thf(fact_2084_max_Oassoc,axiom,
% 4.98/5.25 ! [A: nat,B: nat,C: nat] :
% 4.98/5.25 ( ( ord_max_nat @ ( ord_max_nat @ A @ B ) @ C )
% 4.98/5.25 = ( ord_max_nat @ A @ ( ord_max_nat @ B @ C ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % max.assoc
% 4.98/5.25 thf(fact_2085_max_Oassoc,axiom,
% 4.98/5.25 ! [A: int,B: int,C: int] :
% 4.98/5.25 ( ( ord_max_int @ ( ord_max_int @ A @ B ) @ C )
% 4.98/5.25 = ( ord_max_int @ A @ ( ord_max_int @ B @ C ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % max.assoc
% 4.98/5.25 thf(fact_2086_max_Ocommute,axiom,
% 4.98/5.25 ( ord_max_nat
% 4.98/5.25 = ( ^ [A5: nat,B5: nat] : ( ord_max_nat @ B5 @ A5 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % max.commute
% 4.98/5.25 thf(fact_2087_max_Ocommute,axiom,
% 4.98/5.25 ( ord_max_int
% 4.98/5.25 = ( ^ [A5: int,B5: int] : ( ord_max_int @ B5 @ A5 ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % max.commute
% 4.98/5.25 thf(fact_2088_max_Oleft__commute,axiom,
% 4.98/5.25 ! [B: nat,A: nat,C: nat] :
% 4.98/5.25 ( ( ord_max_nat @ B @ ( ord_max_nat @ A @ C ) )
% 4.98/5.25 = ( ord_max_nat @ A @ ( ord_max_nat @ B @ C ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % max.left_commute
% 4.98/5.25 thf(fact_2089_max_Oleft__commute,axiom,
% 4.98/5.25 ! [B: int,A: int,C: int] :
% 4.98/5.25 ( ( ord_max_int @ B @ ( ord_max_int @ A @ C ) )
% 4.98/5.25 = ( ord_max_int @ A @ ( ord_max_int @ B @ C ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % max.left_commute
% 4.98/5.25 thf(fact_2090_field__le__mult__one__interval,axiom,
% 4.98/5.25 ! [X2: real,Y: real] :
% 4.98/5.25 ( ! [Z3: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 4.98/5.25 => ( ( ord_less_real @ Z3 @ one_one_real )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ Z3 @ X2 ) @ Y ) ) )
% 4.98/5.25 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 4.98/5.25
% 4.98/5.25 % field_le_mult_one_interval
% 4.98/5.25 thf(fact_2091_field__le__mult__one__interval,axiom,
% 4.98/5.25 ! [X2: rat,Y: rat] :
% 4.98/5.25 ( ! [Z3: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 4.98/5.25 => ( ( ord_less_rat @ Z3 @ one_one_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X2 ) @ Y ) ) )
% 4.98/5.25 => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 4.98/5.25
% 4.98/5.25 % field_le_mult_one_interval
% 4.98/5.25 thf(fact_2092_mult__le__cancel__left1,axiom,
% 4.98/5.25 ! [C: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ one_one_real @ B ) )
% 4.98/5.25 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left1
% 4.98/5.25 thf(fact_2093_mult__le__cancel__left1,axiom,
% 4.98/5.25 ! [C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 4.98/5.25 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left1
% 4.98/5.25 thf(fact_2094_mult__le__cancel__left1,axiom,
% 4.98/5.25 ! [C: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ one_one_int @ B ) )
% 4.98/5.25 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left1
% 4.98/5.25 thf(fact_2095_mult__le__cancel__left2,axiom,
% 4.98/5.25 ! [C: real,A: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ A @ one_one_real ) )
% 4.98/5.25 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left2
% 4.98/5.25 thf(fact_2096_mult__le__cancel__left2,axiom,
% 4.98/5.25 ! [C: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 4.98/5.25 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left2
% 4.98/5.25 thf(fact_2097_mult__le__cancel__left2,axiom,
% 4.98/5.25 ! [C: int,A: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ A @ one_one_int ) )
% 4.98/5.25 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_left2
% 4.98/5.25 thf(fact_2098_mult__le__cancel__right1,axiom,
% 4.98/5.25 ! [C: real,B: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ one_one_real @ B ) )
% 4.98/5.25 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right1
% 4.98/5.25 thf(fact_2099_mult__le__cancel__right1,axiom,
% 4.98/5.25 ! [C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 4.98/5.25 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right1
% 4.98/5.25 thf(fact_2100_mult__le__cancel__right1,axiom,
% 4.98/5.25 ! [C: int,B: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ one_one_int @ B ) )
% 4.98/5.25 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right1
% 4.98/5.25 thf(fact_2101_mult__le__cancel__right2,axiom,
% 4.98/5.25 ! [A: real,C: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ A @ one_one_real ) )
% 4.98/5.25 & ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right2
% 4.98/5.25 thf(fact_2102_mult__le__cancel__right2,axiom,
% 4.98/5.25 ! [A: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 4.98/5.25 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right2
% 4.98/5.25 thf(fact_2103_mult__le__cancel__right2,axiom,
% 4.98/5.25 ! [A: int,C: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 4.98/5.25 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_eq_int @ A @ one_one_int ) )
% 4.98/5.25 & ( ( ord_less_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_le_cancel_right2
% 4.98/5.25 thf(fact_2104_mult__less__cancel__left1,axiom,
% 4.98/5.25 ! [C: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ one_one_real @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left1
% 4.98/5.25 thf(fact_2105_mult__less__cancel__left1,axiom,
% 4.98/5.25 ! [C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ one_one_rat @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left1
% 4.98/5.25 thf(fact_2106_mult__less__cancel__left1,axiom,
% 4.98/5.25 ! [C: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 4.98/5.25 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ one_one_int @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left1
% 4.98/5.25 thf(fact_2107_mult__less__cancel__left2,axiom,
% 4.98/5.25 ! [C: real,A: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 4.98/5.25 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ A @ one_one_real ) )
% 4.98/5.25 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left2
% 4.98/5.25 thf(fact_2108_mult__less__cancel__left2,axiom,
% 4.98/5.25 ! [C: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 4.98/5.25 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ A @ one_one_rat ) )
% 4.98/5.25 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left2
% 4.98/5.25 thf(fact_2109_mult__less__cancel__left2,axiom,
% 4.98/5.25 ! [C: int,A: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 4.98/5.25 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ A @ one_one_int ) )
% 4.98/5.25 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_left2
% 4.98/5.25 thf(fact_2110_mult__less__cancel__right1,axiom,
% 4.98/5.25 ! [C: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ one_one_real @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right1
% 4.98/5.25 thf(fact_2111_mult__less__cancel__right1,axiom,
% 4.98/5.25 ! [C: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ one_one_rat @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right1
% 4.98/5.25 thf(fact_2112_mult__less__cancel__right1,axiom,
% 4.98/5.25 ! [C: int,B: int] :
% 4.98/5.25 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ one_one_int @ B ) )
% 4.98/5.25 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right1
% 4.98/5.25 thf(fact_2113_mult__less__cancel__right2,axiom,
% 4.98/5.25 ! [A: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 4.98/5.25 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ A @ one_one_real ) )
% 4.98/5.25 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right2
% 4.98/5.25 thf(fact_2114_mult__less__cancel__right2,axiom,
% 4.98/5.25 ! [A: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 4.98/5.25 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ A @ one_one_rat ) )
% 4.98/5.25 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right2
% 4.98/5.25 thf(fact_2115_mult__less__cancel__right2,axiom,
% 4.98/5.25 ! [A: int,C: int] :
% 4.98/5.25 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 4.98/5.25 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.25 => ( ord_less_int @ A @ one_one_int ) )
% 4.98/5.25 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 4.98/5.25 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_less_cancel_right2
% 4.98/5.25 thf(fact_2116_divide__le__eq,axiom,
% 4.98/5.25 ! [B: real,C: real,A: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_le_eq
% 4.98/5.25 thf(fact_2117_divide__le__eq,axiom,
% 4.98/5.25 ! [B: rat,C: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_le_eq
% 4.98/5.25 thf(fact_2118_le__divide__eq,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % le_divide_eq
% 4.98/5.25 thf(fact_2119_le__divide__eq,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % le_divide_eq
% 4.98/5.25 thf(fact_2120_divide__left__mono,axiom,
% 4.98/5.25 ! [B: real,A: real,C: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ B @ A )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.98/5.25 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_left_mono
% 4.98/5.25 thf(fact_2121_divide__left__mono,axiom,
% 4.98/5.25 ! [B: rat,A: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.98/5.25 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_left_mono
% 4.98/5.25 thf(fact_2122_neg__divide__le__eq,axiom,
% 4.98/5.25 ! [C: real,B: real,A: real] :
% 4.98/5.25 ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.98/5.25 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % neg_divide_le_eq
% 4.98/5.25 thf(fact_2123_neg__divide__le__eq,axiom,
% 4.98/5.25 ! [C: rat,B: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.98/5.25 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % neg_divide_le_eq
% 4.98/5.25 thf(fact_2124_neg__le__divide__eq,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % neg_le_divide_eq
% 4.98/5.25 thf(fact_2125_neg__le__divide__eq,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % neg_le_divide_eq
% 4.98/5.25 thf(fact_2126_pos__divide__le__eq,axiom,
% 4.98/5.25 ! [C: real,B: real,A: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 4.98/5.25 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % pos_divide_le_eq
% 4.98/5.25 thf(fact_2127_pos__divide__le__eq,axiom,
% 4.98/5.25 ! [C: rat,B: rat,A: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 4.98/5.25 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % pos_divide_le_eq
% 4.98/5.25 thf(fact_2128_pos__le__divide__eq,axiom,
% 4.98/5.25 ! [C: real,A: real,B: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % pos_le_divide_eq
% 4.98/5.25 thf(fact_2129_pos__le__divide__eq,axiom,
% 4.98/5.25 ! [C: rat,A: rat,B: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % pos_le_divide_eq
% 4.98/5.25 thf(fact_2130_mult__imp__div__pos__le,axiom,
% 4.98/5.25 ! [Y: real,X2: real,Z: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.25 => ( ( ord_less_eq_real @ X2 @ ( times_times_real @ Z @ Y ) )
% 4.98/5.25 => ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_imp_div_pos_le
% 4.98/5.25 thf(fact_2131_mult__imp__div__pos__le,axiom,
% 4.98/5.25 ! [Y: rat,X2: rat,Z: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.98/5.25 => ( ( ord_less_eq_rat @ X2 @ ( times_times_rat @ Z @ Y ) )
% 4.98/5.25 => ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ Z ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_imp_div_pos_le
% 4.98/5.25 thf(fact_2132_mult__imp__le__div__pos,axiom,
% 4.98/5.25 ! [Y: real,Z: real,X2: real] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.25 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X2 )
% 4.98/5.25 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_imp_le_div_pos
% 4.98/5.25 thf(fact_2133_mult__imp__le__div__pos,axiom,
% 4.98/5.25 ! [Y: rat,Z: rat,X2: rat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 4.98/5.25 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X2 )
% 4.98/5.25 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_imp_le_div_pos
% 4.98/5.25 thf(fact_2134_divide__left__mono__neg,axiom,
% 4.98/5.25 ! [A: real,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 4.98/5.25 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_left_mono_neg
% 4.98/5.25 thf(fact_2135_divide__left__mono__neg,axiom,
% 4.98/5.25 ! [A: rat,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.25 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 4.98/5.25 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_left_mono_neg
% 4.98/5.25 thf(fact_2136_convex__bound__le,axiom,
% 4.98/5.25 ! [X2: real,A: real,Y: real,U: real,V: real] :
% 4.98/5.25 ( ( ord_less_eq_real @ X2 @ A )
% 4.98/5.25 => ( ( ord_less_eq_real @ Y @ A )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 4.98/5.25 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 4.98/5.25 => ( ( ( plus_plus_real @ U @ V )
% 4.98/5.25 = one_one_real )
% 4.98/5.25 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % convex_bound_le
% 4.98/5.25 thf(fact_2137_convex__bound__le,axiom,
% 4.98/5.25 ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
% 4.98/5.25 ( ( ord_less_eq_rat @ X2 @ A )
% 4.98/5.25 => ( ( ord_less_eq_rat @ Y @ A )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 4.98/5.25 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 4.98/5.25 => ( ( ( plus_plus_rat @ U @ V )
% 4.98/5.25 = one_one_rat )
% 4.98/5.25 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % convex_bound_le
% 4.98/5.25 thf(fact_2138_convex__bound__le,axiom,
% 4.98/5.25 ! [X2: int,A: int,Y: int,U: int,V: int] :
% 4.98/5.25 ( ( ord_less_eq_int @ X2 @ A )
% 4.98/5.25 => ( ( ord_less_eq_int @ Y @ A )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 4.98/5.25 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 4.98/5.25 => ( ( ( plus_plus_int @ U @ V )
% 4.98/5.25 = one_one_int )
% 4.98/5.25 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % convex_bound_le
% 4.98/5.25 thf(fact_2139_divide__less__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [B: real,C: real,W: num] :
% 4.98/5.25 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_less_eq_numeral(1)
% 4.98/5.25 thf(fact_2140_divide__less__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [B: rat,C: rat,W: num] :
% 4.98/5.25 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % divide_less_eq_numeral(1)
% 4.98/5.25 thf(fact_2141_less__divide__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [W: num,B: real,C: real] :
% 4.98/5.25 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.25 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.25 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_divide_eq_numeral(1)
% 4.98/5.25 thf(fact_2142_less__divide__eq__numeral_I1_J,axiom,
% 4.98/5.25 ! [W: num,B: rat,C: rat] :
% 4.98/5.25 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.25 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.25 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 4.98/5.25 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.25 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % less_divide_eq_numeral(1)
% 4.98/5.25 thf(fact_2143_power__Suc__less,axiom,
% 4.98/5.25 ! [A: real,N2: nat] :
% 4.98/5.25 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.25 => ( ( ord_less_real @ A @ one_one_real )
% 4.98/5.25 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc_less
% 4.98/5.25 thf(fact_2144_power__Suc__less,axiom,
% 4.98/5.25 ! [A: rat,N2: nat] :
% 4.98/5.25 ( ( ord_less_rat @ zero_zero_rat @ A )
% 4.98/5.25 => ( ( ord_less_rat @ A @ one_one_rat )
% 4.98/5.25 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc_less
% 4.98/5.25 thf(fact_2145_power__Suc__less,axiom,
% 4.98/5.25 ! [A: nat,N2: nat] :
% 4.98/5.25 ( ( ord_less_nat @ zero_zero_nat @ A )
% 4.98/5.25 => ( ( ord_less_nat @ A @ one_one_nat )
% 4.98/5.25 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc_less
% 4.98/5.25 thf(fact_2146_power__Suc__less,axiom,
% 4.98/5.25 ! [A: int,N2: nat] :
% 4.98/5.25 ( ( ord_less_int @ zero_zero_int @ A )
% 4.98/5.25 => ( ( ord_less_int @ A @ one_one_int )
% 4.98/5.25 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 4.98/5.25
% 4.98/5.25 % power_Suc_less
% 4.98/5.25 thf(fact_2147_mult__2,axiom,
% 4.98/5.25 ! [Z: complex] :
% 4.98/5.25 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 4.98/5.25 = ( plus_plus_complex @ Z @ Z ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_2
% 4.98/5.25 thf(fact_2148_mult__2,axiom,
% 4.98/5.25 ! [Z: real] :
% 4.98/5.25 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 4.98/5.25 = ( plus_plus_real @ Z @ Z ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_2
% 4.98/5.25 thf(fact_2149_mult__2,axiom,
% 4.98/5.25 ! [Z: rat] :
% 4.98/5.25 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 4.98/5.25 = ( plus_plus_rat @ Z @ Z ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_2
% 4.98/5.25 thf(fact_2150_mult__2,axiom,
% 4.98/5.25 ! [Z: nat] :
% 4.98/5.25 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 4.98/5.25 = ( plus_plus_nat @ Z @ Z ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_2
% 4.98/5.25 thf(fact_2151_mult__2,axiom,
% 4.98/5.25 ! [Z: int] :
% 4.98/5.25 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 4.98/5.25 = ( plus_plus_int @ Z @ Z ) ) ).
% 4.98/5.25
% 4.98/5.25 % mult_2
% 4.98/5.25 thf(fact_2152_mult__2__right,axiom,
% 4.98/5.25 ! [Z: complex] :
% 4.98/5.25 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 4.98/5.25 = ( plus_plus_complex @ Z @ Z ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_2_right
% 4.98/5.26 thf(fact_2153_mult__2__right,axiom,
% 4.98/5.26 ! [Z: real] :
% 4.98/5.26 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_real @ Z @ Z ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_2_right
% 4.98/5.26 thf(fact_2154_mult__2__right,axiom,
% 4.98/5.26 ! [Z: rat] :
% 4.98/5.26 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_rat @ Z @ Z ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_2_right
% 4.98/5.26 thf(fact_2155_mult__2__right,axiom,
% 4.98/5.26 ! [Z: nat] :
% 4.98/5.26 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_nat @ Z @ Z ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_2_right
% 4.98/5.26 thf(fact_2156_mult__2__right,axiom,
% 4.98/5.26 ! [Z: int] :
% 4.98/5.26 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_int @ Z @ Z ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_2_right
% 4.98/5.26 thf(fact_2157_left__add__twice,axiom,
% 4.98/5.26 ! [A: complex,B: complex] :
% 4.98/5.26 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 4.98/5.26 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % left_add_twice
% 4.98/5.26 thf(fact_2158_left__add__twice,axiom,
% 4.98/5.26 ! [A: real,B: real] :
% 4.98/5.26 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.98/5.26 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % left_add_twice
% 4.98/5.26 thf(fact_2159_left__add__twice,axiom,
% 4.98/5.26 ! [A: rat,B: rat] :
% 4.98/5.26 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.98/5.26 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % left_add_twice
% 4.98/5.26 thf(fact_2160_left__add__twice,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.98/5.26 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % left_add_twice
% 4.98/5.26 thf(fact_2161_left__add__twice,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % left_add_twice
% 4.98/5.26 thf(fact_2162_power4__eq__xxxx,axiom,
% 4.98/5.26 ! [X2: complex] :
% 4.98/5.26 ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % power4_eq_xxxx
% 4.98/5.26 thf(fact_2163_power4__eq__xxxx,axiom,
% 4.98/5.26 ! [X2: real] :
% 4.98/5.26 ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % power4_eq_xxxx
% 4.98/5.26 thf(fact_2164_power4__eq__xxxx,axiom,
% 4.98/5.26 ! [X2: rat] :
% 4.98/5.26 ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % power4_eq_xxxx
% 4.98/5.26 thf(fact_2165_power4__eq__xxxx,axiom,
% 4.98/5.26 ! [X2: nat] :
% 4.98/5.26 ( ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % power4_eq_xxxx
% 4.98/5.26 thf(fact_2166_power4__eq__xxxx,axiom,
% 4.98/5.26 ! [X2: int] :
% 4.98/5.26 ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X2 @ X2 ) @ X2 ) @ X2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % power4_eq_xxxx
% 4.98/5.26 thf(fact_2167_power2__eq__square,axiom,
% 4.98/5.26 ! [A: complex] :
% 4.98/5.26 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( times_times_complex @ A @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_eq_square
% 4.98/5.26 thf(fact_2168_power2__eq__square,axiom,
% 4.98/5.26 ! [A: real] :
% 4.98/5.26 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( times_times_real @ A @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_eq_square
% 4.98/5.26 thf(fact_2169_power2__eq__square,axiom,
% 4.98/5.26 ! [A: rat] :
% 4.98/5.26 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( times_times_rat @ A @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_eq_square
% 4.98/5.26 thf(fact_2170_power2__eq__square,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( times_times_nat @ A @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_eq_square
% 4.98/5.26 thf(fact_2171_power2__eq__square,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( times_times_int @ A @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_eq_square
% 4.98/5.26 thf(fact_2172_power__even__eq,axiom,
% 4.98/5.26 ! [A: nat,N2: nat] :
% 4.98/5.26 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.26 = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_even_eq
% 4.98/5.26 thf(fact_2173_power__even__eq,axiom,
% 4.98/5.26 ! [A: int,N2: nat] :
% 4.98/5.26 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.26 = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_even_eq
% 4.98/5.26 thf(fact_2174_power__even__eq,axiom,
% 4.98/5.26 ! [A: real,N2: nat] :
% 4.98/5.26 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.26 = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_even_eq
% 4.98/5.26 thf(fact_2175_power__even__eq,axiom,
% 4.98/5.26 ! [A: complex,N2: nat] :
% 4.98/5.26 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.26 = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_even_eq
% 4.98/5.26 thf(fact_2176_num_Osize_I4_J,axiom,
% 4.98/5.26 ( ( size_size_num @ one )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % num.size(4)
% 4.98/5.26 thf(fact_2177_div__nat__eqI,axiom,
% 4.98/5.26 ! [N2: nat,Q2: nat,M: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q2 ) @ M )
% 4.98/5.26 => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q2 ) ) )
% 4.98/5.26 => ( ( divide_divide_nat @ M @ N2 )
% 4.98/5.26 = Q2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_nat_eqI
% 4.98/5.26 thf(fact_2178_less__eq__div__iff__mult__less__eq,axiom,
% 4.98/5.26 ! [Q2: nat,M: nat,N2: nat] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 4.98/5.26 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q2 ) )
% 4.98/5.26 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % less_eq_div_iff_mult_less_eq
% 4.98/5.26 thf(fact_2179_split__div,axiom,
% 4.98/5.26 ! [P: nat > $o,M: nat,N2: nat] :
% 4.98/5.26 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 4.98/5.26 = ( ( ( N2 = zero_zero_nat )
% 4.98/5.26 => ( P @ zero_zero_nat ) )
% 4.98/5.26 & ( ( N2 != zero_zero_nat )
% 4.98/5.26 => ! [I5: nat,J3: nat] :
% 4.98/5.26 ( ( ord_less_nat @ J3 @ N2 )
% 4.98/5.26 => ( ( M
% 4.98/5.26 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 4.98/5.26 => ( P @ I5 ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % split_div
% 4.98/5.26 thf(fact_2180_dividend__less__div__times,axiom,
% 4.98/5.26 ! [N2: nat,M: nat] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.26 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dividend_less_div_times
% 4.98/5.26 thf(fact_2181_dividend__less__times__div,axiom,
% 4.98/5.26 ! [N2: nat,M: nat] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.26 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dividend_less_times_div
% 4.98/5.26 thf(fact_2182_convex__bound__lt,axiom,
% 4.98/5.26 ! [X2: real,A: real,Y: real,U: real,V: real] :
% 4.98/5.26 ( ( ord_less_real @ X2 @ A )
% 4.98/5.26 => ( ( ord_less_real @ Y @ A )
% 4.98/5.26 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 4.98/5.26 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 4.98/5.26 => ( ( ( plus_plus_real @ U @ V )
% 4.98/5.26 = one_one_real )
% 4.98/5.26 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X2 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % convex_bound_lt
% 4.98/5.26 thf(fact_2183_convex__bound__lt,axiom,
% 4.98/5.26 ! [X2: rat,A: rat,Y: rat,U: rat,V: rat] :
% 4.98/5.26 ( ( ord_less_rat @ X2 @ A )
% 4.98/5.26 => ( ( ord_less_rat @ Y @ A )
% 4.98/5.26 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 4.98/5.26 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 4.98/5.26 => ( ( ( plus_plus_rat @ U @ V )
% 4.98/5.26 = one_one_rat )
% 4.98/5.26 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X2 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % convex_bound_lt
% 4.98/5.26 thf(fact_2184_convex__bound__lt,axiom,
% 4.98/5.26 ! [X2: int,A: int,Y: int,U: int,V: int] :
% 4.98/5.26 ( ( ord_less_int @ X2 @ A )
% 4.98/5.26 => ( ( ord_less_int @ Y @ A )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 4.98/5.26 => ( ( ( plus_plus_int @ U @ V )
% 4.98/5.26 = one_one_int )
% 4.98/5.26 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X2 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % convex_bound_lt
% 4.98/5.26 thf(fact_2185_divide__le__eq__numeral_I1_J,axiom,
% 4.98/5.26 ! [B: real,C: real,W: num] :
% 4.98/5.26 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 4.98/5.26 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.26 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 4.98/5.26 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.26 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.26 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 4.98/5.26 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.26 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % divide_le_eq_numeral(1)
% 4.98/5.26 thf(fact_2186_divide__le__eq__numeral_I1_J,axiom,
% 4.98/5.26 ! [B: rat,C: rat,W: num] :
% 4.98/5.26 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 4.98/5.26 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.26 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 4.98/5.26 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.26 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.26 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 4.98/5.26 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.26 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % divide_le_eq_numeral(1)
% 4.98/5.26 thf(fact_2187_le__divide__eq__numeral_I1_J,axiom,
% 4.98/5.26 ! [W: num,B: real,C: real] :
% 4.98/5.26 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 4.98/5.26 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.26 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 4.98/5.26 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 4.98/5.26 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.26 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 4.98/5.26 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 4.98/5.26 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % le_divide_eq_numeral(1)
% 4.98/5.26 thf(fact_2188_le__divide__eq__numeral_I1_J,axiom,
% 4.98/5.26 ! [W: num,B: rat,C: rat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 4.98/5.26 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.26 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 4.98/5.26 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 4.98/5.26 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.26 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 4.98/5.26 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 4.98/5.26 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % le_divide_eq_numeral(1)
% 4.98/5.26 thf(fact_2189_split__div_H,axiom,
% 4.98/5.26 ! [P: nat > $o,M: nat,N2: nat] :
% 4.98/5.26 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 4.98/5.26 = ( ( ( N2 = zero_zero_nat )
% 4.98/5.26 & ( P @ zero_zero_nat ) )
% 4.98/5.26 | ? [Q4: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q4 ) @ M )
% 4.98/5.26 & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q4 ) ) )
% 4.98/5.26 & ( P @ Q4 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % split_div'
% 4.98/5.26 thf(fact_2190_power2__sum,axiom,
% 4.98/5.26 ! [X2: complex,Y: complex] :
% 4.98/5.26 ( ( power_power_complex @ ( plus_plus_complex @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_sum
% 4.98/5.26 thf(fact_2191_power2__sum,axiom,
% 4.98/5.26 ! [X2: real,Y: real] :
% 4.98/5.26 ( ( power_power_real @ ( plus_plus_real @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( 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 ) ) @ X2 ) @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_sum
% 4.98/5.26 thf(fact_2192_power2__sum,axiom,
% 4.98/5.26 ! [X2: rat,Y: rat] :
% 4.98/5.26 ( ( power_power_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( 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 ) ) @ X2 ) @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_sum
% 4.98/5.26 thf(fact_2193_power2__sum,axiom,
% 4.98/5.26 ! [X2: nat,Y: nat] :
% 4.98/5.26 ( ( power_power_nat @ ( plus_plus_nat @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_sum
% 4.98/5.26 thf(fact_2194_power2__sum,axiom,
% 4.98/5.26 ! [X2: int,Y: int] :
% 4.98/5.26 ( ( power_power_int @ ( plus_plus_int @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( 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 ) ) @ X2 ) @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power2_sum
% 4.98/5.26 thf(fact_2195_zero__le__even__power_H,axiom,
% 4.98/5.26 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zero_le_even_power'
% 4.98/5.26 thf(fact_2196_zero__le__even__power_H,axiom,
% 4.98/5.26 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zero_le_even_power'
% 4.98/5.26 thf(fact_2197_zero__le__even__power_H,axiom,
% 4.98/5.26 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zero_le_even_power'
% 4.98/5.26 thf(fact_2198_nat__bit__induct,axiom,
% 4.98/5.26 ! [P: nat > $o,N2: nat] :
% 4.98/5.26 ( ( P @ zero_zero_nat )
% 4.98/5.26 => ( ! [N: nat] :
% 4.98/5.26 ( ( P @ N )
% 4.98/5.26 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.98/5.26 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.98/5.26 => ( ! [N: nat] :
% 4.98/5.26 ( ( P @ N )
% 4.98/5.26 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 4.98/5.26 => ( P @ N2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % nat_bit_induct
% 4.98/5.26 thf(fact_2199_field__lbound__gt__zero,axiom,
% 4.98/5.26 ! [D1: real,D22: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ D1 )
% 4.98/5.26 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 4.98/5.26 => ? [E: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ E )
% 4.98/5.26 & ( ord_less_real @ E @ D1 )
% 4.98/5.26 & ( ord_less_real @ E @ D22 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % field_lbound_gt_zero
% 4.98/5.26 thf(fact_2200_field__lbound__gt__zero,axiom,
% 4.98/5.26 ! [D1: rat,D22: rat] :
% 4.98/5.26 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 4.98/5.26 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 4.98/5.26 => ? [E: rat] :
% 4.98/5.26 ( ( ord_less_rat @ zero_zero_rat @ E )
% 4.98/5.26 & ( ord_less_rat @ E @ D1 )
% 4.98/5.26 & ( ord_less_rat @ E @ D22 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % field_lbound_gt_zero
% 4.98/5.26 thf(fact_2201_two__realpow__ge__one,axiom,
% 4.98/5.26 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % two_realpow_ge_one
% 4.98/5.26 thf(fact_2202_option_Osize_I4_J,axiom,
% 4.98/5.26 ! [X22: product_prod_nat_nat] :
% 4.98/5.26 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 4.98/5.26 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % option.size(4)
% 4.98/5.26 thf(fact_2203_option_Osize_I4_J,axiom,
% 4.98/5.26 ! [X22: num] :
% 4.98/5.26 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 4.98/5.26 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % option.size(4)
% 4.98/5.26 thf(fact_2204_max_Omono,axiom,
% 4.98/5.26 ! [C: rat,A: rat,D: rat,B: rat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ C @ A )
% 4.98/5.26 => ( ( ord_less_eq_rat @ D @ B )
% 4.98/5.26 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.mono
% 4.98/5.26 thf(fact_2205_max_Omono,axiom,
% 4.98/5.26 ! [C: num,A: num,D: num,B: num] :
% 4.98/5.26 ( ( ord_less_eq_num @ C @ A )
% 4.98/5.26 => ( ( ord_less_eq_num @ D @ B )
% 4.98/5.26 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.mono
% 4.98/5.26 thf(fact_2206_max_Omono,axiom,
% 4.98/5.26 ! [C: nat,A: nat,D: nat,B: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ C @ A )
% 4.98/5.26 => ( ( ord_less_eq_nat @ D @ B )
% 4.98/5.26 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.mono
% 4.98/5.26 thf(fact_2207_max_Omono,axiom,
% 4.98/5.26 ! [C: int,A: int,D: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ C @ A )
% 4.98/5.26 => ( ( ord_less_eq_int @ D @ B )
% 4.98/5.26 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.mono
% 4.98/5.26 thf(fact_2208_max_OorderE,axiom,
% 4.98/5.26 ! [B: rat,A: rat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.26 => ( A
% 4.98/5.26 = ( ord_max_rat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.orderE
% 4.98/5.26 thf(fact_2209_max_OorderE,axiom,
% 4.98/5.26 ! [B: num,A: num] :
% 4.98/5.26 ( ( ord_less_eq_num @ B @ A )
% 4.98/5.26 => ( A
% 4.98/5.26 = ( ord_max_num @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.orderE
% 4.98/5.26 thf(fact_2210_max_OorderE,axiom,
% 4.98/5.26 ! [B: nat,A: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.26 => ( A
% 4.98/5.26 = ( ord_max_nat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.orderE
% 4.98/5.26 thf(fact_2211_max_OorderE,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ B @ A )
% 4.98/5.26 => ( A
% 4.98/5.26 = ( ord_max_int @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.orderE
% 4.98/5.26 thf(fact_2212_max_OorderI,axiom,
% 4.98/5.26 ! [A: rat,B: rat] :
% 4.98/5.26 ( ( A
% 4.98/5.26 = ( ord_max_rat @ A @ B ) )
% 4.98/5.26 => ( ord_less_eq_rat @ B @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.orderI
% 4.98/5.26 thf(fact_2213_max_OorderI,axiom,
% 4.98/5.26 ! [A: num,B: num] :
% 4.98/5.26 ( ( A
% 4.98/5.26 = ( ord_max_num @ A @ B ) )
% 4.98/5.26 => ( ord_less_eq_num @ B @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.orderI
% 4.98/5.26 thf(fact_2214_max_OorderI,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( A
% 4.98/5.26 = ( ord_max_nat @ A @ B ) )
% 4.98/5.26 => ( ord_less_eq_nat @ B @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.orderI
% 4.98/5.26 thf(fact_2215_max_OorderI,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( A
% 4.98/5.26 = ( ord_max_int @ A @ B ) )
% 4.98/5.26 => ( ord_less_eq_int @ B @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.orderI
% 4.98/5.26 thf(fact_2216_max_OboundedE,axiom,
% 4.98/5.26 ! [B: rat,C: rat,A: rat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.26 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.boundedE
% 4.98/5.26 thf(fact_2217_max_OboundedE,axiom,
% 4.98/5.26 ! [B: num,C: num,A: num] :
% 4.98/5.26 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_eq_num @ B @ A )
% 4.98/5.26 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.boundedE
% 4.98/5.26 thf(fact_2218_max_OboundedE,axiom,
% 4.98/5.26 ! [B: nat,C: nat,A: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.26 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.boundedE
% 4.98/5.26 thf(fact_2219_max_OboundedE,axiom,
% 4.98/5.26 ! [B: int,C: int,A: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_eq_int @ B @ A )
% 4.98/5.26 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.boundedE
% 4.98/5.26 thf(fact_2220_max_OboundedI,axiom,
% 4.98/5.26 ! [B: rat,A: rat,C: rat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.26 => ( ( ord_less_eq_rat @ C @ A )
% 4.98/5.26 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.boundedI
% 4.98/5.26 thf(fact_2221_max_OboundedI,axiom,
% 4.98/5.26 ! [B: num,A: num,C: num] :
% 4.98/5.26 ( ( ord_less_eq_num @ B @ A )
% 4.98/5.26 => ( ( ord_less_eq_num @ C @ A )
% 4.98/5.26 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.boundedI
% 4.98/5.26 thf(fact_2222_max_OboundedI,axiom,
% 4.98/5.26 ! [B: nat,A: nat,C: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.26 => ( ( ord_less_eq_nat @ C @ A )
% 4.98/5.26 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.boundedI
% 4.98/5.26 thf(fact_2223_max_OboundedI,axiom,
% 4.98/5.26 ! [B: int,A: int,C: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ B @ A )
% 4.98/5.26 => ( ( ord_less_eq_int @ C @ A )
% 4.98/5.26 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.boundedI
% 4.98/5.26 thf(fact_2224_max_Oorder__iff,axiom,
% 4.98/5.26 ( ord_less_eq_rat
% 4.98/5.26 = ( ^ [B5: rat,A5: rat] :
% 4.98/5.26 ( A5
% 4.98/5.26 = ( ord_max_rat @ A5 @ B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.order_iff
% 4.98/5.26 thf(fact_2225_max_Oorder__iff,axiom,
% 4.98/5.26 ( ord_less_eq_num
% 4.98/5.26 = ( ^ [B5: num,A5: num] :
% 4.98/5.26 ( A5
% 4.98/5.26 = ( ord_max_num @ A5 @ B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.order_iff
% 4.98/5.26 thf(fact_2226_max_Oorder__iff,axiom,
% 4.98/5.26 ( ord_less_eq_nat
% 4.98/5.26 = ( ^ [B5: nat,A5: nat] :
% 4.98/5.26 ( A5
% 4.98/5.26 = ( ord_max_nat @ A5 @ B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.order_iff
% 4.98/5.26 thf(fact_2227_max_Oorder__iff,axiom,
% 4.98/5.26 ( ord_less_eq_int
% 4.98/5.26 = ( ^ [B5: int,A5: int] :
% 4.98/5.26 ( A5
% 4.98/5.26 = ( ord_max_int @ A5 @ B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.order_iff
% 4.98/5.26 thf(fact_2228_max_Ocobounded1,axiom,
% 4.98/5.26 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.cobounded1
% 4.98/5.26 thf(fact_2229_max_Ocobounded1,axiom,
% 4.98/5.26 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.cobounded1
% 4.98/5.26 thf(fact_2230_max_Ocobounded1,axiom,
% 4.98/5.26 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.cobounded1
% 4.98/5.26 thf(fact_2231_max_Ocobounded1,axiom,
% 4.98/5.26 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.cobounded1
% 4.98/5.26 thf(fact_2232_max_Ocobounded2,axiom,
% 4.98/5.26 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.cobounded2
% 4.98/5.26 thf(fact_2233_max_Ocobounded2,axiom,
% 4.98/5.26 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.cobounded2
% 4.98/5.26 thf(fact_2234_max_Ocobounded2,axiom,
% 4.98/5.26 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.cobounded2
% 4.98/5.26 thf(fact_2235_max_Ocobounded2,axiom,
% 4.98/5.26 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.cobounded2
% 4.98/5.26 thf(fact_2236_le__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: rat,X2: rat,Y: rat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_eq_rat @ Z @ X2 )
% 4.98/5.26 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % le_max_iff_disj
% 4.98/5.26 thf(fact_2237_le__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: num,X2: num,Y: num] :
% 4.98/5.26 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_eq_num @ Z @ X2 )
% 4.98/5.26 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % le_max_iff_disj
% 4.98/5.26 thf(fact_2238_le__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: nat,X2: nat,Y: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_eq_nat @ Z @ X2 )
% 4.98/5.26 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % le_max_iff_disj
% 4.98/5.26 thf(fact_2239_le__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: int,X2: int,Y: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_eq_int @ Z @ X2 )
% 4.98/5.26 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % le_max_iff_disj
% 4.98/5.26 thf(fact_2240_max_Oabsorb__iff1,axiom,
% 4.98/5.26 ( ord_less_eq_rat
% 4.98/5.26 = ( ^ [B5: rat,A5: rat] :
% 4.98/5.26 ( ( ord_max_rat @ A5 @ B5 )
% 4.98/5.26 = A5 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.absorb_iff1
% 4.98/5.26 thf(fact_2241_max_Oabsorb__iff1,axiom,
% 4.98/5.26 ( ord_less_eq_num
% 4.98/5.26 = ( ^ [B5: num,A5: num] :
% 4.98/5.26 ( ( ord_max_num @ A5 @ B5 )
% 4.98/5.26 = A5 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.absorb_iff1
% 4.98/5.26 thf(fact_2242_max_Oabsorb__iff1,axiom,
% 4.98/5.26 ( ord_less_eq_nat
% 4.98/5.26 = ( ^ [B5: nat,A5: nat] :
% 4.98/5.26 ( ( ord_max_nat @ A5 @ B5 )
% 4.98/5.26 = A5 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.absorb_iff1
% 4.98/5.26 thf(fact_2243_max_Oabsorb__iff1,axiom,
% 4.98/5.26 ( ord_less_eq_int
% 4.98/5.26 = ( ^ [B5: int,A5: int] :
% 4.98/5.26 ( ( ord_max_int @ A5 @ B5 )
% 4.98/5.26 = A5 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.absorb_iff1
% 4.98/5.26 thf(fact_2244_max_Oabsorb__iff2,axiom,
% 4.98/5.26 ( ord_less_eq_rat
% 4.98/5.26 = ( ^ [A5: rat,B5: rat] :
% 4.98/5.26 ( ( ord_max_rat @ A5 @ B5 )
% 4.98/5.26 = B5 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.absorb_iff2
% 4.98/5.26 thf(fact_2245_max_Oabsorb__iff2,axiom,
% 4.98/5.26 ( ord_less_eq_num
% 4.98/5.26 = ( ^ [A5: num,B5: num] :
% 4.98/5.26 ( ( ord_max_num @ A5 @ B5 )
% 4.98/5.26 = B5 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.absorb_iff2
% 4.98/5.26 thf(fact_2246_max_Oabsorb__iff2,axiom,
% 4.98/5.26 ( ord_less_eq_nat
% 4.98/5.26 = ( ^ [A5: nat,B5: nat] :
% 4.98/5.26 ( ( ord_max_nat @ A5 @ B5 )
% 4.98/5.26 = B5 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.absorb_iff2
% 4.98/5.26 thf(fact_2247_max_Oabsorb__iff2,axiom,
% 4.98/5.26 ( ord_less_eq_int
% 4.98/5.26 = ( ^ [A5: int,B5: int] :
% 4.98/5.26 ( ( ord_max_int @ A5 @ B5 )
% 4.98/5.26 = B5 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.absorb_iff2
% 4.98/5.26 thf(fact_2248_max_OcoboundedI1,axiom,
% 4.98/5.26 ! [C: rat,A: rat,B: rat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ C @ A )
% 4.98/5.26 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.coboundedI1
% 4.98/5.26 thf(fact_2249_max_OcoboundedI1,axiom,
% 4.98/5.26 ! [C: num,A: num,B: num] :
% 4.98/5.26 ( ( ord_less_eq_num @ C @ A )
% 4.98/5.26 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.coboundedI1
% 4.98/5.26 thf(fact_2250_max_OcoboundedI1,axiom,
% 4.98/5.26 ! [C: nat,A: nat,B: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ C @ A )
% 4.98/5.26 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.coboundedI1
% 4.98/5.26 thf(fact_2251_max_OcoboundedI1,axiom,
% 4.98/5.26 ! [C: int,A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ C @ A )
% 4.98/5.26 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.coboundedI1
% 4.98/5.26 thf(fact_2252_max_OcoboundedI2,axiom,
% 4.98/5.26 ! [C: rat,B: rat,A: rat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ C @ B )
% 4.98/5.26 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.coboundedI2
% 4.98/5.26 thf(fact_2253_max_OcoboundedI2,axiom,
% 4.98/5.26 ! [C: num,B: num,A: num] :
% 4.98/5.26 ( ( ord_less_eq_num @ C @ B )
% 4.98/5.26 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.coboundedI2
% 4.98/5.26 thf(fact_2254_max_OcoboundedI2,axiom,
% 4.98/5.26 ! [C: nat,B: nat,A: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ C @ B )
% 4.98/5.26 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.coboundedI2
% 4.98/5.26 thf(fact_2255_max_OcoboundedI2,axiom,
% 4.98/5.26 ! [C: int,B: int,A: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ C @ B )
% 4.98/5.26 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.coboundedI2
% 4.98/5.26 thf(fact_2256_less__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: real,X2: real,Y: real] :
% 4.98/5.26 ( ( ord_less_real @ Z @ ( ord_max_real @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_real @ Z @ X2 )
% 4.98/5.26 | ( ord_less_real @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % less_max_iff_disj
% 4.98/5.26 thf(fact_2257_less__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: rat,X2: rat,Y: rat] :
% 4.98/5.26 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_rat @ Z @ X2 )
% 4.98/5.26 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % less_max_iff_disj
% 4.98/5.26 thf(fact_2258_less__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: num,X2: num,Y: num] :
% 4.98/5.26 ( ( ord_less_num @ Z @ ( ord_max_num @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_num @ Z @ X2 )
% 4.98/5.26 | ( ord_less_num @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % less_max_iff_disj
% 4.98/5.26 thf(fact_2259_less__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: nat,X2: nat,Y: nat] :
% 4.98/5.26 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_nat @ Z @ X2 )
% 4.98/5.26 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % less_max_iff_disj
% 4.98/5.26 thf(fact_2260_less__max__iff__disj,axiom,
% 4.98/5.26 ! [Z: int,X2: int,Y: int] :
% 4.98/5.26 ( ( ord_less_int @ Z @ ( ord_max_int @ X2 @ Y ) )
% 4.98/5.26 = ( ( ord_less_int @ Z @ X2 )
% 4.98/5.26 | ( ord_less_int @ Z @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % less_max_iff_disj
% 4.98/5.26 thf(fact_2261_max_Ostrict__boundedE,axiom,
% 4.98/5.26 ! [B: real,C: real,A: real] :
% 4.98/5.26 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_real @ B @ A )
% 4.98/5.26 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_boundedE
% 4.98/5.26 thf(fact_2262_max_Ostrict__boundedE,axiom,
% 4.98/5.26 ! [B: rat,C: rat,A: rat] :
% 4.98/5.26 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_rat @ B @ A )
% 4.98/5.26 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_boundedE
% 4.98/5.26 thf(fact_2263_max_Ostrict__boundedE,axiom,
% 4.98/5.26 ! [B: num,C: num,A: num] :
% 4.98/5.26 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_num @ B @ A )
% 4.98/5.26 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_boundedE
% 4.98/5.26 thf(fact_2264_max_Ostrict__boundedE,axiom,
% 4.98/5.26 ! [B: nat,C: nat,A: nat] :
% 4.98/5.26 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_nat @ B @ A )
% 4.98/5.26 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_boundedE
% 4.98/5.26 thf(fact_2265_max_Ostrict__boundedE,axiom,
% 4.98/5.26 ! [B: int,C: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 4.98/5.26 => ~ ( ( ord_less_int @ B @ A )
% 4.98/5.26 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_boundedE
% 4.98/5.26 thf(fact_2266_max_Ostrict__order__iff,axiom,
% 4.98/5.26 ( ord_less_real
% 4.98/5.26 = ( ^ [B5: real,A5: real] :
% 4.98/5.26 ( ( A5
% 4.98/5.26 = ( ord_max_real @ A5 @ B5 ) )
% 4.98/5.26 & ( A5 != B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_order_iff
% 4.98/5.26 thf(fact_2267_max_Ostrict__order__iff,axiom,
% 4.98/5.26 ( ord_less_rat
% 4.98/5.26 = ( ^ [B5: rat,A5: rat] :
% 4.98/5.26 ( ( A5
% 4.98/5.26 = ( ord_max_rat @ A5 @ B5 ) )
% 4.98/5.26 & ( A5 != B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_order_iff
% 4.98/5.26 thf(fact_2268_max_Ostrict__order__iff,axiom,
% 4.98/5.26 ( ord_less_num
% 4.98/5.26 = ( ^ [B5: num,A5: num] :
% 4.98/5.26 ( ( A5
% 4.98/5.26 = ( ord_max_num @ A5 @ B5 ) )
% 4.98/5.26 & ( A5 != B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_order_iff
% 4.98/5.26 thf(fact_2269_max_Ostrict__order__iff,axiom,
% 4.98/5.26 ( ord_less_nat
% 4.98/5.26 = ( ^ [B5: nat,A5: nat] :
% 4.98/5.26 ( ( A5
% 4.98/5.26 = ( ord_max_nat @ A5 @ B5 ) )
% 4.98/5.26 & ( A5 != B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_order_iff
% 4.98/5.26 thf(fact_2270_max_Ostrict__order__iff,axiom,
% 4.98/5.26 ( ord_less_int
% 4.98/5.26 = ( ^ [B5: int,A5: int] :
% 4.98/5.26 ( ( A5
% 4.98/5.26 = ( ord_max_int @ A5 @ B5 ) )
% 4.98/5.26 & ( A5 != B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_order_iff
% 4.98/5.26 thf(fact_2271_max_Ostrict__coboundedI1,axiom,
% 4.98/5.26 ! [C: real,A: real,B: real] :
% 4.98/5.26 ( ( ord_less_real @ C @ A )
% 4.98/5.26 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI1
% 4.98/5.26 thf(fact_2272_max_Ostrict__coboundedI1,axiom,
% 4.98/5.26 ! [C: rat,A: rat,B: rat] :
% 4.98/5.26 ( ( ord_less_rat @ C @ A )
% 4.98/5.26 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI1
% 4.98/5.26 thf(fact_2273_max_Ostrict__coboundedI1,axiom,
% 4.98/5.26 ! [C: num,A: num,B: num] :
% 4.98/5.26 ( ( ord_less_num @ C @ A )
% 4.98/5.26 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI1
% 4.98/5.26 thf(fact_2274_max_Ostrict__coboundedI1,axiom,
% 4.98/5.26 ! [C: nat,A: nat,B: nat] :
% 4.98/5.26 ( ( ord_less_nat @ C @ A )
% 4.98/5.26 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI1
% 4.98/5.26 thf(fact_2275_max_Ostrict__coboundedI1,axiom,
% 4.98/5.26 ! [C: int,A: int,B: int] :
% 4.98/5.26 ( ( ord_less_int @ C @ A )
% 4.98/5.26 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI1
% 4.98/5.26 thf(fact_2276_max_Ostrict__coboundedI2,axiom,
% 4.98/5.26 ! [C: real,B: real,A: real] :
% 4.98/5.26 ( ( ord_less_real @ C @ B )
% 4.98/5.26 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI2
% 4.98/5.26 thf(fact_2277_max_Ostrict__coboundedI2,axiom,
% 4.98/5.26 ! [C: rat,B: rat,A: rat] :
% 4.98/5.26 ( ( ord_less_rat @ C @ B )
% 4.98/5.26 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI2
% 4.98/5.26 thf(fact_2278_max_Ostrict__coboundedI2,axiom,
% 4.98/5.26 ! [C: num,B: num,A: num] :
% 4.98/5.26 ( ( ord_less_num @ C @ B )
% 4.98/5.26 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI2
% 4.98/5.26 thf(fact_2279_max_Ostrict__coboundedI2,axiom,
% 4.98/5.26 ! [C: nat,B: nat,A: nat] :
% 4.98/5.26 ( ( ord_less_nat @ C @ B )
% 4.98/5.26 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI2
% 4.98/5.26 thf(fact_2280_max_Ostrict__coboundedI2,axiom,
% 4.98/5.26 ! [C: int,B: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ C @ B )
% 4.98/5.26 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % max.strict_coboundedI2
% 4.98/5.26 thf(fact_2281_odd__0__le__power__imp__0__le,axiom,
% 4.98/5.26 ! [A: real,N2: nat] :
% 4.98/5.26 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 4.98/5.26 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % odd_0_le_power_imp_0_le
% 4.98/5.26 thf(fact_2282_odd__0__le__power__imp__0__le,axiom,
% 4.98/5.26 ! [A: rat,N2: nat] :
% 4.98/5.26 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 4.98/5.26 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % odd_0_le_power_imp_0_le
% 4.98/5.26 thf(fact_2283_odd__0__le__power__imp__0__le,axiom,
% 4.98/5.26 ! [A: int,N2: nat] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 4.98/5.26 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % odd_0_le_power_imp_0_le
% 4.98/5.26 thf(fact_2284_less__eq__int__code_I1_J,axiom,
% 4.98/5.26 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 4.98/5.26
% 4.98/5.26 % less_eq_int_code(1)
% 4.98/5.26 thf(fact_2285_odd__power__less__zero,axiom,
% 4.98/5.26 ! [A: real,N2: nat] :
% 4.98/5.26 ( ( ord_less_real @ A @ zero_zero_real )
% 4.98/5.26 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 4.98/5.26
% 4.98/5.26 % odd_power_less_zero
% 4.98/5.26 thf(fact_2286_odd__power__less__zero,axiom,
% 4.98/5.26 ! [A: rat,N2: nat] :
% 4.98/5.26 ( ( ord_less_rat @ A @ zero_zero_rat )
% 4.98/5.26 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 4.98/5.26
% 4.98/5.26 % odd_power_less_zero
% 4.98/5.26 thf(fact_2287_odd__power__less__zero,axiom,
% 4.98/5.26 ! [A: int,N2: nat] :
% 4.98/5.26 ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.26 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % odd_power_less_zero
% 4.98/5.26 thf(fact_2288_odd__less__0__iff,axiom,
% 4.98/5.26 ! [Z: int] :
% 4.98/5.26 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 4.98/5.26 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % odd_less_0_iff
% 4.98/5.26 thf(fact_2289_less__int__code_I1_J,axiom,
% 4.98/5.26 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % less_int_code(1)
% 4.98/5.26 thf(fact_2290_zless__imp__add1__zle,axiom,
% 4.98/5.26 ! [W: int,Z: int] :
% 4.98/5.26 ( ( ord_less_int @ W @ Z )
% 4.98/5.26 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 4.98/5.26
% 4.98/5.26 % zless_imp_add1_zle
% 4.98/5.26 thf(fact_2291_add1__zle__eq,axiom,
% 4.98/5.26 ! [W: int,Z: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 4.98/5.26 = ( ord_less_int @ W @ Z ) ) ).
% 4.98/5.26
% 4.98/5.26 % add1_zle_eq
% 4.98/5.26 thf(fact_2292_num_Osize_I5_J,axiom,
% 4.98/5.26 ! [X22: num] :
% 4.98/5.26 ( ( size_size_num @ ( bit0 @ X22 ) )
% 4.98/5.26 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % num.size(5)
% 4.98/5.26 thf(fact_2293_int__one__le__iff__zero__less,axiom,
% 4.98/5.26 ! [Z: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ one_one_int @ Z )
% 4.98/5.26 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 4.98/5.26
% 4.98/5.26 % int_one_le_iff_zero_less
% 4.98/5.26 thf(fact_2294_le__imp__0__less,axiom,
% 4.98/5.26 ! [Z: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 4.98/5.26 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % le_imp_0_less
% 4.98/5.26 thf(fact_2295_pos__imp__zdiv__neg__iff,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.26 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 4.98/5.26 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % pos_imp_zdiv_neg_iff
% 4.98/5.26 thf(fact_2296_neg__imp__zdiv__neg__iff,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.26 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 4.98/5.26 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % neg_imp_zdiv_neg_iff
% 4.98/5.26 thf(fact_2297_int__div__less__self,axiom,
% 4.98/5.26 ! [X2: int,K: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ X2 )
% 4.98/5.26 => ( ( ord_less_int @ one_one_int @ K )
% 4.98/5.26 => ( ord_less_int @ ( divide_divide_int @ X2 @ K ) @ X2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % int_div_less_self
% 4.98/5.26 thf(fact_2298_div__neg__pos__less0,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.26 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_neg_pos_less0
% 4.98/5.26 thf(fact_2299_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 4.98/5.26 ! [Uz: product_prod_nat_nat,Va2: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 4.98/5.26 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va2 @ Vb @ Vc ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.minNull.simps(5)
% 4.98/5.26 thf(fact_2300_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.26 => ( ( ord_less_nat @ A @ B )
% 4.98/5.26 => ( ( divide_divide_nat @ A @ B )
% 4.98/5.26 = zero_zero_nat ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.div_less
% 4.98/5.26 thf(fact_2301_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.26 => ( ( ord_less_int @ A @ B )
% 4.98/5.26 => ( ( divide_divide_int @ A @ B )
% 4.98/5.26 = zero_zero_int ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.div_less
% 4.98/5.26 thf(fact_2302_div__positive,axiom,
% 4.98/5.26 ! [B: nat,A: nat] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.26 => ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.26 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_positive
% 4.98/5.26 thf(fact_2303_div__positive,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.26 => ( ( ord_less_eq_int @ B @ A )
% 4.98/5.26 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_positive
% 4.98/5.26 thf(fact_2304_discrete,axiom,
% 4.98/5.26 ( ord_less_nat
% 4.98/5.26 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % discrete
% 4.98/5.26 thf(fact_2305_discrete,axiom,
% 4.98/5.26 ( ord_less_int
% 4.98/5.26 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % discrete
% 4.98/5.26 thf(fact_2306_nonneg1__imp__zdiv__pos__iff,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 4.98/5.26 = ( ( ord_less_eq_int @ B @ A )
% 4.98/5.26 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % nonneg1_imp_zdiv_pos_iff
% 4.98/5.26 thf(fact_2307_pos__imp__zdiv__nonneg__iff,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 4.98/5.26 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % pos_imp_zdiv_nonneg_iff
% 4.98/5.26 thf(fact_2308_neg__imp__zdiv__nonneg__iff,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 4.98/5.26 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % neg_imp_zdiv_nonneg_iff
% 4.98/5.26 thf(fact_2309_pos__imp__zdiv__pos__iff,axiom,
% 4.98/5.26 ! [K: int,I3: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ K )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I3 @ K ) )
% 4.98/5.26 = ( ord_less_eq_int @ K @ I3 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % pos_imp_zdiv_pos_iff
% 4.98/5.26 thf(fact_2310_div__nonpos__pos__le0,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.26 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_nonpos_pos_le0
% 4.98/5.26 thf(fact_2311_div__nonneg__neg__le0,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.26 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.26 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_nonneg_neg_le0
% 4.98/5.26 thf(fact_2312_div__positive__int,axiom,
% 4.98/5.26 ! [L: int,K: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ L @ K )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ L )
% 4.98/5.26 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_positive_int
% 4.98/5.26 thf(fact_2313_div__int__pos__iff,axiom,
% 4.98/5.26 ! [K: int,L: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 4.98/5.26 = ( ( K = zero_zero_int )
% 4.98/5.26 | ( L = zero_zero_int )
% 4.98/5.26 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.98/5.26 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 4.98/5.26 | ( ( ord_less_int @ K @ zero_zero_int )
% 4.98/5.26 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_int_pos_iff
% 4.98/5.26 thf(fact_2314_zdiv__mono2__neg,axiom,
% 4.98/5.26 ! [A: int,B2: int,B: int] :
% 4.98/5.26 ( ( ord_less_int @ A @ zero_zero_int )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 4.98/5.26 => ( ( ord_less_eq_int @ B2 @ B )
% 4.98/5.26 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zdiv_mono2_neg
% 4.98/5.26 thf(fact_2315_zdiv__mono1__neg,axiom,
% 4.98/5.26 ! [A: int,A2: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ A @ A2 )
% 4.98/5.26 => ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.26 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zdiv_mono1_neg
% 4.98/5.26 thf(fact_2316_zdiv__eq__0__iff,axiom,
% 4.98/5.26 ! [I3: int,K: int] :
% 4.98/5.26 ( ( ( divide_divide_int @ I3 @ K )
% 4.98/5.26 = zero_zero_int )
% 4.98/5.26 = ( ( K = zero_zero_int )
% 4.98/5.26 | ( ( ord_less_eq_int @ zero_zero_int @ I3 )
% 4.98/5.26 & ( ord_less_int @ I3 @ K ) )
% 4.98/5.26 | ( ( ord_less_eq_int @ I3 @ zero_zero_int )
% 4.98/5.26 & ( ord_less_int @ K @ I3 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zdiv_eq_0_iff
% 4.98/5.26 thf(fact_2317_zdiv__mono2,axiom,
% 4.98/5.26 ! [A: int,B2: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 4.98/5.26 => ( ( ord_less_eq_int @ B2 @ B )
% 4.98/5.26 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zdiv_mono2
% 4.98/5.26 thf(fact_2318_zdiv__mono1,axiom,
% 4.98/5.26 ! [A: int,A2: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ A @ A2 )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.26 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zdiv_mono1
% 4.98/5.26 thf(fact_2319_vebt__member_Osimps_I3_J,axiom,
% 4.98/5.26 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X2: nat] :
% 4.98/5.26 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X2 ) ).
% 4.98/5.26
% 4.98/5.26 % vebt_member.simps(3)
% 4.98/5.26 thf(fact_2320_field__sum__of__halves,axiom,
% 4.98/5.26 ! [X2: real] :
% 4.98/5.26 ( ( plus_plus_real @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = X2 ) ).
% 4.98/5.26
% 4.98/5.26 % field_sum_of_halves
% 4.98/5.26 thf(fact_2321_field__sum__of__halves,axiom,
% 4.98/5.26 ! [X2: rat] :
% 4.98/5.26 ( ( plus_plus_rat @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = X2 ) ).
% 4.98/5.26
% 4.98/5.26 % field_sum_of_halves
% 4.98/5.26 thf(fact_2322_arith__geo__mean,axiom,
% 4.98/5.26 ! [U: real,X2: real,Y: real] :
% 4.98/5.26 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( times_times_real @ X2 @ Y ) )
% 4.98/5.26 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 4.98/5.26 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 4.98/5.26 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % arith_geo_mean
% 4.98/5.26 thf(fact_2323_arith__geo__mean,axiom,
% 4.98/5.26 ! [U: rat,X2: rat,Y: rat] :
% 4.98/5.26 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( times_times_rat @ X2 @ Y ) )
% 4.98/5.26 => ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 4.98/5.26 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 4.98/5.26 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % arith_geo_mean
% 4.98/5.26 thf(fact_2324_sum__squares__bound,axiom,
% 4.98/5.26 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % sum_squares_bound
% 4.98/5.26 thf(fact_2325_sum__squares__bound,axiom,
% 4.98/5.26 ! [X2: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X2 ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % sum_squares_bound
% 4.98/5.26 thf(fact_2326_set__bit__0,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 4.98/5.26 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % set_bit_0
% 4.98/5.26 thf(fact_2327_set__bit__0,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 4.98/5.26 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % set_bit_0
% 4.98/5.26 thf(fact_2328_enat__ord__number_I1_J,axiom,
% 4.98/5.26 ! [M: num,N2: num] :
% 4.98/5.26 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 4.98/5.26 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % enat_ord_number(1)
% 4.98/5.26 thf(fact_2329_enat__ord__number_I2_J,axiom,
% 4.98/5.26 ! [M: num,N2: num] :
% 4.98/5.26 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 4.98/5.26 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % enat_ord_number(2)
% 4.98/5.26 thf(fact_2330_pos2,axiom,
% 4.98/5.26 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 4.98/5.26
% 4.98/5.26 % pos2
% 4.98/5.26 thf(fact_2331_unset__bit__0,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 4.98/5.26 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unset_bit_0
% 4.98/5.26 thf(fact_2332_unset__bit__0,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 4.98/5.26 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unset_bit_0
% 4.98/5.26 thf(fact_2333_mult__le__cancel__iff1,axiom,
% 4.98/5.26 ! [Z: real,X2: real,Y: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ Z )
% 4.98/5.26 => ( ( ord_less_eq_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 4.98/5.26 = ( ord_less_eq_real @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_le_cancel_iff1
% 4.98/5.26 thf(fact_2334_mult__le__cancel__iff1,axiom,
% 4.98/5.26 ! [Z: rat,X2: rat,Y: rat] :
% 4.98/5.26 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.98/5.26 => ( ( ord_less_eq_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 4.98/5.26 = ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_le_cancel_iff1
% 4.98/5.26 thf(fact_2335_mult__le__cancel__iff1,axiom,
% 4.98/5.26 ! [Z: int,X2: int,Y: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.98/5.26 => ( ( ord_less_eq_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 4.98/5.26 = ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_le_cancel_iff1
% 4.98/5.26 thf(fact_2336_mult__le__cancel__iff2,axiom,
% 4.98/5.26 ! [Z: real,X2: real,Y: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ Z )
% 4.98/5.26 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X2 ) @ ( times_times_real @ Z @ Y ) )
% 4.98/5.26 = ( ord_less_eq_real @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_le_cancel_iff2
% 4.98/5.26 thf(fact_2337_mult__le__cancel__iff2,axiom,
% 4.98/5.26 ! [Z: rat,X2: rat,Y: rat] :
% 4.98/5.26 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.98/5.26 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X2 ) @ ( times_times_rat @ Z @ Y ) )
% 4.98/5.26 = ( ord_less_eq_rat @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_le_cancel_iff2
% 4.98/5.26 thf(fact_2338_mult__le__cancel__iff2,axiom,
% 4.98/5.26 ! [Z: int,X2: int,Y: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.98/5.26 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X2 ) @ ( times_times_int @ Z @ Y ) )
% 4.98/5.26 = ( ord_less_eq_int @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_le_cancel_iff2
% 4.98/5.26 thf(fact_2339_divides__aux__eq,axiom,
% 4.98/5.26 ! [Q2: nat,R2: nat] :
% 4.98/5.26 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 4.98/5.26 = ( R2 = zero_zero_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % divides_aux_eq
% 4.98/5.26 thf(fact_2340_divides__aux__eq,axiom,
% 4.98/5.26 ! [Q2: int,R2: int] :
% 4.98/5.26 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 4.98/5.26 = ( R2 = zero_zero_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % divides_aux_eq
% 4.98/5.26 thf(fact_2341_unset__bit__nonnegative__int__iff,axiom,
% 4.98/5.26 ! [N2: nat,K: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) )
% 4.98/5.26 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.98/5.26
% 4.98/5.26 % unset_bit_nonnegative_int_iff
% 4.98/5.26 thf(fact_2342_set__bit__nonnegative__int__iff,axiom,
% 4.98/5.26 ! [N2: nat,K: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) )
% 4.98/5.26 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.98/5.26
% 4.98/5.26 % set_bit_nonnegative_int_iff
% 4.98/5.26 thf(fact_2343_unset__bit__negative__int__iff,axiom,
% 4.98/5.26 ! [N2: nat,K: int] :
% 4.98/5.26 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 4.98/5.26 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % unset_bit_negative_int_iff
% 4.98/5.26 thf(fact_2344_set__bit__negative__int__iff,axiom,
% 4.98/5.26 ! [N2: nat,K: int] :
% 4.98/5.26 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 4.98/5.26 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % set_bit_negative_int_iff
% 4.98/5.26 thf(fact_2345_semiring__norm_I13_J,axiom,
% 4.98/5.26 ! [M: num,N2: num] :
% 4.98/5.26 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 4.98/5.26 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % semiring_norm(13)
% 4.98/5.26 thf(fact_2346_semiring__norm_I11_J,axiom,
% 4.98/5.26 ! [M: num] :
% 4.98/5.26 ( ( times_times_num @ M @ one )
% 4.98/5.26 = M ) ).
% 4.98/5.26
% 4.98/5.26 % semiring_norm(11)
% 4.98/5.26 thf(fact_2347_semiring__norm_I12_J,axiom,
% 4.98/5.26 ! [N2: num] :
% 4.98/5.26 ( ( times_times_num @ one @ N2 )
% 4.98/5.26 = N2 ) ).
% 4.98/5.26
% 4.98/5.26 % semiring_norm(12)
% 4.98/5.26 thf(fact_2348_num__double,axiom,
% 4.98/5.26 ! [N2: num] :
% 4.98/5.26 ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 4.98/5.26 = ( bit0 @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % num_double
% 4.98/5.26 thf(fact_2349_power__mult__numeral,axiom,
% 4.98/5.26 ! [A: nat,M: num,N2: num] :
% 4.98/5.26 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.26 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_mult_numeral
% 4.98/5.26 thf(fact_2350_power__mult__numeral,axiom,
% 4.98/5.26 ! [A: int,M: num,N2: num] :
% 4.98/5.26 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.26 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_mult_numeral
% 4.98/5.26 thf(fact_2351_power__mult__numeral,axiom,
% 4.98/5.26 ! [A: real,M: num,N2: num] :
% 4.98/5.26 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.26 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_mult_numeral
% 4.98/5.26 thf(fact_2352_power__mult__numeral,axiom,
% 4.98/5.26 ! [A: complex,M: num,N2: num] :
% 4.98/5.26 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 4.98/5.26 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_mult_numeral
% 4.98/5.26 thf(fact_2353_complete__real,axiom,
% 4.98/5.26 ! [S3: set_real] :
% 4.98/5.26 ( ? [X3: real] : ( member_real @ X3 @ S3 )
% 4.98/5.26 => ( ? [Z4: real] :
% 4.98/5.26 ! [X5: real] :
% 4.98/5.26 ( ( member_real @ X5 @ S3 )
% 4.98/5.26 => ( ord_less_eq_real @ X5 @ Z4 ) )
% 4.98/5.26 => ? [Y3: real] :
% 4.98/5.26 ( ! [X3: real] :
% 4.98/5.26 ( ( member_real @ X3 @ S3 )
% 4.98/5.26 => ( ord_less_eq_real @ X3 @ Y3 ) )
% 4.98/5.26 & ! [Z4: real] :
% 4.98/5.26 ( ! [X5: real] :
% 4.98/5.26 ( ( member_real @ X5 @ S3 )
% 4.98/5.26 => ( ord_less_eq_real @ X5 @ Z4 ) )
% 4.98/5.26 => ( ord_less_eq_real @ Y3 @ Z4 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % complete_real
% 4.98/5.26 thf(fact_2354_real__arch__pow,axiom,
% 4.98/5.26 ! [X2: real,Y: real] :
% 4.98/5.26 ( ( ord_less_real @ one_one_real @ X2 )
% 4.98/5.26 => ? [N: nat] : ( ord_less_real @ Y @ ( power_power_real @ X2 @ N ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % real_arch_pow
% 4.98/5.26 thf(fact_2355_less__eq__real__def,axiom,
% 4.98/5.26 ( ord_less_eq_real
% 4.98/5.26 = ( ^ [X: real,Y6: real] :
% 4.98/5.26 ( ( ord_less_real @ X @ Y6 )
% 4.98/5.26 | ( X = Y6 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % less_eq_real_def
% 4.98/5.26 thf(fact_2356_real__arch__pow__inv,axiom,
% 4.98/5.26 ! [Y: real,X2: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ Y )
% 4.98/5.26 => ( ( ord_less_real @ X2 @ one_one_real )
% 4.98/5.26 => ? [N: nat] : ( ord_less_real @ ( power_power_real @ X2 @ N ) @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % real_arch_pow_inv
% 4.98/5.26 thf(fact_2357_enat__0__less__mult__iff,axiom,
% 4.98/5.26 ! [M: extended_enat,N2: extended_enat] :
% 4.98/5.26 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 4.98/5.26 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 4.98/5.26 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % enat_0_less_mult_iff
% 4.98/5.26 thf(fact_2358_times__int__code_I1_J,axiom,
% 4.98/5.26 ! [K: int] :
% 4.98/5.26 ( ( times_times_int @ K @ zero_zero_int )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % times_int_code(1)
% 4.98/5.26 thf(fact_2359_times__int__code_I2_J,axiom,
% 4.98/5.26 ! [L: int] :
% 4.98/5.26 ( ( times_times_int @ zero_zero_int @ L )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % times_int_code(2)
% 4.98/5.26 thf(fact_2360_int__distrib_I2_J,axiom,
% 4.98/5.26 ! [W: int,Z1: int,Z22: int] :
% 4.98/5.26 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % int_distrib(2)
% 4.98/5.26 thf(fact_2361_int__distrib_I1_J,axiom,
% 4.98/5.26 ! [Z1: int,Z22: int,W: int] :
% 4.98/5.26 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % int_distrib(1)
% 4.98/5.26 thf(fact_2362_unset__bit__less__eq,axiom,
% 4.98/5.26 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ K ) ).
% 4.98/5.26
% 4.98/5.26 % unset_bit_less_eq
% 4.98/5.26 thf(fact_2363_set__bit__greater__eq,axiom,
% 4.98/5.26 ! [K: int,N2: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N2 @ K ) ) ).
% 4.98/5.26
% 4.98/5.26 % set_bit_greater_eq
% 4.98/5.26 thf(fact_2364_L2__set__mult__ineq__lemma,axiom,
% 4.98/5.26 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % L2_set_mult_ineq_lemma
% 4.98/5.26 thf(fact_2365_four__x__squared,axiom,
% 4.98/5.26 ! [X2: real] :
% 4.98/5.26 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % four_x_squared
% 4.98/5.26 thf(fact_2366_div__mult2__numeral__eq,axiom,
% 4.98/5.26 ! [A: nat,K: num,L: num] :
% 4.98/5.26 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 4.98/5.26 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_mult2_numeral_eq
% 4.98/5.26 thf(fact_2367_div__mult2__numeral__eq,axiom,
% 4.98/5.26 ! [A: int,K: num,L: num] :
% 4.98/5.26 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 4.98/5.26 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_mult2_numeral_eq
% 4.98/5.26 thf(fact_2368_zmult__zless__mono2,axiom,
% 4.98/5.26 ! [I3: int,J: int,K: int] :
% 4.98/5.26 ( ( ord_less_int @ I3 @ J )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ K )
% 4.98/5.26 => ( ord_less_int @ ( times_times_int @ K @ I3 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zmult_zless_mono2
% 4.98/5.26 thf(fact_2369_pos__zmult__eq__1__iff,axiom,
% 4.98/5.26 ! [M: int,N2: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ M )
% 4.98/5.26 => ( ( ( times_times_int @ M @ N2 )
% 4.98/5.26 = one_one_int )
% 4.98/5.26 = ( ( M = one_one_int )
% 4.98/5.26 & ( N2 = one_one_int ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % pos_zmult_eq_1_iff
% 4.98/5.26 thf(fact_2370_realpow__pos__nth2,axiom,
% 4.98/5.26 ! [A: real,N2: nat] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.26 => ? [R3: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ R3 )
% 4.98/5.26 & ( ( power_power_real @ R3 @ ( suc @ N2 ) )
% 4.98/5.26 = A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % realpow_pos_nth2
% 4.98/5.26 thf(fact_2371_zdiv__zmult2__eq,axiom,
% 4.98/5.26 ! [C: int,A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.26 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 4.98/5.26 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zdiv_zmult2_eq
% 4.98/5.26 thf(fact_2372_q__pos__lemma,axiom,
% 4.98/5.26 ! [B2: int,Q5: int,R4: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) )
% 4.98/5.26 => ( ( ord_less_int @ R4 @ B2 )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 4.98/5.26 => ( ord_less_eq_int @ zero_zero_int @ Q5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % q_pos_lemma
% 4.98/5.26 thf(fact_2373_zdiv__mono2__lemma,axiom,
% 4.98/5.26 ! [B: int,Q2: int,R2: int,B2: int,Q5: int,R4: int] :
% 4.98/5.26 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) )
% 4.98/5.26 => ( ( ord_less_int @ R4 @ B2 )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 4.98/5.26 => ( ( ord_less_eq_int @ B2 @ B )
% 4.98/5.26 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zdiv_mono2_lemma
% 4.98/5.26 thf(fact_2374_zdiv__mono2__neg__lemma,axiom,
% 4.98/5.26 ! [B: int,Q2: int,R2: int,B2: int,Q5: int,R4: int] :
% 4.98/5.26 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 )
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) )
% 4.98/5.26 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q5 ) @ R4 ) @ zero_zero_int )
% 4.98/5.26 => ( ( ord_less_int @ R2 @ B )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 4.98/5.26 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 4.98/5.26 => ( ( ord_less_eq_int @ B2 @ B )
% 4.98/5.26 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % zdiv_mono2_neg_lemma
% 4.98/5.26 thf(fact_2375_unique__quotient__lemma,axiom,
% 4.98/5.26 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 4.98/5.26 => ( ( ord_less_int @ R4 @ B )
% 4.98/5.26 => ( ( ord_less_int @ R2 @ B )
% 4.98/5.26 => ( ord_less_eq_int @ Q5 @ Q2 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_quotient_lemma
% 4.98/5.26 thf(fact_2376_unique__quotient__lemma__neg,axiom,
% 4.98/5.26 ! [B: int,Q5: int,R4: int,Q2: int,R2: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q5 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 4.98/5.26 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.98/5.26 => ( ( ord_less_int @ B @ R2 )
% 4.98/5.26 => ( ( ord_less_int @ B @ R4 )
% 4.98/5.26 => ( ord_less_eq_int @ Q2 @ Q5 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_quotient_lemma_neg
% 4.98/5.26 thf(fact_2377_split__zdiv,axiom,
% 4.98/5.26 ! [P: int > $o,N2: int,K: int] :
% 4.98/5.26 ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 4.98/5.26 = ( ( ( K = zero_zero_int )
% 4.98/5.26 => ( P @ zero_zero_int ) )
% 4.98/5.26 & ( ( ord_less_int @ zero_zero_int @ K )
% 4.98/5.26 => ! [I5: int,J3: int] :
% 4.98/5.26 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.98/5.26 & ( ord_less_int @ J3 @ K )
% 4.98/5.26 & ( N2
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 4.98/5.26 => ( P @ I5 ) ) )
% 4.98/5.26 & ( ( ord_less_int @ K @ zero_zero_int )
% 4.98/5.26 => ! [I5: int,J3: int] :
% 4.98/5.26 ( ( ( ord_less_int @ K @ J3 )
% 4.98/5.26 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.98/5.26 & ( N2
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 4.98/5.26 => ( P @ I5 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % split_zdiv
% 4.98/5.26 thf(fact_2378_int__div__neg__eq,axiom,
% 4.98/5.26 ! [A: int,B: int,Q2: int,R2: int] :
% 4.98/5.26 ( ( A
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 4.98/5.26 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.98/5.26 => ( ( ord_less_int @ B @ R2 )
% 4.98/5.26 => ( ( divide_divide_int @ A @ B )
% 4.98/5.26 = Q2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % int_div_neg_eq
% 4.98/5.26 thf(fact_2379_int__div__pos__eq,axiom,
% 4.98/5.26 ! [A: int,B: int,Q2: int,R2: int] :
% 4.98/5.26 ( ( A
% 4.98/5.26 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.98/5.26 => ( ( ord_less_int @ R2 @ B )
% 4.98/5.26 => ( ( divide_divide_int @ A @ B )
% 4.98/5.26 = Q2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % int_div_pos_eq
% 4.98/5.26 thf(fact_2380_realpow__pos__nth__unique,axiom,
% 4.98/5.26 ! [N2: nat,A: real] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.26 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.26 => ? [X5: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ X5 )
% 4.98/5.26 & ( ( power_power_real @ X5 @ N2 )
% 4.98/5.26 = A )
% 4.98/5.26 & ! [Y5: real] :
% 4.98/5.26 ( ( ( ord_less_real @ zero_zero_real @ Y5 )
% 4.98/5.26 & ( ( power_power_real @ Y5 @ N2 )
% 4.98/5.26 = A ) )
% 4.98/5.26 => ( Y5 = X5 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % realpow_pos_nth_unique
% 4.98/5.26 thf(fact_2381_realpow__pos__nth,axiom,
% 4.98/5.26 ! [N2: nat,A: real] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.26 => ( ( ord_less_real @ zero_zero_real @ A )
% 4.98/5.26 => ? [R3: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ R3 )
% 4.98/5.26 & ( ( power_power_real @ R3 @ N2 )
% 4.98/5.26 = A ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % realpow_pos_nth
% 4.98/5.26 thf(fact_2382_pos__zdiv__mult__2,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.26 => ( ( 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 ) )
% 4.98/5.26 = ( divide_divide_int @ B @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % pos_zdiv_mult_2
% 4.98/5.26 thf(fact_2383_neg__zdiv__mult__2,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 4.98/5.26 => ( ( 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 ) )
% 4.98/5.26 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % neg_zdiv_mult_2
% 4.98/5.26 thf(fact_2384_mult__less__iff1,axiom,
% 4.98/5.26 ! [Z: real,X2: real,Y: real] :
% 4.98/5.26 ( ( ord_less_real @ zero_zero_real @ Z )
% 4.98/5.26 => ( ( ord_less_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 4.98/5.26 = ( ord_less_real @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_less_iff1
% 4.98/5.26 thf(fact_2385_mult__less__iff1,axiom,
% 4.98/5.26 ! [Z: rat,X2: rat,Y: rat] :
% 4.98/5.26 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 4.98/5.26 => ( ( ord_less_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 4.98/5.26 = ( ord_less_rat @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_less_iff1
% 4.98/5.26 thf(fact_2386_mult__less__iff1,axiom,
% 4.98/5.26 ! [Z: int,X2: int,Y: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ Z )
% 4.98/5.26 => ( ( ord_less_int @ ( times_times_int @ X2 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 4.98/5.26 = ( ord_less_int @ X2 @ Y ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_less_iff1
% 4.98/5.26 thf(fact_2387_incr__mult__lemma,axiom,
% 4.98/5.26 ! [D: int,P: int > $o,K: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ D )
% 4.98/5.26 => ( ! [X5: int] :
% 4.98/5.26 ( ( P @ X5 )
% 4.98/5.26 => ( P @ ( plus_plus_int @ X5 @ D ) ) )
% 4.98/5.26 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.98/5.26 => ! [X3: int] :
% 4.98/5.26 ( ( P @ X3 )
% 4.98/5.26 => ( P @ ( plus_plus_int @ X3 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % incr_mult_lemma
% 4.98/5.26 thf(fact_2388_low__def,axiom,
% 4.98/5.26 ( vEBT_VEBT_low
% 4.98/5.26 = ( ^ [X: nat,N3: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % low_def
% 4.98/5.26 thf(fact_2389_invar__vebt_Ointros_I3_J,axiom,
% 4.98/5.26 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 4.98/5.26 ( ! [X5: vEBT_VEBT] :
% 4.98/5.26 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.26 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 4.98/5.26 => ( ( vEBT_invar_vebt @ Summary @ M )
% 4.98/5.26 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.98/5.26 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.26 => ( ( M
% 4.98/5.26 = ( suc @ N2 ) )
% 4.98/5.26 => ( ( Deg
% 4.98/5.26 = ( plus_plus_nat @ N2 @ M ) )
% 4.98/5.26 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 4.98/5.26 => ( ! [X5: vEBT_VEBT] :
% 4.98/5.26 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.26 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 4.98/5.26 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % invar_vebt.intros(3)
% 4.98/5.26 thf(fact_2390_dbl__simps_I3_J,axiom,
% 4.98/5.26 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 4.98/5.26 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(3)
% 4.98/5.26 thf(fact_2391_dbl__simps_I3_J,axiom,
% 4.98/5.26 ( ( neg_numeral_dbl_real @ one_one_real )
% 4.98/5.26 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(3)
% 4.98/5.26 thf(fact_2392_dbl__simps_I3_J,axiom,
% 4.98/5.26 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 4.98/5.26 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(3)
% 4.98/5.26 thf(fact_2393_dbl__simps_I3_J,axiom,
% 4.98/5.26 ( ( neg_numeral_dbl_int @ one_one_int )
% 4.98/5.26 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(3)
% 4.98/5.26 thf(fact_2394_Leaf__0__not,axiom,
% 4.98/5.26 ! [A: $o,B: $o] :
% 4.98/5.26 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % Leaf_0_not
% 4.98/5.26 thf(fact_2395_deg1Leaf,axiom,
% 4.98/5.26 ! [T2: vEBT_VEBT] :
% 4.98/5.26 ( ( vEBT_invar_vebt @ T2 @ one_one_nat )
% 4.98/5.26 = ( ? [A5: $o,B5: $o] :
% 4.98/5.26 ( T2
% 4.98/5.26 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % deg1Leaf
% 4.98/5.26 thf(fact_2396_deg__1__Leaf,axiom,
% 4.98/5.26 ! [T2: vEBT_VEBT] :
% 4.98/5.26 ( ( vEBT_invar_vebt @ T2 @ one_one_nat )
% 4.98/5.26 => ? [A4: $o,B3: $o] :
% 4.98/5.26 ( T2
% 4.98/5.26 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % deg_1_Leaf
% 4.98/5.26 thf(fact_2397_deg__1__Leafy,axiom,
% 4.98/5.26 ! [T2: vEBT_VEBT,N2: nat] :
% 4.98/5.26 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 4.98/5.26 => ( ( N2 = one_one_nat )
% 4.98/5.26 => ? [A4: $o,B3: $o] :
% 4.98/5.26 ( T2
% 4.98/5.26 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % deg_1_Leafy
% 4.98/5.26 thf(fact_2398_mod__mod__trivial,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 4.98/5.26 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mod_trivial
% 4.98/5.26 thf(fact_2399_mod__mod__trivial,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 4.98/5.26 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mod_trivial
% 4.98/5.26 thf(fact_2400_real__divide__square__eq,axiom,
% 4.98/5.26 ! [R2: real,A: real] :
% 4.98/5.26 ( ( divide_divide_real @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ R2 ) )
% 4.98/5.26 = ( divide_divide_real @ A @ R2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % real_divide_square_eq
% 4.98/5.26 thf(fact_2401_VEBT_Oinject_I2_J,axiom,
% 4.98/5.26 ! [X21: $o,X222: $o,Y21: $o,Y22: $o] :
% 4.98/5.26 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 4.98/5.26 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 4.98/5.26 = ( ( X21 = Y21 )
% 4.98/5.26 & ( X222 = Y22 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT.inject(2)
% 4.98/5.26 thf(fact_2402_bits__mod__0,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % bits_mod_0
% 4.98/5.26 thf(fact_2403_bits__mod__0,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % bits_mod_0
% 4.98/5.26 thf(fact_2404_mod__0,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % mod_0
% 4.98/5.26 thf(fact_2405_mod__0,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % mod_0
% 4.98/5.26 thf(fact_2406_mod__by__0,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 4.98/5.26 = A ) ).
% 4.98/5.26
% 4.98/5.26 % mod_by_0
% 4.98/5.26 thf(fact_2407_mod__by__0,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 4.98/5.26 = A ) ).
% 4.98/5.26
% 4.98/5.26 % mod_by_0
% 4.98/5.26 thf(fact_2408_mod__self,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ A @ A )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % mod_self
% 4.98/5.26 thf(fact_2409_mod__self,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ A @ A )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % mod_self
% 4.98/5.26 thf(fact_2410_mod__add__self1,axiom,
% 4.98/5.26 ! [B: nat,A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 4.98/5.26 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_self1
% 4.98/5.26 thf(fact_2411_mod__add__self1,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 4.98/5.26 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_self1
% 4.98/5.26 thf(fact_2412_mod__add__self2,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.98/5.26 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_self2
% 4.98/5.26 thf(fact_2413_mod__add__self2,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.98/5.26 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_self2
% 4.98/5.26 thf(fact_2414_mod__less,axiom,
% 4.98/5.26 ! [M: nat,N2: nat] :
% 4.98/5.26 ( ( ord_less_nat @ M @ N2 )
% 4.98/5.26 => ( ( modulo_modulo_nat @ M @ N2 )
% 4.98/5.26 = M ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_less
% 4.98/5.26 thf(fact_2415_not__Some__eq,axiom,
% 4.98/5.26 ! [X2: option4927543243414619207at_nat] :
% 4.98/5.26 ( ( ! [Y6: product_prod_nat_nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( some_P7363390416028606310at_nat @ Y6 ) ) )
% 4.98/5.26 = ( X2 = none_P5556105721700978146at_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_Some_eq
% 4.98/5.26 thf(fact_2416_not__Some__eq,axiom,
% 4.98/5.26 ! [X2: option_num] :
% 4.98/5.26 ( ( ! [Y6: num] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( some_num @ Y6 ) ) )
% 4.98/5.26 = ( X2 = none_num ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_Some_eq
% 4.98/5.26 thf(fact_2417_not__None__eq,axiom,
% 4.98/5.26 ! [X2: option4927543243414619207at_nat] :
% 4.98/5.26 ( ( X2 != none_P5556105721700978146at_nat )
% 4.98/5.26 = ( ? [Y6: product_prod_nat_nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 = ( some_P7363390416028606310at_nat @ Y6 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_None_eq
% 4.98/5.26 thf(fact_2418_not__None__eq,axiom,
% 4.98/5.26 ! [X2: option_num] :
% 4.98/5.26 ( ( X2 != none_num )
% 4.98/5.26 = ( ? [Y6: num] :
% 4.98/5.26 ( X2
% 4.98/5.26 = ( some_num @ Y6 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_None_eq
% 4.98/5.26 thf(fact_2419_dbl__simps_I2_J,axiom,
% 4.98/5.26 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 4.98/5.26 = zero_zero_complex ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(2)
% 4.98/5.26 thf(fact_2420_dbl__simps_I2_J,axiom,
% 4.98/5.26 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 4.98/5.26 = zero_zero_real ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(2)
% 4.98/5.26 thf(fact_2421_dbl__simps_I2_J,axiom,
% 4.98/5.26 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 4.98/5.26 = zero_zero_rat ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(2)
% 4.98/5.26 thf(fact_2422_dbl__simps_I2_J,axiom,
% 4.98/5.26 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(2)
% 4.98/5.26 thf(fact_2423_mod__mult__self1__is__0,axiom,
% 4.98/5.26 ! [B: nat,A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self1_is_0
% 4.98/5.26 thf(fact_2424_mod__mult__self1__is__0,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self1_is_0
% 4.98/5.26 thf(fact_2425_mod__mult__self2__is__0,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self2_is_0
% 4.98/5.26 thf(fact_2426_mod__mult__self2__is__0,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self2_is_0
% 4.98/5.26 thf(fact_2427_bits__mod__by__1,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % bits_mod_by_1
% 4.98/5.26 thf(fact_2428_bits__mod__by__1,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ A @ one_one_int )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % bits_mod_by_1
% 4.98/5.26 thf(fact_2429_mod__by__1,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % mod_by_1
% 4.98/5.26 thf(fact_2430_mod__by__1,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ A @ one_one_int )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % mod_by_1
% 4.98/5.26 thf(fact_2431_mod__div__trivial,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % mod_div_trivial
% 4.98/5.26 thf(fact_2432_mod__div__trivial,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % mod_div_trivial
% 4.98/5.26 thf(fact_2433_bits__mod__div__trivial,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % bits_mod_div_trivial
% 4.98/5.26 thf(fact_2434_bits__mod__div__trivial,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % bits_mod_div_trivial
% 4.98/5.26 thf(fact_2435_mod__mult__self1,axiom,
% 4.98/5.26 ! [A: nat,C: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 4.98/5.26 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self1
% 4.98/5.26 thf(fact_2436_mod__mult__self1,axiom,
% 4.98/5.26 ! [A: int,C: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 4.98/5.26 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self1
% 4.98/5.26 thf(fact_2437_mod__mult__self2,axiom,
% 4.98/5.26 ! [A: nat,B: nat,C: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 4.98/5.26 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self2
% 4.98/5.26 thf(fact_2438_mod__mult__self2,axiom,
% 4.98/5.26 ! [A: int,B: int,C: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 4.98/5.26 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self2
% 4.98/5.26 thf(fact_2439_mod__mult__self3,axiom,
% 4.98/5.26 ! [C: nat,B: nat,A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 4.98/5.26 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self3
% 4.98/5.26 thf(fact_2440_mod__mult__self3,axiom,
% 4.98/5.26 ! [C: int,B: int,A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 4.98/5.26 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self3
% 4.98/5.26 thf(fact_2441_mod__mult__self4,axiom,
% 4.98/5.26 ! [B: nat,C: nat,A: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 4.98/5.26 = ( modulo_modulo_nat @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self4
% 4.98/5.26 thf(fact_2442_mod__mult__self4,axiom,
% 4.98/5.26 ! [B: int,C: int,A: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 4.98/5.26 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_self4
% 4.98/5.26 thf(fact_2443_not__real__square__gt__zero,axiom,
% 4.98/5.26 ! [X2: real] :
% 4.98/5.26 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X2 @ X2 ) ) )
% 4.98/5.26 = ( X2 = zero_zero_real ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_real_square_gt_zero
% 4.98/5.26 thf(fact_2444_mod__by__Suc__0,axiom,
% 4.98/5.26 ! [M: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % mod_by_Suc_0
% 4.98/5.26 thf(fact_2445_dbl__simps_I5_J,axiom,
% 4.98/5.26 ! [K: num] :
% 4.98/5.26 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 4.98/5.26 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(5)
% 4.98/5.26 thf(fact_2446_dbl__simps_I5_J,axiom,
% 4.98/5.26 ! [K: num] :
% 4.98/5.26 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 4.98/5.26 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(5)
% 4.98/5.26 thf(fact_2447_dbl__simps_I5_J,axiom,
% 4.98/5.26 ! [K: num] :
% 4.98/5.26 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 4.98/5.26 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(5)
% 4.98/5.26 thf(fact_2448_dbl__simps_I5_J,axiom,
% 4.98/5.26 ! [K: num] :
% 4.98/5.26 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 4.98/5.26 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_simps(5)
% 4.98/5.26 thf(fact_2449_Suc__mod__mult__self1,axiom,
% 4.98/5.26 ! [M: nat,K: nat,N2: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 4.98/5.26 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % Suc_mod_mult_self1
% 4.98/5.26 thf(fact_2450_Suc__mod__mult__self2,axiom,
% 4.98/5.26 ! [M: nat,N2: nat,K: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 4.98/5.26 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % Suc_mod_mult_self2
% 4.98/5.26 thf(fact_2451_Suc__mod__mult__self3,axiom,
% 4.98/5.26 ! [K: nat,N2: nat,M: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 4.98/5.26 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % Suc_mod_mult_self3
% 4.98/5.26 thf(fact_2452_Suc__mod__mult__self4,axiom,
% 4.98/5.26 ! [N2: nat,K: nat,M: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 4.98/5.26 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % Suc_mod_mult_self4
% 4.98/5.26 thf(fact_2453_bits__one__mod__two__eq__one,axiom,
% 4.98/5.26 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = one_one_nat ) ).
% 4.98/5.26
% 4.98/5.26 % bits_one_mod_two_eq_one
% 4.98/5.26 thf(fact_2454_bits__one__mod__two__eq__one,axiom,
% 4.98/5.26 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.26 = one_one_int ) ).
% 4.98/5.26
% 4.98/5.26 % bits_one_mod_two_eq_one
% 4.98/5.26 thf(fact_2455_one__mod__two__eq__one,axiom,
% 4.98/5.26 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = one_one_nat ) ).
% 4.98/5.26
% 4.98/5.26 % one_mod_two_eq_one
% 4.98/5.26 thf(fact_2456_one__mod__two__eq__one,axiom,
% 4.98/5.26 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.26 = one_one_int ) ).
% 4.98/5.26
% 4.98/5.26 % one_mod_two_eq_one
% 4.98/5.26 thf(fact_2457_mod2__Suc__Suc,axiom,
% 4.98/5.26 ! [M: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod2_Suc_Suc
% 4.98/5.26 thf(fact_2458_Suc__times__numeral__mod__eq,axiom,
% 4.98/5.26 ! [K: num,N2: nat] :
% 4.98/5.26 ( ( ( numeral_numeral_nat @ K )
% 4.98/5.26 != one_one_nat )
% 4.98/5.26 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 4.98/5.26 = one_one_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % Suc_times_numeral_mod_eq
% 4.98/5.26 thf(fact_2459_not__mod__2__eq__0__eq__1,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 != zero_zero_nat )
% 4.98/5.26 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = one_one_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_mod_2_eq_0_eq_1
% 4.98/5.26 thf(fact_2460_not__mod__2__eq__0__eq__1,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.26 != zero_zero_int )
% 4.98/5.26 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.26 = one_one_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_mod_2_eq_0_eq_1
% 4.98/5.26 thf(fact_2461_not__mod__2__eq__1__eq__0,axiom,
% 4.98/5.26 ! [A: nat] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 != one_one_nat )
% 4.98/5.26 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = zero_zero_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_mod_2_eq_1_eq_0
% 4.98/5.26 thf(fact_2462_not__mod__2__eq__1__eq__0,axiom,
% 4.98/5.26 ! [A: int] :
% 4.98/5.26 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.26 != one_one_int )
% 4.98/5.26 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.26 = zero_zero_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_mod_2_eq_1_eq_0
% 4.98/5.26 thf(fact_2463_not__mod2__eq__Suc__0__eq__0,axiom,
% 4.98/5.26 ! [N2: nat] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 != ( suc @ zero_zero_nat ) )
% 4.98/5.26 = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = zero_zero_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % not_mod2_eq_Suc_0_eq_0
% 4.98/5.26 thf(fact_2464_add__self__mod__2,axiom,
% 4.98/5.26 ! [M: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % add_self_mod_2
% 4.98/5.26 thf(fact_2465_mod2__gr__0,axiom,
% 4.98/5.26 ! [M: nat] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.26 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.26 = one_one_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod2_gr_0
% 4.98/5.26 thf(fact_2466_zero__one__enat__neq_I1_J,axiom,
% 4.98/5.26 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 4.98/5.26
% 4.98/5.26 % zero_one_enat_neq(1)
% 4.98/5.26 thf(fact_2467_iadd__is__0,axiom,
% 4.98/5.26 ! [M: extended_enat,N2: extended_enat] :
% 4.98/5.26 ( ( ( plus_p3455044024723400733d_enat @ M @ N2 )
% 4.98/5.26 = zero_z5237406670263579293d_enat )
% 4.98/5.26 = ( ( M = zero_z5237406670263579293d_enat )
% 4.98/5.26 & ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % iadd_is_0
% 4.98/5.26 thf(fact_2468_imult__is__0,axiom,
% 4.98/5.26 ! [M: extended_enat,N2: extended_enat] :
% 4.98/5.26 ( ( ( times_7803423173614009249d_enat @ M @ N2 )
% 4.98/5.26 = zero_z5237406670263579293d_enat )
% 4.98/5.26 = ( ( M = zero_z5237406670263579293d_enat )
% 4.98/5.26 | ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % imult_is_0
% 4.98/5.26 thf(fact_2469_VEBT__internal_OminNull_Ocases,axiom,
% 4.98/5.26 ! [X2: vEBT_VEBT] :
% 4.98/5.26 ( ( X2
% 4.98/5.26 != ( vEBT_Leaf @ $false @ $false ) )
% 4.98/5.26 => ( ! [Uv2: $o] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 4.98/5.26 => ( ! [Uu2: $o] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 4.98/5.26 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 4.98/5.26 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.minNull.cases
% 4.98/5.26 thf(fact_2470_VEBT_Osize_I4_J,axiom,
% 4.98/5.26 ! [X21: $o,X222: $o] :
% 4.98/5.26 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT.size(4)
% 4.98/5.26 thf(fact_2471_mod__mult__right__eq,axiom,
% 4.98/5.26 ! [A: nat,B: nat,C: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_right_eq
% 4.98/5.26 thf(fact_2472_mod__mult__right__eq,axiom,
% 4.98/5.26 ! [A: int,B: int,C: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 4.98/5.26 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_right_eq
% 4.98/5.26 thf(fact_2473_mod__mult__left__eq,axiom,
% 4.98/5.26 ! [A: nat,C: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_left_eq
% 4.98/5.26 thf(fact_2474_mod__mult__left__eq,axiom,
% 4.98/5.26 ! [A: int,C: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 4.98/5.26 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_left_eq
% 4.98/5.26 thf(fact_2475_mult__mod__right,axiom,
% 4.98/5.26 ! [C: nat,A: nat,B: nat] :
% 4.98/5.26 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 4.98/5.26 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_mod_right
% 4.98/5.26 thf(fact_2476_mult__mod__right,axiom,
% 4.98/5.26 ! [C: int,A: int,B: int] :
% 4.98/5.26 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 4.98/5.26 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mult_mod_right
% 4.98/5.26 thf(fact_2477_mod__mult__mult2,axiom,
% 4.98/5.26 ! [A: nat,C: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 4.98/5.26 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_mult2
% 4.98/5.26 thf(fact_2478_mod__mult__mult2,axiom,
% 4.98/5.26 ! [A: int,C: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.98/5.26 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_mult2
% 4.98/5.26 thf(fact_2479_mod__mult__cong,axiom,
% 4.98/5.26 ! [A: nat,C: nat,A2: nat,B: nat,B2: nat] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ A @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ A2 @ C ) )
% 4.98/5.26 => ( ( ( modulo_modulo_nat @ B @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ B2 @ C ) )
% 4.98/5.26 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_cong
% 4.98/5.26 thf(fact_2480_mod__mult__cong,axiom,
% 4.98/5.26 ! [A: int,C: int,A2: int,B: int,B2: int] :
% 4.98/5.26 ( ( ( modulo_modulo_int @ A @ C )
% 4.98/5.26 = ( modulo_modulo_int @ A2 @ C ) )
% 4.98/5.26 => ( ( ( modulo_modulo_int @ B @ C )
% 4.98/5.26 = ( modulo_modulo_int @ B2 @ C ) )
% 4.98/5.26 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 4.98/5.26 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_cong
% 4.98/5.26 thf(fact_2481_mod__mult__eq,axiom,
% 4.98/5.26 ! [A: nat,C: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_eq
% 4.98/5.26 thf(fact_2482_mod__mult__eq,axiom,
% 4.98/5.26 ! [A: int,C: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 4.98/5.26 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_mult_eq
% 4.98/5.26 thf(fact_2483_mod__add__eq,axiom,
% 4.98/5.26 ! [A: nat,C: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_eq
% 4.98/5.26 thf(fact_2484_mod__add__eq,axiom,
% 4.98/5.26 ! [A: int,C: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 4.98/5.26 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_eq
% 4.98/5.26 thf(fact_2485_mod__add__cong,axiom,
% 4.98/5.26 ! [A: nat,C: nat,A2: nat,B: nat,B2: nat] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ A @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ A2 @ C ) )
% 4.98/5.26 => ( ( ( modulo_modulo_nat @ B @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ B2 @ C ) )
% 4.98/5.26 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ ( plus_plus_nat @ A2 @ B2 ) @ C ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_cong
% 4.98/5.26 thf(fact_2486_mod__add__cong,axiom,
% 4.98/5.26 ! [A: int,C: int,A2: int,B: int,B2: int] :
% 4.98/5.26 ( ( ( modulo_modulo_int @ A @ C )
% 4.98/5.26 = ( modulo_modulo_int @ A2 @ C ) )
% 4.98/5.26 => ( ( ( modulo_modulo_int @ B @ C )
% 4.98/5.26 = ( modulo_modulo_int @ B2 @ C ) )
% 4.98/5.26 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.26 = ( modulo_modulo_int @ ( plus_plus_int @ A2 @ B2 ) @ C ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_cong
% 4.98/5.26 thf(fact_2487_mod__add__left__eq,axiom,
% 4.98/5.26 ! [A: nat,C: nat,B: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_left_eq
% 4.98/5.26 thf(fact_2488_mod__add__left__eq,axiom,
% 4.98/5.26 ! [A: int,C: int,B: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 4.98/5.26 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_left_eq
% 4.98/5.26 thf(fact_2489_mod__add__right__eq,axiom,
% 4.98/5.26 ! [A: nat,B: nat,C: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 4.98/5.26 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_right_eq
% 4.98/5.26 thf(fact_2490_mod__add__right__eq,axiom,
% 4.98/5.26 ! [A: int,B: int,C: int] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 4.98/5.26 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_add_right_eq
% 4.98/5.26 thf(fact_2491_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 4.98/5.26 ! [X2: vEBT_VEBT] :
% 4.98/5.26 ( ( vEBT_VEBT_minNull @ X2 )
% 4.98/5.26 => ( ( X2
% 4.98/5.26 != ( vEBT_Leaf @ $false @ $false ) )
% 4.98/5.26 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.minNull.elims(2)
% 4.98/5.26 thf(fact_2492_power__mod,axiom,
% 4.98/5.26 ! [A: nat,B: nat,N2: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
% 4.98/5.26 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_mod
% 4.98/5.26 thf(fact_2493_power__mod,axiom,
% 4.98/5.26 ! [A: int,B: int,N2: nat] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N2 ) @ B )
% 4.98/5.26 = ( modulo_modulo_int @ ( power_power_int @ A @ N2 ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % power_mod
% 4.98/5.26 thf(fact_2494_VEBT__internal_Ovalid_H_Ocases,axiom,
% 4.98/5.26 ! [X2: produc9072475918466114483BT_nat] :
% 4.98/5.26 ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 4.98/5.26 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Deg3 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.valid'.cases
% 4.98/5.26 thf(fact_2495_VEBT_Oexhaust,axiom,
% 4.98/5.26 ! [Y: vEBT_VEBT] :
% 4.98/5.26 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 4.98/5.26 ( Y
% 4.98/5.26 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 4.98/5.26 => ~ ! [X212: $o,X223: $o] :
% 4.98/5.26 ( Y
% 4.98/5.26 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT.exhaust
% 4.98/5.26 thf(fact_2496_VEBT_Odistinct_I1_J,axiom,
% 4.98/5.26 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 4.98/5.26 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 4.98/5.26 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT.distinct(1)
% 4.98/5.26 thf(fact_2497_mod__Suc__eq,axiom,
% 4.98/5.26 ! [M: nat,N2: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) @ N2 )
% 4.98/5.26 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_Suc_eq
% 4.98/5.26 thf(fact_2498_mod__Suc__Suc__eq,axiom,
% 4.98/5.26 ! [M: nat,N2: nat] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ N2 )
% 4.98/5.26 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_Suc_Suc_eq
% 4.98/5.26 thf(fact_2499_mod__less__eq__dividend,axiom,
% 4.98/5.26 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 4.98/5.26
% 4.98/5.26 % mod_less_eq_dividend
% 4.98/5.26 thf(fact_2500_combine__options__cases,axiom,
% 4.98/5.26 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 4.98/5.26 ( ( ( X2 = none_P5556105721700978146at_nat )
% 4.98/5.26 => ( P @ X2 @ Y ) )
% 4.98/5.26 => ( ( ( Y = none_P5556105721700978146at_nat )
% 4.98/5.26 => ( P @ X2 @ Y ) )
% 4.98/5.26 => ( ! [A4: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 4.98/5.26 ( ( X2
% 4.98/5.26 = ( some_P7363390416028606310at_nat @ A4 ) )
% 4.98/5.26 => ( ( Y
% 4.98/5.26 = ( some_P7363390416028606310at_nat @ B3 ) )
% 4.98/5.26 => ( P @ X2 @ Y ) ) )
% 4.98/5.26 => ( P @ X2 @ Y ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % combine_options_cases
% 4.98/5.26 thf(fact_2501_combine__options__cases,axiom,
% 4.98/5.26 ! [X2: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 4.98/5.26 ( ( ( X2 = none_P5556105721700978146at_nat )
% 4.98/5.26 => ( P @ X2 @ Y ) )
% 4.98/5.26 => ( ( ( Y = none_num )
% 4.98/5.26 => ( P @ X2 @ Y ) )
% 4.98/5.26 => ( ! [A4: product_prod_nat_nat,B3: num] :
% 4.98/5.26 ( ( X2
% 4.98/5.26 = ( some_P7363390416028606310at_nat @ A4 ) )
% 4.98/5.26 => ( ( Y
% 4.98/5.26 = ( some_num @ B3 ) )
% 4.98/5.26 => ( P @ X2 @ Y ) ) )
% 4.98/5.26 => ( P @ X2 @ Y ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % combine_options_cases
% 4.98/5.26 thf(fact_2502_combine__options__cases,axiom,
% 4.98/5.26 ! [X2: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 4.98/5.26 ( ( ( X2 = none_num )
% 4.98/5.26 => ( P @ X2 @ Y ) )
% 4.98/5.26 => ( ( ( Y = none_P5556105721700978146at_nat )
% 4.98/5.26 => ( P @ X2 @ Y ) )
% 4.98/5.26 => ( ! [A4: num,B3: product_prod_nat_nat] :
% 4.98/5.26 ( ( X2
% 4.98/5.26 = ( some_num @ A4 ) )
% 4.98/5.26 => ( ( Y
% 4.98/5.26 = ( some_P7363390416028606310at_nat @ B3 ) )
% 4.98/5.26 => ( P @ X2 @ Y ) ) )
% 4.98/5.26 => ( P @ X2 @ Y ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % combine_options_cases
% 4.98/5.26 thf(fact_2503_combine__options__cases,axiom,
% 4.98/5.26 ! [X2: option_num,P: option_num > option_num > $o,Y: option_num] :
% 4.98/5.26 ( ( ( X2 = none_num )
% 4.98/5.26 => ( P @ X2 @ Y ) )
% 4.98/5.26 => ( ( ( Y = none_num )
% 4.98/5.26 => ( P @ X2 @ Y ) )
% 4.98/5.26 => ( ! [A4: num,B3: num] :
% 4.98/5.26 ( ( X2
% 4.98/5.26 = ( some_num @ A4 ) )
% 4.98/5.26 => ( ( Y
% 4.98/5.26 = ( some_num @ B3 ) )
% 4.98/5.26 => ( P @ X2 @ Y ) ) )
% 4.98/5.26 => ( P @ X2 @ Y ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % combine_options_cases
% 4.98/5.26 thf(fact_2504_split__option__all,axiom,
% 4.98/5.26 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 4.98/5.26 ! [X7: option4927543243414619207at_nat] : ( P3 @ X7 ) )
% 4.98/5.26 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 4.98/5.26 ( ( P4 @ none_P5556105721700978146at_nat )
% 4.98/5.26 & ! [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % split_option_all
% 4.98/5.26 thf(fact_2505_split__option__all,axiom,
% 4.98/5.26 ( ( ^ [P3: option_num > $o] :
% 4.98/5.26 ! [X7: option_num] : ( P3 @ X7 ) )
% 4.98/5.26 = ( ^ [P4: option_num > $o] :
% 4.98/5.26 ( ( P4 @ none_num )
% 4.98/5.26 & ! [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % split_option_all
% 4.98/5.26 thf(fact_2506_split__option__ex,axiom,
% 4.98/5.26 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 4.98/5.26 ? [X7: option4927543243414619207at_nat] : ( P3 @ X7 ) )
% 4.98/5.26 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 4.98/5.26 ( ( P4 @ none_P5556105721700978146at_nat )
% 4.98/5.26 | ? [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % split_option_ex
% 4.98/5.26 thf(fact_2507_split__option__ex,axiom,
% 4.98/5.26 ( ( ^ [P3: option_num > $o] :
% 4.98/5.26 ? [X7: option_num] : ( P3 @ X7 ) )
% 4.98/5.26 = ( ^ [P4: option_num > $o] :
% 4.98/5.26 ( ( P4 @ none_num )
% 4.98/5.26 | ? [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % split_option_ex
% 4.98/5.26 thf(fact_2508_option_Oexhaust,axiom,
% 4.98/5.26 ! [Y: option4927543243414619207at_nat] :
% 4.98/5.26 ( ( Y != none_P5556105721700978146at_nat )
% 4.98/5.26 => ~ ! [X23: product_prod_nat_nat] :
% 4.98/5.26 ( Y
% 4.98/5.26 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % option.exhaust
% 4.98/5.26 thf(fact_2509_option_Oexhaust,axiom,
% 4.98/5.26 ! [Y: option_num] :
% 4.98/5.26 ( ( Y != none_num )
% 4.98/5.26 => ~ ! [X23: num] :
% 4.98/5.26 ( Y
% 4.98/5.26 != ( some_num @ X23 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % option.exhaust
% 4.98/5.26 thf(fact_2510_option_OdiscI,axiom,
% 4.98/5.26 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 4.98/5.26 ( ( Option
% 4.98/5.26 = ( some_P7363390416028606310at_nat @ X22 ) )
% 4.98/5.26 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % option.discI
% 4.98/5.26 thf(fact_2511_option_OdiscI,axiom,
% 4.98/5.26 ! [Option: option_num,X22: num] :
% 4.98/5.26 ( ( Option
% 4.98/5.26 = ( some_num @ X22 ) )
% 4.98/5.26 => ( Option != none_num ) ) ).
% 4.98/5.26
% 4.98/5.26 % option.discI
% 4.98/5.26 thf(fact_2512_option_Odistinct_I1_J,axiom,
% 4.98/5.26 ! [X22: product_prod_nat_nat] :
% 4.98/5.26 ( none_P5556105721700978146at_nat
% 4.98/5.26 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 4.98/5.26
% 4.98/5.26 % option.distinct(1)
% 4.98/5.26 thf(fact_2513_option_Odistinct_I1_J,axiom,
% 4.98/5.26 ! [X22: num] :
% 4.98/5.26 ( none_num
% 4.98/5.26 != ( some_num @ X22 ) ) ).
% 4.98/5.26
% 4.98/5.26 % option.distinct(1)
% 4.98/5.26 thf(fact_2514_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 4.98/5.26 ! [Uu: $o,Uv: $o,Uw: nat] :
% 4.98/5.26 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.membermima.simps(1)
% 4.98/5.26 thf(fact_2515_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 4.98/5.26 ! [Uu: $o] :
% 4.98/5.26 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.minNull.simps(3)
% 4.98/5.26 thf(fact_2516_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 4.98/5.26 ! [Uv: $o] :
% 4.98/5.26 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.minNull.simps(2)
% 4.98/5.26 thf(fact_2517_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 4.98/5.26 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.minNull.simps(1)
% 4.98/5.26 thf(fact_2518_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 4.98/5.26 ! [X2: vEBT_VEBT,Y: $o] :
% 4.98/5.26 ( ( ( vEBT_VEBT_minNull @ X2 )
% 4.98/5.26 = Y )
% 4.98/5.26 => ( ( ( X2
% 4.98/5.26 = ( vEBT_Leaf @ $false @ $false ) )
% 4.98/5.26 => ~ Y )
% 4.98/5.26 => ( ( ? [Uv2: $o] :
% 4.98/5.26 ( X2
% 4.98/5.26 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 4.98/5.26 => Y )
% 4.98/5.26 => ( ( ? [Uu2: $o] :
% 4.98/5.26 ( X2
% 4.98/5.26 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 4.98/5.26 => Y )
% 4.98/5.26 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 4.98/5.26 ( X2
% 4.98/5.26 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 4.98/5.26 => ~ Y )
% 4.98/5.26 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.98/5.26 ( X2
% 4.98/5.26 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 4.98/5.26 => Y ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.minNull.elims(1)
% 4.98/5.26 thf(fact_2519_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.26 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 4.98/5.26 thf(fact_2520_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.26 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 4.98/5.26 thf(fact_2521_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 4.98/5.26 ! [B: nat,A: nat] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.26 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 4.98/5.26 thf(fact_2522_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.26 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 4.98/5.26 thf(fact_2523_mod__eq__self__iff__div__eq__0,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ A @ B )
% 4.98/5.26 = A )
% 4.98/5.26 = ( ( divide_divide_nat @ A @ B )
% 4.98/5.26 = zero_zero_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_eq_self_iff_div_eq_0
% 4.98/5.26 thf(fact_2524_mod__eq__self__iff__div__eq__0,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ( modulo_modulo_int @ A @ B )
% 4.98/5.26 = A )
% 4.98/5.26 = ( ( divide_divide_int @ A @ B )
% 4.98/5.26 = zero_zero_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_eq_self_iff_div_eq_0
% 4.98/5.26 thf(fact_2525_cong__exp__iff__simps_I9_J,axiom,
% 4.98/5.26 ! [M: num,Q2: num,N2: num] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 4.98/5.26 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 4.98/5.26 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 4.98/5.26 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(9)
% 4.98/5.26 thf(fact_2526_cong__exp__iff__simps_I9_J,axiom,
% 4.98/5.26 ! [M: num,Q2: num,N2: num] :
% 4.98/5.26 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 4.98/5.26 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 4.98/5.26 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 4.98/5.26 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(9)
% 4.98/5.26 thf(fact_2527_cong__exp__iff__simps_I4_J,axiom,
% 4.98/5.26 ! [M: num,N2: num] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 4.98/5.26 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(4)
% 4.98/5.26 thf(fact_2528_cong__exp__iff__simps_I4_J,axiom,
% 4.98/5.26 ! [M: num,N2: num] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 4.98/5.26 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(4)
% 4.98/5.26 thf(fact_2529_mod__eqE,axiom,
% 4.98/5.26 ! [A: int,C: int,B: int] :
% 4.98/5.26 ( ( ( modulo_modulo_int @ A @ C )
% 4.98/5.26 = ( modulo_modulo_int @ B @ C ) )
% 4.98/5.26 => ~ ! [D3: int] :
% 4.98/5.26 ( B
% 4.98/5.26 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_eqE
% 4.98/5.26 thf(fact_2530_div__add1__eq,axiom,
% 4.98/5.26 ! [A: nat,B: nat,C: nat] :
% 4.98/5.26 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.26 = ( 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 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_add1_eq
% 4.98/5.26 thf(fact_2531_div__add1__eq,axiom,
% 4.98/5.26 ! [A: int,B: int,C: int] :
% 4.98/5.26 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.26 = ( 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 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_add1_eq
% 4.98/5.26 thf(fact_2532_mod__Suc,axiom,
% 4.98/5.26 ! [M: nat,N2: nat] :
% 4.98/5.26 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 4.98/5.26 = N2 )
% 4.98/5.26 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 4.98/5.26 = zero_zero_nat ) )
% 4.98/5.26 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 4.98/5.26 != N2 )
% 4.98/5.26 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 4.98/5.26 = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_Suc
% 4.98/5.26 thf(fact_2533_mod__induct,axiom,
% 4.98/5.26 ! [P: nat > $o,N2: nat,P2: nat,M: nat] :
% 4.98/5.26 ( ( P @ N2 )
% 4.98/5.26 => ( ( ord_less_nat @ N2 @ P2 )
% 4.98/5.26 => ( ( ord_less_nat @ M @ P2 )
% 4.98/5.26 => ( ! [N: nat] :
% 4.98/5.26 ( ( ord_less_nat @ N @ P2 )
% 4.98/5.26 => ( ( P @ N )
% 4.98/5.26 => ( P @ ( modulo_modulo_nat @ ( suc @ N ) @ P2 ) ) ) )
% 4.98/5.26 => ( P @ M ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_induct
% 4.98/5.26 thf(fact_2534_mod__less__divisor,axiom,
% 4.98/5.26 ! [N2: nat,M: nat] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.26 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_less_divisor
% 4.98/5.26 thf(fact_2535_mod__Suc__le__divisor,axiom,
% 4.98/5.26 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 4.98/5.26
% 4.98/5.26 % mod_Suc_le_divisor
% 4.98/5.26 thf(fact_2536_mod__eq__0D,axiom,
% 4.98/5.26 ! [M: nat,D: nat] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ M @ D )
% 4.98/5.26 = zero_zero_nat )
% 4.98/5.26 => ? [Q3: nat] :
% 4.98/5.26 ( M
% 4.98/5.26 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % mod_eq_0D
% 4.98/5.26 thf(fact_2537_nat__mod__eq__iff,axiom,
% 4.98/5.26 ! [X2: nat,N2: nat,Y: nat] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ X2 @ N2 )
% 4.98/5.26 = ( modulo_modulo_nat @ Y @ N2 ) )
% 4.98/5.26 = ( ? [Q1: nat,Q22: nat] :
% 4.98/5.26 ( ( plus_plus_nat @ X2 @ ( times_times_nat @ N2 @ Q1 ) )
% 4.98/5.26 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % nat_mod_eq_iff
% 4.98/5.26 thf(fact_2538_vebt__buildup_Osimps_I1_J,axiom,
% 4.98/5.26 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 4.98/5.26 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 4.98/5.26
% 4.98/5.26 % vebt_buildup.simps(1)
% 4.98/5.26 thf(fact_2539_dbl__def,axiom,
% 4.98/5.26 ( neg_numeral_dbl_real
% 4.98/5.26 = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_def
% 4.98/5.26 thf(fact_2540_dbl__def,axiom,
% 4.98/5.26 ( neg_numeral_dbl_rat
% 4.98/5.26 = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_def
% 4.98/5.26 thf(fact_2541_dbl__def,axiom,
% 4.98/5.26 ( neg_numeral_dbl_int
% 4.98/5.26 = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % dbl_def
% 4.98/5.26 thf(fact_2542_vebt__member_Osimps_I2_J,axiom,
% 4.98/5.26 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X2: nat] :
% 4.98/5.26 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X2 ) ).
% 4.98/5.26
% 4.98/5.26 % vebt_member.simps(2)
% 4.98/5.26 thf(fact_2543_vebt__member_Ocases,axiom,
% 4.98/5.26 ! [X2: produc9072475918466114483BT_nat] :
% 4.98/5.26 ( ! [A4: $o,B3: $o,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X5 ) )
% 4.98/5.26 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X5 ) )
% 4.98/5.26 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X5 ) )
% 4.98/5.26 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X5 ) )
% 4.98/5.26 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % vebt_member.cases
% 4.98/5.26 thf(fact_2544_VEBT__internal_Omembermima_Ocases,axiom,
% 4.98/5.26 ! [X2: produc9072475918466114483BT_nat] :
% 4.98/5.26 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 4.98/5.26 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 4.98/5.26 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 4.98/5.26 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ X5 ) )
% 4.98/5.26 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) @ X5 ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.membermima.cases
% 4.98/5.26 thf(fact_2545_vebt__insert_Ocases,axiom,
% 4.98/5.26 ! [X2: produc9072475918466114483BT_nat] :
% 4.98/5.26 ( ! [A4: $o,B3: $o,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X5 ) )
% 4.98/5.26 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ X5 ) )
% 4.98/5.26 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ X5 ) )
% 4.98/5.26 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ X5 ) )
% 4.98/5.26 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ X5 ) ) ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % vebt_insert.cases
% 4.98/5.26 thf(fact_2546_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 4.98/5.26 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.minNull.simps(4)
% 4.98/5.26 thf(fact_2547_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 4.98/5.26 ! [A: nat,B: nat] :
% 4.98/5.26 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.26 => ( ( ord_less_nat @ A @ B )
% 4.98/5.26 => ( ( modulo_modulo_nat @ A @ B )
% 4.98/5.26 = A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.mod_less
% 4.98/5.26 thf(fact_2548_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 4.98/5.26 ! [A: int,B: int] :
% 4.98/5.26 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.26 => ( ( ord_less_int @ A @ B )
% 4.98/5.26 => ( ( modulo_modulo_int @ A @ B )
% 4.98/5.26 = A ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.mod_less
% 4.98/5.26 thf(fact_2549_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 4.98/5.26 ! [B: nat,A: nat] :
% 4.98/5.26 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.26 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 4.98/5.26 thf(fact_2550_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 4.98/5.26 ! [B: int,A: int] :
% 4.98/5.26 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.26 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 4.98/5.26 thf(fact_2551_cong__exp__iff__simps_I2_J,axiom,
% 4.98/5.26 ! [N2: num,Q2: num] :
% 4.98/5.26 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 4.98/5.26 = zero_zero_nat )
% 4.98/5.26 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 4.98/5.26 = zero_zero_nat ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(2)
% 4.98/5.26 thf(fact_2552_cong__exp__iff__simps_I2_J,axiom,
% 4.98/5.26 ! [N2: num,Q2: num] :
% 4.98/5.26 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 4.98/5.26 = zero_zero_int )
% 4.98/5.26 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 4.98/5.26 = zero_zero_int ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(2)
% 4.98/5.26 thf(fact_2553_cong__exp__iff__simps_I1_J,axiom,
% 4.98/5.26 ! [N2: num] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) )
% 4.98/5.26 = zero_zero_nat ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(1)
% 4.98/5.26 thf(fact_2554_cong__exp__iff__simps_I1_J,axiom,
% 4.98/5.26 ! [N2: num] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) )
% 4.98/5.26 = zero_zero_int ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(1)
% 4.98/5.26 thf(fact_2555_VEBT__internal_Onaive__member_Ocases,axiom,
% 4.98/5.26 ! [X2: produc9072475918466114483BT_nat] :
% 4.98/5.26 ( ! [A4: $o,B3: $o,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ X5 ) )
% 4.98/5.26 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 4.98/5.26 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X5: nat] :
% 4.98/5.26 ( X2
% 4.98/5.26 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ X5 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % VEBT_internal.naive_member.cases
% 4.98/5.26 thf(fact_2556_cong__exp__iff__simps_I8_J,axiom,
% 4.98/5.26 ! [M: num,Q2: num] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 4.98/5.26 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(8)
% 4.98/5.26 thf(fact_2557_cong__exp__iff__simps_I8_J,axiom,
% 4.98/5.26 ! [M: num,Q2: num] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 4.98/5.26 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(8)
% 4.98/5.26 thf(fact_2558_cong__exp__iff__simps_I6_J,axiom,
% 4.98/5.26 ! [Q2: num,N2: num] :
% 4.98/5.26 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 4.98/5.26 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(6)
% 4.98/5.26 thf(fact_2559_cong__exp__iff__simps_I6_J,axiom,
% 4.98/5.26 ! [Q2: num,N2: num] :
% 4.98/5.26 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 4.98/5.26 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % cong_exp_iff_simps(6)
% 4.98/5.26 thf(fact_2560_div__mult1__eq,axiom,
% 4.98/5.26 ! [A: nat,B: nat,C: nat] :
% 4.98/5.26 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.98/5.26 = ( 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 ) ) ) ).
% 4.98/5.26
% 4.98/5.26 % div_mult1_eq
% 4.98/5.26 thf(fact_2561_div__mult1__eq,axiom,
% 4.98/5.26 ! [A: int,B: int,C: int] :
% 4.98/5.26 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 4.98/5.26 = ( 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 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_mult1_eq
% 4.98/5.27 thf(fact_2562_mult__div__mod__eq,axiom,
% 4.98/5.27 ! [B: nat,A: nat] :
% 4.98/5.27 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % mult_div_mod_eq
% 4.98/5.27 thf(fact_2563_mult__div__mod__eq,axiom,
% 4.98/5.27 ! [B: int,A: int] :
% 4.98/5.27 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % mult_div_mod_eq
% 4.98/5.27 thf(fact_2564_mod__mult__div__eq,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % mod_mult_div_eq
% 4.98/5.27 thf(fact_2565_mod__mult__div__eq,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % mod_mult_div_eq
% 4.98/5.27 thf(fact_2566_mod__div__mult__eq,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % mod_div_mult_eq
% 4.98/5.27 thf(fact_2567_mod__div__mult__eq,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % mod_div_mult_eq
% 4.98/5.27 thf(fact_2568_div__mult__mod__eq,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % div_mult_mod_eq
% 4.98/5.27 thf(fact_2569_div__mult__mod__eq,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % div_mult_mod_eq
% 4.98/5.27 thf(fact_2570_mod__div__decomp,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( A
% 4.98/5.27 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_div_decomp
% 4.98/5.27 thf(fact_2571_mod__div__decomp,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( A
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_div_decomp
% 4.98/5.27 thf(fact_2572_cancel__div__mod__rules_I1_J,axiom,
% 4.98/5.27 ! [A: nat,B: nat,C: nat] :
% 4.98/5.27 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 4.98/5.27 = ( plus_plus_nat @ A @ C ) ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_div_mod_rules(1)
% 4.98/5.27 thf(fact_2573_cancel__div__mod__rules_I1_J,axiom,
% 4.98/5.27 ! [A: int,B: int,C: int] :
% 4.98/5.27 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 4.98/5.27 = ( plus_plus_int @ A @ C ) ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_div_mod_rules(1)
% 4.98/5.27 thf(fact_2574_cancel__div__mod__rules_I2_J,axiom,
% 4.98/5.27 ! [B: nat,A: nat,C: nat] :
% 4.98/5.27 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 4.98/5.27 = ( plus_plus_nat @ A @ C ) ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_div_mod_rules(2)
% 4.98/5.27 thf(fact_2575_cancel__div__mod__rules_I2_J,axiom,
% 4.98/5.27 ! [B: int,A: int,C: int] :
% 4.98/5.27 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 4.98/5.27 = ( plus_plus_int @ A @ C ) ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_div_mod_rules(2)
% 4.98/5.27 thf(fact_2576_invar__vebt_Ointros_I1_J,axiom,
% 4.98/5.27 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % invar_vebt.intros(1)
% 4.98/5.27 thf(fact_2577_mod__le__divisor,axiom,
% 4.98/5.27 ! [N2: nat,M: nat] :
% 4.98/5.27 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_le_divisor
% 4.98/5.27 thf(fact_2578_vebt__member_Osimps_I1_J,axiom,
% 4.98/5.27 ! [A: $o,B: $o,X2: nat] :
% 4.98/5.27 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 4.98/5.27 = ( ( ( X2 = zero_zero_nat )
% 4.98/5.27 => A )
% 4.98/5.27 & ( ( X2 != zero_zero_nat )
% 4.98/5.27 => ( ( ( X2 = one_one_nat )
% 4.98/5.27 => B )
% 4.98/5.27 & ( X2 = one_one_nat ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % vebt_member.simps(1)
% 4.98/5.27 thf(fact_2579_mod__eq__nat1E,axiom,
% 4.98/5.27 ! [M: nat,Q2: nat,N2: nat] :
% 4.98/5.27 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 4.98/5.27 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 4.98/5.27 => ( ( ord_less_eq_nat @ N2 @ M )
% 4.98/5.27 => ~ ! [S: nat] :
% 4.98/5.27 ( M
% 4.98/5.27 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_eq_nat1E
% 4.98/5.27 thf(fact_2580_mod__eq__nat2E,axiom,
% 4.98/5.27 ! [M: nat,Q2: nat,N2: nat] :
% 4.98/5.27 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 4.98/5.27 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 4.98/5.27 => ( ( ord_less_eq_nat @ M @ N2 )
% 4.98/5.27 => ~ ! [S: nat] :
% 4.98/5.27 ( N2
% 4.98/5.27 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_eq_nat2E
% 4.98/5.27 thf(fact_2581_nat__mod__eq__lemma,axiom,
% 4.98/5.27 ! [X2: nat,N2: nat,Y: nat] :
% 4.98/5.27 ( ( ( modulo_modulo_nat @ X2 @ N2 )
% 4.98/5.27 = ( modulo_modulo_nat @ Y @ N2 ) )
% 4.98/5.27 => ( ( ord_less_eq_nat @ Y @ X2 )
% 4.98/5.27 => ? [Q3: nat] :
% 4.98/5.27 ( X2
% 4.98/5.27 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q3 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % nat_mod_eq_lemma
% 4.98/5.27 thf(fact_2582_vebt__buildup_Osimps_I2_J,axiom,
% 4.98/5.27 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 4.98/5.27 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 4.98/5.27
% 4.98/5.27 % vebt_buildup.simps(2)
% 4.98/5.27 thf(fact_2583_vebt__insert_Osimps_I1_J,axiom,
% 4.98/5.27 ! [X2: nat,A: $o,B: $o] :
% 4.98/5.27 ( ( ( X2 = zero_zero_nat )
% 4.98/5.27 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 4.98/5.27 = ( vEBT_Leaf @ $true @ B ) ) )
% 4.98/5.27 & ( ( X2 != zero_zero_nat )
% 4.98/5.27 => ( ( ( X2 = one_one_nat )
% 4.98/5.27 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 4.98/5.27 = ( vEBT_Leaf @ A @ $true ) ) )
% 4.98/5.27 & ( ( X2 != one_one_nat )
% 4.98/5.27 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 4.98/5.27 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % vebt_insert.simps(1)
% 4.98/5.27 thf(fact_2584_mod__mult2__eq,axiom,
% 4.98/5.27 ! [M: nat,N2: nat,Q2: nat] :
% 4.98/5.27 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q2 ) )
% 4.98/5.27 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_mult2_eq
% 4.98/5.27 thf(fact_2585_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 4.98/5.27 ! [A: $o,B: $o,X2: nat] :
% 4.98/5.27 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X2 )
% 4.98/5.27 = ( ( ( X2 = zero_zero_nat )
% 4.98/5.27 => A )
% 4.98/5.27 & ( ( X2 != zero_zero_nat )
% 4.98/5.27 => ( ( ( X2 = one_one_nat )
% 4.98/5.27 => B )
% 4.98/5.27 & ( X2 = one_one_nat ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % VEBT_internal.naive_member.simps(1)
% 4.98/5.27 thf(fact_2586_minf_I7_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_real @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(7)
% 4.98/5.27 thf(fact_2587_minf_I7_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_rat @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(7)
% 4.98/5.27 thf(fact_2588_minf_I7_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_num @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(7)
% 4.98/5.27 thf(fact_2589_minf_I7_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_nat @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(7)
% 4.98/5.27 thf(fact_2590_minf_I7_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_int @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(7)
% 4.98/5.27 thf(fact_2591_minf_I5_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_real @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(5)
% 4.98/5.27 thf(fact_2592_minf_I5_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_rat @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(5)
% 4.98/5.27 thf(fact_2593_minf_I5_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_num @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(5)
% 4.98/5.27 thf(fact_2594_minf_I5_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_nat @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(5)
% 4.98/5.27 thf(fact_2595_minf_I5_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_int @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(5)
% 4.98/5.27 thf(fact_2596_minf_I4_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(4)
% 4.98/5.27 thf(fact_2597_minf_I4_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(4)
% 4.98/5.27 thf(fact_2598_minf_I4_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(4)
% 4.98/5.27 thf(fact_2599_minf_I4_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(4)
% 4.98/5.27 thf(fact_2600_minf_I4_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(4)
% 4.98/5.27 thf(fact_2601_minf_I3_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(3)
% 4.98/5.27 thf(fact_2602_minf_I3_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(3)
% 4.98/5.27 thf(fact_2603_minf_I3_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(3)
% 4.98/5.27 thf(fact_2604_minf_I3_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(3)
% 4.98/5.27 thf(fact_2605_minf_I3_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(3)
% 4.98/5.27 thf(fact_2606_minf_I2_J,axiom,
% 4.98/5.27 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 4.98/5.27 ( ? [Z4: real] :
% 4.98/5.27 ! [X5: real] :
% 4.98/5.27 ( ( ord_less_real @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: real] :
% 4.98/5.27 ! [X5: real] :
% 4.98/5.27 ( ( ord_less_real @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(2)
% 4.98/5.27 thf(fact_2607_minf_I2_J,axiom,
% 4.98/5.27 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 4.98/5.27 ( ? [Z4: rat] :
% 4.98/5.27 ! [X5: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: rat] :
% 4.98/5.27 ! [X5: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(2)
% 4.98/5.27 thf(fact_2608_minf_I2_J,axiom,
% 4.98/5.27 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 4.98/5.27 ( ? [Z4: num] :
% 4.98/5.27 ! [X5: num] :
% 4.98/5.27 ( ( ord_less_num @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: num] :
% 4.98/5.27 ! [X5: num] :
% 4.98/5.27 ( ( ord_less_num @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(2)
% 4.98/5.27 thf(fact_2609_minf_I2_J,axiom,
% 4.98/5.27 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 4.98/5.27 ( ? [Z4: nat] :
% 4.98/5.27 ! [X5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: nat] :
% 4.98/5.27 ! [X5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(2)
% 4.98/5.27 thf(fact_2610_minf_I2_J,axiom,
% 4.98/5.27 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 4.98/5.27 ( ? [Z4: int] :
% 4.98/5.27 ! [X5: int] :
% 4.98/5.27 ( ( ord_less_int @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: int] :
% 4.98/5.27 ! [X5: int] :
% 4.98/5.27 ( ( ord_less_int @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(2)
% 4.98/5.27 thf(fact_2611_minf_I1_J,axiom,
% 4.98/5.27 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 4.98/5.27 ( ? [Z4: real] :
% 4.98/5.27 ! [X5: real] :
% 4.98/5.27 ( ( ord_less_real @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: real] :
% 4.98/5.27 ! [X5: real] :
% 4.98/5.27 ( ( ord_less_real @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(1)
% 4.98/5.27 thf(fact_2612_minf_I1_J,axiom,
% 4.98/5.27 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 4.98/5.27 ( ? [Z4: rat] :
% 4.98/5.27 ! [X5: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: rat] :
% 4.98/5.27 ! [X5: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(1)
% 4.98/5.27 thf(fact_2613_minf_I1_J,axiom,
% 4.98/5.27 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 4.98/5.27 ( ? [Z4: num] :
% 4.98/5.27 ! [X5: num] :
% 4.98/5.27 ( ( ord_less_num @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: num] :
% 4.98/5.27 ! [X5: num] :
% 4.98/5.27 ( ( ord_less_num @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(1)
% 4.98/5.27 thf(fact_2614_minf_I1_J,axiom,
% 4.98/5.27 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 4.98/5.27 ( ? [Z4: nat] :
% 4.98/5.27 ! [X5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: nat] :
% 4.98/5.27 ! [X5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(1)
% 4.98/5.27 thf(fact_2615_minf_I1_J,axiom,
% 4.98/5.27 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 4.98/5.27 ( ? [Z4: int] :
% 4.98/5.27 ! [X5: int] :
% 4.98/5.27 ( ( ord_less_int @ X5 @ Z4 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: int] :
% 4.98/5.27 ! [X5: int] :
% 4.98/5.27 ( ( ord_less_int @ X5 @ Z4 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(1)
% 4.98/5.27 thf(fact_2616_pinf_I7_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_real @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(7)
% 4.98/5.27 thf(fact_2617_pinf_I7_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_rat @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(7)
% 4.98/5.27 thf(fact_2618_pinf_I7_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_num @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(7)
% 4.98/5.27 thf(fact_2619_pinf_I7_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_nat @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(7)
% 4.98/5.27 thf(fact_2620_pinf_I7_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_int @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(7)
% 4.98/5.27 thf(fact_2621_pinf_I5_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_real @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(5)
% 4.98/5.27 thf(fact_2622_pinf_I5_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_rat @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(5)
% 4.98/5.27 thf(fact_2623_pinf_I5_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_num @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(5)
% 4.98/5.27 thf(fact_2624_pinf_I5_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_nat @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(5)
% 4.98/5.27 thf(fact_2625_pinf_I5_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_int @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(5)
% 4.98/5.27 thf(fact_2626_pinf_I4_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(4)
% 4.98/5.27 thf(fact_2627_pinf_I4_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(4)
% 4.98/5.27 thf(fact_2628_pinf_I4_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(4)
% 4.98/5.27 thf(fact_2629_pinf_I4_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(4)
% 4.98/5.27 thf(fact_2630_pinf_I4_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(4)
% 4.98/5.27 thf(fact_2631_pinf_I3_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(3)
% 4.98/5.27 thf(fact_2632_pinf_I3_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(3)
% 4.98/5.27 thf(fact_2633_pinf_I3_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(3)
% 4.98/5.27 thf(fact_2634_pinf_I3_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(3)
% 4.98/5.27 thf(fact_2635_pinf_I3_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.27 => ( X3 != T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(3)
% 4.98/5.27 thf(fact_2636_pinf_I2_J,axiom,
% 4.98/5.27 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 4.98/5.27 ( ? [Z4: real] :
% 4.98/5.27 ! [X5: real] :
% 4.98/5.27 ( ( ord_less_real @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: real] :
% 4.98/5.27 ! [X5: real] :
% 4.98/5.27 ( ( ord_less_real @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(2)
% 4.98/5.27 thf(fact_2637_pinf_I2_J,axiom,
% 4.98/5.27 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 4.98/5.27 ( ? [Z4: rat] :
% 4.98/5.27 ! [X5: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: rat] :
% 4.98/5.27 ! [X5: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(2)
% 4.98/5.27 thf(fact_2638_pinf_I2_J,axiom,
% 4.98/5.27 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 4.98/5.27 ( ? [Z4: num] :
% 4.98/5.27 ! [X5: num] :
% 4.98/5.27 ( ( ord_less_num @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: num] :
% 4.98/5.27 ! [X5: num] :
% 4.98/5.27 ( ( ord_less_num @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(2)
% 4.98/5.27 thf(fact_2639_pinf_I2_J,axiom,
% 4.98/5.27 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 4.98/5.27 ( ? [Z4: nat] :
% 4.98/5.27 ! [X5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: nat] :
% 4.98/5.27 ! [X5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(2)
% 4.98/5.27 thf(fact_2640_pinf_I2_J,axiom,
% 4.98/5.27 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 4.98/5.27 ( ? [Z4: int] :
% 4.98/5.27 ! [X5: int] :
% 4.98/5.27 ( ( ord_less_int @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: int] :
% 4.98/5.27 ! [X5: int] :
% 4.98/5.27 ( ( ord_less_int @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 | ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 | ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(2)
% 4.98/5.27 thf(fact_2641_pinf_I1_J,axiom,
% 4.98/5.27 ! [P: real > $o,P5: real > $o,Q: real > $o,Q6: real > $o] :
% 4.98/5.27 ( ? [Z4: real] :
% 4.98/5.27 ! [X5: real] :
% 4.98/5.27 ( ( ord_less_real @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: real] :
% 4.98/5.27 ! [X5: real] :
% 4.98/5.27 ( ( ord_less_real @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(1)
% 4.98/5.27 thf(fact_2642_pinf_I1_J,axiom,
% 4.98/5.27 ! [P: rat > $o,P5: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 4.98/5.27 ( ? [Z4: rat] :
% 4.98/5.27 ! [X5: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: rat] :
% 4.98/5.27 ! [X5: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(1)
% 4.98/5.27 thf(fact_2643_pinf_I1_J,axiom,
% 4.98/5.27 ! [P: num > $o,P5: num > $o,Q: num > $o,Q6: num > $o] :
% 4.98/5.27 ( ? [Z4: num] :
% 4.98/5.27 ! [X5: num] :
% 4.98/5.27 ( ( ord_less_num @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: num] :
% 4.98/5.27 ! [X5: num] :
% 4.98/5.27 ( ( ord_less_num @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(1)
% 4.98/5.27 thf(fact_2644_pinf_I1_J,axiom,
% 4.98/5.27 ! [P: nat > $o,P5: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 4.98/5.27 ( ? [Z4: nat] :
% 4.98/5.27 ! [X5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: nat] :
% 4.98/5.27 ! [X5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(1)
% 4.98/5.27 thf(fact_2645_pinf_I1_J,axiom,
% 4.98/5.27 ! [P: int > $o,P5: int > $o,Q: int > $o,Q6: int > $o] :
% 4.98/5.27 ( ? [Z4: int] :
% 4.98/5.27 ! [X5: int] :
% 4.98/5.27 ( ( ord_less_int @ Z4 @ X5 )
% 4.98/5.27 => ( ( P @ X5 )
% 4.98/5.27 = ( P5 @ X5 ) ) )
% 4.98/5.27 => ( ? [Z4: int] :
% 4.98/5.27 ! [X5: int] :
% 4.98/5.27 ( ( ord_less_int @ Z4 @ X5 )
% 4.98/5.27 => ( ( Q @ X5 )
% 4.98/5.27 = ( Q6 @ X5 ) ) )
% 4.98/5.27 => ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.27 => ( ( ( P @ X3 )
% 4.98/5.27 & ( Q @ X3 ) )
% 4.98/5.27 = ( ( P5 @ X3 )
% 4.98/5.27 & ( Q6 @ X3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(1)
% 4.98/5.27 thf(fact_2646_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 4.98/5.27 ! [X2: vEBT_VEBT] :
% 4.98/5.27 ( ~ ( vEBT_VEBT_minNull @ X2 )
% 4.98/5.27 => ( ! [Uv2: $o] :
% 4.98/5.27 ( X2
% 4.98/5.27 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 4.98/5.27 => ( ! [Uu2: $o] :
% 4.98/5.27 ( X2
% 4.98/5.27 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 4.98/5.27 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 4.98/5.27 ( X2
% 4.98/5.27 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % VEBT_internal.minNull.elims(3)
% 4.98/5.27 thf(fact_2647_bounded__Max__nat,axiom,
% 4.98/5.27 ! [P: nat > $o,X2: nat,M7: nat] :
% 4.98/5.27 ( ( P @ X2 )
% 4.98/5.27 => ( ! [X5: nat] :
% 4.98/5.27 ( ( P @ X5 )
% 4.98/5.27 => ( ord_less_eq_nat @ X5 @ M7 ) )
% 4.98/5.27 => ~ ! [M3: nat] :
% 4.98/5.27 ( ( P @ M3 )
% 4.98/5.27 => ~ ! [X3: nat] :
% 4.98/5.27 ( ( P @ X3 )
% 4.98/5.27 => ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % bounded_Max_nat
% 4.98/5.27 thf(fact_2648_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 4.98/5.27 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 4.98/5.27 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 4.98/5.27
% 4.98/5.27 % VEBT_internal.membermima.simps(2)
% 4.98/5.27 thf(fact_2649_fold__atLeastAtMost__nat_Ocases,axiom,
% 4.98/5.27 ! [X2: produc3368934014287244435at_num] :
% 4.98/5.27 ~ ! [F2: nat > num > num,A4: nat,B3: nat,Acc: num] :
% 4.98/5.27 ( X2
% 4.98/5.27 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A4 @ ( product_Pair_nat_num @ B3 @ Acc ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % fold_atLeastAtMost_nat.cases
% 4.98/5.27 thf(fact_2650_fold__atLeastAtMost__nat_Ocases,axiom,
% 4.98/5.27 ! [X2: produc4471711990508489141at_nat] :
% 4.98/5.27 ~ ! [F2: nat > nat > nat,A4: nat,B3: nat,Acc: nat] :
% 4.98/5.27 ( X2
% 4.98/5.27 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A4 @ ( product_Pair_nat_nat @ B3 @ Acc ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % fold_atLeastAtMost_nat.cases
% 4.98/5.27 thf(fact_2651_option_Osize_I3_J,axiom,
% 4.98/5.27 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 4.98/5.27 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % option.size(3)
% 4.98/5.27 thf(fact_2652_option_Osize_I3_J,axiom,
% 4.98/5.27 ( ( size_size_option_num @ none_num )
% 4.98/5.27 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % option.size(3)
% 4.98/5.27 thf(fact_2653_split__mod,axiom,
% 4.98/5.27 ! [P: nat > $o,M: nat,N2: nat] :
% 4.98/5.27 ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 4.98/5.27 = ( ( ( N2 = zero_zero_nat )
% 4.98/5.27 => ( P @ M ) )
% 4.98/5.27 & ( ( N2 != zero_zero_nat )
% 4.98/5.27 => ! [I5: nat,J3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ J3 @ N2 )
% 4.98/5.27 => ( ( M
% 4.98/5.27 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I5 ) @ J3 ) )
% 4.98/5.27 => ( P @ J3 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % split_mod
% 4.98/5.27 thf(fact_2654_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 4.98/5.27 ! [C: nat,A: nat,B: nat] :
% 4.98/5.27 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 4.98/5.27 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 4.98/5.27 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 4.98/5.27 thf(fact_2655_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 4.98/5.27 ! [C: int,A: int,B: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.27 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 4.98/5.27 thf(fact_2656_Suc__times__mod__eq,axiom,
% 4.98/5.27 ! [M: nat,N2: nat] :
% 4.98/5.27 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 4.98/5.27 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 4.98/5.27 = one_one_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % Suc_times_mod_eq
% 4.98/5.27 thf(fact_2657_vebt__insert_Osimps_I4_J,axiom,
% 4.98/5.27 ! [V: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 4.98/5.27 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) @ X2 )
% 4.98/5.27 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X2 @ X2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary ) ) ).
% 4.98/5.27
% 4.98/5.27 % vebt_insert.simps(4)
% 4.98/5.27 thf(fact_2658_divmod__digit__0_I2_J,axiom,
% 4.98/5.27 ! [B: nat,A: nat] :
% 4.98/5.27 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.27 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.98/5.27 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 4.98/5.27 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % divmod_digit_0(2)
% 4.98/5.27 thf(fact_2659_divmod__digit__0_I2_J,axiom,
% 4.98/5.27 ! [B: int,A: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.27 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.98/5.27 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 4.98/5.27 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % divmod_digit_0(2)
% 4.98/5.27 thf(fact_2660_bits__stable__imp__add__self,axiom,
% 4.98/5.27 ! [A: nat] :
% 4.98/5.27 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.27 = A )
% 4.98/5.27 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.27 = zero_zero_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % bits_stable_imp_add_self
% 4.98/5.27 thf(fact_2661_bits__stable__imp__add__self,axiom,
% 4.98/5.27 ! [A: int] :
% 4.98/5.27 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.27 = A )
% 4.98/5.27 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 4.98/5.27 = zero_zero_int ) ) ).
% 4.98/5.27
% 4.98/5.27 % bits_stable_imp_add_self
% 4.98/5.27 thf(fact_2662_div__exp__mod__exp__eq,axiom,
% 4.98/5.27 ! [A: nat,N2: nat,M: nat] :
% 4.98/5.27 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.27 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_exp_mod_exp_eq
% 4.98/5.27 thf(fact_2663_div__exp__mod__exp__eq,axiom,
% 4.98/5.27 ! [A: int,N2: nat,M: nat] :
% 4.98/5.27 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.27 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_exp_mod_exp_eq
% 4.98/5.27 thf(fact_2664_divmod__digit__0_I1_J,axiom,
% 4.98/5.27 ! [B: nat,A: nat] :
% 4.98/5.27 ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.27 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.98/5.27 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 4.98/5.27 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % divmod_digit_0(1)
% 4.98/5.27 thf(fact_2665_divmod__digit__0_I1_J,axiom,
% 4.98/5.27 ! [B: int,A: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.27 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 4.98/5.27 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 4.98/5.27 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % divmod_digit_0(1)
% 4.98/5.27 thf(fact_2666_minf_I8_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_eq_real @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(8)
% 4.98/5.27 thf(fact_2667_minf_I8_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_eq_rat @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(8)
% 4.98/5.27 thf(fact_2668_minf_I8_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_eq_num @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(8)
% 4.98/5.27 thf(fact_2669_minf_I8_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_eq_nat @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(8)
% 4.98/5.27 thf(fact_2670_minf_I8_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.27 => ~ ( ord_less_eq_int @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(8)
% 4.98/5.27 thf(fact_2671_minf_I6_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_eq_real @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(6)
% 4.98/5.27 thf(fact_2672_minf_I6_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_eq_rat @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(6)
% 4.98/5.27 thf(fact_2673_minf_I6_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_eq_num @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(6)
% 4.98/5.27 thf(fact_2674_minf_I6_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_eq_nat @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(6)
% 4.98/5.27 thf(fact_2675_minf_I6_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.27 => ( ord_less_eq_int @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % minf(6)
% 4.98/5.27 thf(fact_2676_pinf_I8_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_eq_real @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(8)
% 4.98/5.27 thf(fact_2677_pinf_I8_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_eq_rat @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(8)
% 4.98/5.27 thf(fact_2678_pinf_I8_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_eq_num @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(8)
% 4.98/5.27 thf(fact_2679_pinf_I8_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_eq_nat @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(8)
% 4.98/5.27 thf(fact_2680_pinf_I8_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.27 => ( ord_less_eq_int @ T2 @ X3 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(8)
% 4.98/5.27 thf(fact_2681_pinf_I6_J,axiom,
% 4.98/5.27 ! [T2: real] :
% 4.98/5.27 ? [Z3: real] :
% 4.98/5.27 ! [X3: real] :
% 4.98/5.27 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_eq_real @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(6)
% 4.98/5.27 thf(fact_2682_pinf_I6_J,axiom,
% 4.98/5.27 ! [T2: rat] :
% 4.98/5.27 ? [Z3: rat] :
% 4.98/5.27 ! [X3: rat] :
% 4.98/5.27 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_eq_rat @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(6)
% 4.98/5.27 thf(fact_2683_pinf_I6_J,axiom,
% 4.98/5.27 ! [T2: num] :
% 4.98/5.27 ? [Z3: num] :
% 4.98/5.27 ! [X3: num] :
% 4.98/5.27 ( ( ord_less_num @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_eq_num @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(6)
% 4.98/5.27 thf(fact_2684_pinf_I6_J,axiom,
% 4.98/5.27 ! [T2: nat] :
% 4.98/5.27 ? [Z3: nat] :
% 4.98/5.27 ! [X3: nat] :
% 4.98/5.27 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_eq_nat @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(6)
% 4.98/5.27 thf(fact_2685_pinf_I6_J,axiom,
% 4.98/5.27 ! [T2: int] :
% 4.98/5.27 ? [Z3: int] :
% 4.98/5.27 ! [X3: int] :
% 4.98/5.27 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.27 => ~ ( ord_less_eq_int @ X3 @ T2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % pinf(6)
% 4.98/5.27 thf(fact_2686_conj__le__cong,axiom,
% 4.98/5.27 ! [X2: int,X6: int,P: $o,P5: $o] :
% 4.98/5.27 ( ( X2 = X6 )
% 4.98/5.27 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 4.98/5.27 => ( P = P5 ) )
% 4.98/5.27 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 4.98/5.27 & P )
% 4.98/5.27 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 4.98/5.27 & P5 ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % conj_le_cong
% 4.98/5.27 thf(fact_2687_imp__le__cong,axiom,
% 4.98/5.27 ! [X2: int,X6: int,P: $o,P5: $o] :
% 4.98/5.27 ( ( X2 = X6 )
% 4.98/5.27 => ( ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 4.98/5.27 => ( P = P5 ) )
% 4.98/5.27 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 4.98/5.27 => P )
% 4.98/5.27 = ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 4.98/5.27 => P5 ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % imp_le_cong
% 4.98/5.27 thf(fact_2688_mod__double__modulus,axiom,
% 4.98/5.27 ! [M: nat,X2: nat] :
% 4.98/5.27 ( ( ord_less_nat @ zero_zero_nat @ M )
% 4.98/5.27 => ( ( ord_less_eq_nat @ zero_zero_nat @ X2 )
% 4.98/5.27 => ( ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.27 = ( modulo_modulo_nat @ X2 @ M ) )
% 4.98/5.27 | ( ( modulo_modulo_nat @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.27 = ( plus_plus_nat @ ( modulo_modulo_nat @ X2 @ M ) @ M ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_double_modulus
% 4.98/5.27 thf(fact_2689_mod__double__modulus,axiom,
% 4.98/5.27 ! [M: int,X2: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ M )
% 4.98/5.27 => ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 4.98/5.27 => ( ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.27 = ( modulo_modulo_int @ X2 @ M ) )
% 4.98/5.27 | ( ( modulo_modulo_int @ X2 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.27 = ( plus_plus_int @ ( modulo_modulo_int @ X2 @ M ) @ M ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_double_modulus
% 4.98/5.27 thf(fact_2690_unset__bit__Suc,axiom,
% 4.98/5.27 ! [N2: nat,A: int] :
% 4.98/5.27 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 4.98/5.27 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % unset_bit_Suc
% 4.98/5.27 thf(fact_2691_unset__bit__Suc,axiom,
% 4.98/5.27 ! [N2: nat,A: nat] :
% 4.98/5.27 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 4.98/5.27 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % unset_bit_Suc
% 4.98/5.27 thf(fact_2692_set__bit__Suc,axiom,
% 4.98/5.27 ! [N2: nat,A: int] :
% 4.98/5.27 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 4.98/5.27 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % set_bit_Suc
% 4.98/5.27 thf(fact_2693_set__bit__Suc,axiom,
% 4.98/5.27 ! [N2: nat,A: nat] :
% 4.98/5.27 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 4.98/5.27 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % set_bit_Suc
% 4.98/5.27 thf(fact_2694_divmod__digit__1_I1_J,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 4.98/5.27 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 4.98/5.27 => ( ( 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 )
% 4.98/5.27 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % divmod_digit_1(1)
% 4.98/5.27 thf(fact_2695_divmod__digit__1_I1_J,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.27 => ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.27 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 4.98/5.27 => ( ( 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 )
% 4.98/5.27 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % divmod_digit_1(1)
% 4.98/5.27 thf(fact_2696_invar__vebt_Osimps,axiom,
% 4.98/5.27 ( vEBT_invar_vebt
% 4.98/5.27 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 4.98/5.27 ( ( ? [A5: $o,B5: $o] :
% 4.98/5.27 ( A1
% 4.98/5.27 = ( vEBT_Leaf @ A5 @ B5 ) )
% 4.98/5.27 & ( A22
% 4.98/5.27 = ( suc @ zero_zero_nat ) ) )
% 4.98/5.27 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 4.98/5.27 ( ( A1
% 4.98/5.27 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 4.98/5.27 & ! [X: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X @ N3 ) )
% 4.98/5.27 & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 4.98/5.27 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 4.98/5.27 & ( A22
% 4.98/5.27 = ( plus_plus_nat @ N3 @ N3 ) )
% 4.98/5.27 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 4.98/5.27 & ! [X: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.98/5.27 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 4.98/5.27 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT] :
% 4.98/5.27 ( ( A1
% 4.98/5.27 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList3 @ Summary3 ) )
% 4.98/5.27 & ! [X: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X @ N3 ) )
% 4.98/5.27 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 4.98/5.27 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 4.98/5.27 & ( A22
% 4.98/5.27 = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 4.98/5.27 & ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X4 )
% 4.98/5.27 & ! [X: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.98/5.27 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 4.98/5.27 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 4.98/5.27 ( ( A1
% 4.98/5.27 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 4.98/5.27 & ! [X: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X @ N3 ) )
% 4.98/5.27 & ( vEBT_invar_vebt @ Summary3 @ N3 )
% 4.98/5.27 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 4.98/5.27 & ( A22
% 4.98/5.27 = ( plus_plus_nat @ N3 @ N3 ) )
% 4.98/5.27 & ! [I5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 4.98/5.27 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 4.98/5.27 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 4.98/5.27 & ( ( Mi3 = Ma3 )
% 4.98/5.27 => ! [X: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.98/5.27 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 4.98/5.27 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.98/5.27 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 4.98/5.27 & ( ( Mi3 != Ma3 )
% 4.98/5.27 => ! [I5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) )
% 4.98/5.27 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 4.98/5.27 = I5 )
% 4.98/5.27 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 4.98/5.27 & ! [X: nat] :
% 4.98/5.27 ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 4.98/5.27 = I5 )
% 4.98/5.27 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 4.98/5.27 => ( ( ord_less_nat @ Mi3 @ X )
% 4.98/5.27 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) )
% 4.98/5.27 | ? [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 4.98/5.27 ( ( A1
% 4.98/5.27 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList3 @ Summary3 ) )
% 4.98/5.27 & ! [X: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X @ N3 ) )
% 4.98/5.27 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N3 ) )
% 4.98/5.27 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 4.98/5.27 & ( A22
% 4.98/5.27 = ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) )
% 4.98/5.27 & ! [I5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 4.98/5.27 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X4 ) )
% 4.98/5.27 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 4.98/5.27 & ( ( Mi3 = Ma3 )
% 4.98/5.27 => ! [X: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 4.98/5.27 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 4.98/5.27 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 4.98/5.27 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 4.98/5.27 & ( ( Mi3 != Ma3 )
% 4.98/5.27 => ! [I5: nat] :
% 4.98/5.27 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) )
% 4.98/5.27 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N3 )
% 4.98/5.27 = I5 )
% 4.98/5.27 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 4.98/5.27 & ! [X: nat] :
% 4.98/5.27 ( ( ( ( vEBT_VEBT_high @ X @ N3 )
% 4.98/5.27 = I5 )
% 4.98/5.27 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ ( vEBT_VEBT_low @ X @ N3 ) ) )
% 4.98/5.27 => ( ( ord_less_nat @ Mi3 @ X )
% 4.98/5.27 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % invar_vebt.simps
% 4.98/5.27 thf(fact_2697_invar__vebt_Ocases,axiom,
% 4.98/5.27 ! [A12: vEBT_VEBT,A23: nat] :
% 4.98/5.27 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 4.98/5.27 => ( ( ? [A4: $o,B3: $o] :
% 4.98/5.27 ( A12
% 4.98/5.27 = ( vEBT_Leaf @ A4 @ B3 ) )
% 4.98/5.27 => ( A23
% 4.98/5.27 != ( suc @ zero_zero_nat ) ) )
% 4.98/5.27 => ( ! [TreeList2: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 4.98/5.27 ( ( A12
% 4.98/5.27 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.98/5.27 => ( ( A23 = Deg2 )
% 4.98/5.27 => ( ! [X3: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X3 @ N ) )
% 4.98/5.27 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 4.98/5.27 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.98/5.27 => ( ( M3 = N )
% 4.98/5.27 => ( ( Deg2
% 4.98/5.27 = ( plus_plus_nat @ N @ M3 ) )
% 4.98/5.27 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 4.98/5.27 => ~ ! [X3: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.98/5.27 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ) ) ) ) ) ) )
% 4.98/5.27 => ( ! [TreeList2: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat] :
% 4.98/5.27 ( ( A12
% 4.98/5.27 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.98/5.27 => ( ( A23 = Deg2 )
% 4.98/5.27 => ( ! [X3: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X3 @ N ) )
% 4.98/5.27 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 4.98/5.27 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.98/5.27 => ( ( M3
% 4.98/5.27 = ( suc @ N ) )
% 4.98/5.27 => ( ( Deg2
% 4.98/5.27 = ( plus_plus_nat @ N @ M3 ) )
% 4.98/5.27 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 4.98/5.27 => ~ ! [X3: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.98/5.27 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) ) ) ) ) ) ) ) )
% 4.98/5.27 => ( ! [TreeList2: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 4.98/5.27 ( ( A12
% 4.98/5.27 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.98/5.27 => ( ( A23 = Deg2 )
% 4.98/5.27 => ( ! [X3: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X3 @ N ) )
% 4.98/5.27 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 4.98/5.27 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.98/5.27 => ( ( M3 = N )
% 4.98/5.27 => ( ( Deg2
% 4.98/5.27 = ( plus_plus_nat @ N @ M3 ) )
% 4.98/5.27 => ( ! [I: nat] :
% 4.98/5.27 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.98/5.27 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X4 ) )
% 4.98/5.27 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 4.98/5.27 => ( ( ( Mi2 = Ma2 )
% 4.98/5.27 => ! [X3: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.98/5.27 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 4.98/5.27 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 4.98/5.27 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.98/5.27 => ~ ( ( Mi2 != Ma2 )
% 4.98/5.27 => ! [I: nat] :
% 4.98/5.27 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.98/5.27 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 4.98/5.27 = I )
% 4.98/5.27 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 4.98/5.27 & ! [X3: nat] :
% 4.98/5.27 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 4.98/5.27 = I )
% 4.98/5.27 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 4.98/5.27 => ( ( ord_less_nat @ Mi2 @ X3 )
% 4.98/5.27 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 4.98/5.27 => ~ ! [TreeList2: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,M3: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 4.98/5.27 ( ( A12
% 4.98/5.27 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList2 @ Summary2 ) )
% 4.98/5.27 => ( ( A23 = Deg2 )
% 4.98/5.27 => ( ! [X3: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X3 @ N ) )
% 4.98/5.27 => ( ( vEBT_invar_vebt @ Summary2 @ M3 )
% 4.98/5.27 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.98/5.27 => ( ( M3
% 4.98/5.27 = ( suc @ N ) )
% 4.98/5.27 => ( ( Deg2
% 4.98/5.27 = ( plus_plus_nat @ N @ M3 ) )
% 4.98/5.27 => ( ! [I: nat] :
% 4.98/5.27 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.98/5.27 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X4 ) )
% 4.98/5.27 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 4.98/5.27 => ( ( ( Mi2 = Ma2 )
% 4.98/5.27 => ! [X3: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 4.98/5.27 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_1 ) ) )
% 4.98/5.27 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 4.98/5.27 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 4.98/5.27 => ~ ( ( Mi2 != Ma2 )
% 4.98/5.27 => ! [I: nat] :
% 4.98/5.27 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 4.98/5.27 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 4.98/5.27 = I )
% 4.98/5.27 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 4.98/5.27 & ! [X3: nat] :
% 4.98/5.27 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 4.98/5.27 = I )
% 4.98/5.27 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 4.98/5.27 => ( ( ord_less_nat @ Mi2 @ X3 )
% 4.98/5.27 & ( ord_less_eq_nat @ X3 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % invar_vebt.cases
% 4.98/5.27 thf(fact_2698_invar__vebt_Ointros_I2_J,axiom,
% 4.98/5.27 ! [TreeList: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 4.98/5.27 ( ! [X5: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 4.98/5.27 => ( ( vEBT_invar_vebt @ Summary @ M )
% 4.98/5.27 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 4.98/5.27 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 4.98/5.27 => ( ( M = N2 )
% 4.98/5.27 => ( ( Deg
% 4.98/5.27 = ( plus_plus_nat @ N2 @ M ) )
% 4.98/5.27 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 4.98/5.27 => ( ! [X5: vEBT_VEBT] :
% 4.98/5.27 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 4.98/5.27 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 4.98/5.27 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % invar_vebt.intros(2)
% 4.98/5.27 thf(fact_2699_verit__le__mono__div,axiom,
% 4.98/5.27 ! [A3: nat,B4: nat,N2: nat] :
% 4.98/5.27 ( ( ord_less_nat @ A3 @ B4 )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ord_less_eq_nat
% 4.98/5.27 @ ( plus_plus_nat @ ( divide_divide_nat @ A3 @ N2 )
% 4.98/5.27 @ ( if_nat
% 4.98/5.27 @ ( ( modulo_modulo_nat @ B4 @ N2 )
% 4.98/5.27 = zero_zero_nat )
% 4.98/5.27 @ one_one_nat
% 4.98/5.27 @ zero_zero_nat ) )
% 4.98/5.27 @ ( divide_divide_nat @ B4 @ N2 ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_le_mono_div
% 4.98/5.27 thf(fact_2700_div__mod__decomp,axiom,
% 4.98/5.27 ! [A3: nat,N2: nat] :
% 4.98/5.27 ( A3
% 4.98/5.27 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A3 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A3 @ N2 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_mod_decomp
% 4.98/5.27 thf(fact_2701_div__less__mono,axiom,
% 4.98/5.27 ! [A3: nat,B4: nat,N2: nat] :
% 4.98/5.27 ( ( ord_less_nat @ A3 @ B4 )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ( ( modulo_modulo_nat @ A3 @ N2 )
% 4.98/5.27 = zero_zero_nat )
% 4.98/5.27 => ( ( ( modulo_modulo_nat @ B4 @ N2 )
% 4.98/5.27 = zero_zero_nat )
% 4.98/5.27 => ( ord_less_nat @ ( divide_divide_nat @ A3 @ N2 ) @ ( divide_divide_nat @ B4 @ N2 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_less_mono
% 4.98/5.27 thf(fact_2702_flip__bit__Suc,axiom,
% 4.98/5.27 ! [N2: nat,A: int] :
% 4.98/5.27 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 4.98/5.27 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % flip_bit_Suc
% 4.98/5.27 thf(fact_2703_flip__bit__Suc,axiom,
% 4.98/5.27 ! [N2: nat,A: nat] :
% 4.98/5.27 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 4.98/5.27 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % flip_bit_Suc
% 4.98/5.27 thf(fact_2704_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_num,Ys: list_num] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_num @ Xs ) @ ( size_size_list_num @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( product_Pair_num_num @ ( nth_num @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2705_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_Code_integer,Ys: list_o] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2706_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2707_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2708_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2709_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2710_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2711_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_o,Ys: list_o] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2712_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_o,Ys: list_nat] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2713_product__nth,axiom,
% 4.98/5.27 ! [N2: nat,Xs: list_o,Ys: list_int] :
% 4.98/5.27 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 4.98/5.27 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N2 )
% 4.98/5.27 = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % product_nth
% 4.98/5.27 thf(fact_2714_pos__eucl__rel__int__mult__2,axiom,
% 4.98/5.27 ! [B: int,A: int,Q2: int,R2: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 4.98/5.27 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 4.98/5.27 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pos_eucl_rel_int_mult_2
% 4.98/5.27 thf(fact_2715_gcd__nat__induct,axiom,
% 4.98/5.27 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 4.98/5.27 ( ! [M3: nat] : ( P @ M3 @ zero_zero_nat )
% 4.98/5.27 => ( ! [M3: nat,N: nat] :
% 4.98/5.27 ( ( ord_less_nat @ zero_zero_nat @ N )
% 4.98/5.27 => ( ( P @ N @ ( modulo_modulo_nat @ M3 @ N ) )
% 4.98/5.27 => ( P @ M3 @ N ) ) )
% 4.98/5.27 => ( P @ M @ N2 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % gcd_nat_induct
% 4.98/5.27 thf(fact_2716_option_Osize__gen_I2_J,axiom,
% 4.98/5.27 ! [X2: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 4.98/5.27 ( ( size_o8335143837870341156at_nat @ X2 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 4.98/5.27 = ( plus_plus_nat @ ( X2 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % option.size_gen(2)
% 4.98/5.27 thf(fact_2717_option_Osize__gen_I2_J,axiom,
% 4.98/5.27 ! [X2: num > nat,X22: num] :
% 4.98/5.27 ( ( size_option_num @ X2 @ ( some_num @ X22 ) )
% 4.98/5.27 = ( plus_plus_nat @ ( X2 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % option.size_gen(2)
% 4.98/5.27 thf(fact_2718_verit__eq__simplify_I8_J,axiom,
% 4.98/5.27 ! [X22: num,Y2: num] :
% 4.98/5.27 ( ( ( bit0 @ X22 )
% 4.98/5.27 = ( bit0 @ Y2 ) )
% 4.98/5.27 = ( X22 = Y2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_eq_simplify(8)
% 4.98/5.27 thf(fact_2719_flip__bit__nonnegative__int__iff,axiom,
% 4.98/5.27 ! [N2: nat,K: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) )
% 4.98/5.27 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 4.98/5.27
% 4.98/5.27 % flip_bit_nonnegative_int_iff
% 4.98/5.27 thf(fact_2720_flip__bit__negative__int__iff,axiom,
% 4.98/5.27 ! [N2: nat,K: int] :
% 4.98/5.27 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 4.98/5.27 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 4.98/5.27
% 4.98/5.27 % flip_bit_negative_int_iff
% 4.98/5.27 thf(fact_2721_mod__neg__neg__trivial,axiom,
% 4.98/5.27 ! [K: int,L: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 4.98/5.27 => ( ( ord_less_int @ L @ K )
% 4.98/5.27 => ( ( modulo_modulo_int @ K @ L )
% 4.98/5.27 = K ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_neg_neg_trivial
% 4.98/5.27 thf(fact_2722_mod__pos__pos__trivial,axiom,
% 4.98/5.27 ! [K: int,L: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 4.98/5.27 => ( ( ord_less_int @ K @ L )
% 4.98/5.27 => ( ( modulo_modulo_int @ K @ L )
% 4.98/5.27 = K ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_pos_pos_trivial
% 4.98/5.27 thf(fact_2723_length__product,axiom,
% 4.98/5.27 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 4.98/5.27 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2724_length__product,axiom,
% 4.98/5.27 ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 4.98/5.27 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2725_length__product,axiom,
% 4.98/5.27 ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 4.98/5.27 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2726_length__product,axiom,
% 4.98/5.27 ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 4.98/5.27 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2727_length__product,axiom,
% 4.98/5.27 ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 4.98/5.27 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2728_length__product,axiom,
% 4.98/5.27 ! [Xs: list_o,Ys: list_o] :
% 4.98/5.27 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2729_length__product,axiom,
% 4.98/5.27 ! [Xs: list_o,Ys: list_nat] :
% 4.98/5.27 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2730_length__product,axiom,
% 4.98/5.27 ! [Xs: list_o,Ys: list_int] :
% 4.98/5.27 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2731_length__product,axiom,
% 4.98/5.27 ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 4.98/5.27 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2732_length__product,axiom,
% 4.98/5.27 ! [Xs: list_nat,Ys: list_o] :
% 4.98/5.27 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 4.98/5.27 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % length_product
% 4.98/5.27 thf(fact_2733_zmod__numeral__Bit0,axiom,
% 4.98/5.27 ! [V: num,W: num] :
% 4.98/5.27 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 4.98/5.27 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % zmod_numeral_Bit0
% 4.98/5.27 thf(fact_2734_mod__int__unique,axiom,
% 4.98/5.27 ! [K: int,L: int,Q2: int,R2: int] :
% 4.98/5.27 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 4.98/5.27 => ( ( modulo_modulo_int @ K @ L )
% 4.98/5.27 = R2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_int_unique
% 4.98/5.27 thf(fact_2735_unique__quotient,axiom,
% 4.98/5.27 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 4.98/5.27 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 4.98/5.27 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 4.98/5.27 => ( Q2 = Q5 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % unique_quotient
% 4.98/5.27 thf(fact_2736_unique__remainder,axiom,
% 4.98/5.27 ! [A: int,B: int,Q2: int,R2: int,Q5: int,R4: int] :
% 4.98/5.27 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 4.98/5.27 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q5 @ R4 ) )
% 4.98/5.27 => ( R2 = R4 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % unique_remainder
% 4.98/5.27 thf(fact_2737_eucl__rel__int,axiom,
% 4.98/5.27 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % eucl_rel_int
% 4.98/5.27 thf(fact_2738_eucl__rel__int__by0,axiom,
% 4.98/5.27 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 4.98/5.27
% 4.98/5.27 % eucl_rel_int_by0
% 4.98/5.27 thf(fact_2739_div__int__unique,axiom,
% 4.98/5.27 ! [K: int,L: int,Q2: int,R2: int] :
% 4.98/5.27 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 4.98/5.27 => ( ( divide_divide_int @ K @ L )
% 4.98/5.27 = Q2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_int_unique
% 4.98/5.27 thf(fact_2740_zmod__le__nonneg__dividend,axiom,
% 4.98/5.27 ! [M: int,K: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 4.98/5.27 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 4.98/5.27
% 4.98/5.27 % zmod_le_nonneg_dividend
% 4.98/5.27 thf(fact_2741_neg__mod__bound,axiom,
% 4.98/5.27 ! [L: int,K: int] :
% 4.98/5.27 ( ( ord_less_int @ L @ zero_zero_int )
% 4.98/5.27 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % neg_mod_bound
% 4.98/5.27 thf(fact_2742_Euclidean__Division_Opos__mod__bound,axiom,
% 4.98/5.27 ! [L: int,K: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ L )
% 4.98/5.27 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 4.98/5.27
% 4.98/5.27 % Euclidean_Division.pos_mod_bound
% 4.98/5.27 thf(fact_2743_zmod__eq__0__iff,axiom,
% 4.98/5.27 ! [M: int,D: int] :
% 4.98/5.27 ( ( ( modulo_modulo_int @ M @ D )
% 4.98/5.27 = zero_zero_int )
% 4.98/5.27 = ( ? [Q4: int] :
% 4.98/5.27 ( M
% 4.98/5.27 = ( times_times_int @ D @ Q4 ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % zmod_eq_0_iff
% 4.98/5.27 thf(fact_2744_zmod__eq__0D,axiom,
% 4.98/5.27 ! [M: int,D: int] :
% 4.98/5.27 ( ( ( modulo_modulo_int @ M @ D )
% 4.98/5.27 = zero_zero_int )
% 4.98/5.27 => ? [Q3: int] :
% 4.98/5.27 ( M
% 4.98/5.27 = ( times_times_int @ D @ Q3 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % zmod_eq_0D
% 4.98/5.27 thf(fact_2745_zdiv__mono__strict,axiom,
% 4.98/5.27 ! [A3: int,B4: int,N2: int] :
% 4.98/5.27 ( ( ord_less_int @ A3 @ B4 )
% 4.98/5.27 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 4.98/5.27 => ( ( ( modulo_modulo_int @ A3 @ N2 )
% 4.98/5.27 = zero_zero_int )
% 4.98/5.27 => ( ( ( modulo_modulo_int @ B4 @ N2 )
% 4.98/5.27 = zero_zero_int )
% 4.98/5.27 => ( ord_less_int @ ( divide_divide_int @ A3 @ N2 ) @ ( divide_divide_int @ B4 @ N2 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % zdiv_mono_strict
% 4.98/5.27 thf(fact_2746_div__mod__decomp__int,axiom,
% 4.98/5.27 ! [A3: int,N2: int] :
% 4.98/5.27 ( A3
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A3 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A3 @ N2 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_mod_decomp_int
% 4.98/5.27 thf(fact_2747_eucl__rel__int__dividesI,axiom,
% 4.98/5.27 ! [L: int,K: int,Q2: int] :
% 4.98/5.27 ( ( L != zero_zero_int )
% 4.98/5.27 => ( ( K
% 4.98/5.27 = ( times_times_int @ Q2 @ L ) )
% 4.98/5.27 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % eucl_rel_int_dividesI
% 4.98/5.27 thf(fact_2748_neg__mod__sign,axiom,
% 4.98/5.27 ! [L: int,K: int] :
% 4.98/5.27 ( ( ord_less_int @ L @ zero_zero_int )
% 4.98/5.27 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 4.98/5.27
% 4.98/5.27 % neg_mod_sign
% 4.98/5.27 thf(fact_2749_Euclidean__Division_Opos__mod__sign,axiom,
% 4.98/5.27 ! [L: int,K: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ L )
% 4.98/5.27 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % Euclidean_Division.pos_mod_sign
% 4.98/5.27 thf(fact_2750_neg__mod__conj,axiom,
% 4.98/5.27 ! [B: int,A: int] :
% 4.98/5.27 ( ( ord_less_int @ B @ zero_zero_int )
% 4.98/5.27 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 4.98/5.27 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % neg_mod_conj
% 4.98/5.27 thf(fact_2751_pos__mod__conj,axiom,
% 4.98/5.27 ! [B: int,A: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ B )
% 4.98/5.27 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 4.98/5.27 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pos_mod_conj
% 4.98/5.27 thf(fact_2752_zmod__trivial__iff,axiom,
% 4.98/5.27 ! [I3: int,K: int] :
% 4.98/5.27 ( ( ( modulo_modulo_int @ I3 @ K )
% 4.98/5.27 = I3 )
% 4.98/5.27 = ( ( K = zero_zero_int )
% 4.98/5.27 | ( ( ord_less_eq_int @ zero_zero_int @ I3 )
% 4.98/5.27 & ( ord_less_int @ I3 @ K ) )
% 4.98/5.27 | ( ( ord_less_eq_int @ I3 @ zero_zero_int )
% 4.98/5.27 & ( ord_less_int @ K @ I3 ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % zmod_trivial_iff
% 4.98/5.27 thf(fact_2753_verit__la__disequality,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( A = B )
% 4.98/5.27 | ~ ( ord_less_eq_rat @ A @ B )
% 4.98/5.27 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_la_disequality
% 4.98/5.27 thf(fact_2754_verit__la__disequality,axiom,
% 4.98/5.27 ! [A: num,B: num] :
% 4.98/5.27 ( ( A = B )
% 4.98/5.27 | ~ ( ord_less_eq_num @ A @ B )
% 4.98/5.27 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_la_disequality
% 4.98/5.27 thf(fact_2755_verit__la__disequality,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( A = B )
% 4.98/5.27 | ~ ( ord_less_eq_nat @ A @ B )
% 4.98/5.27 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_la_disequality
% 4.98/5.27 thf(fact_2756_verit__la__disequality,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( A = B )
% 4.98/5.27 | ~ ( ord_less_eq_int @ A @ B )
% 4.98/5.27 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_la_disequality
% 4.98/5.27 thf(fact_2757_verit__comp__simplify1_I2_J,axiom,
% 4.98/5.27 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(2)
% 4.98/5.27 thf(fact_2758_verit__comp__simplify1_I2_J,axiom,
% 4.98/5.27 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(2)
% 4.98/5.27 thf(fact_2759_verit__comp__simplify1_I2_J,axiom,
% 4.98/5.27 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(2)
% 4.98/5.27 thf(fact_2760_verit__comp__simplify1_I2_J,axiom,
% 4.98/5.27 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(2)
% 4.98/5.27 thf(fact_2761_verit__comp__simplify1_I2_J,axiom,
% 4.98/5.27 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(2)
% 4.98/5.27 thf(fact_2762_verit__comp__simplify1_I1_J,axiom,
% 4.98/5.27 ! [A: real] :
% 4.98/5.27 ~ ( ord_less_real @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(1)
% 4.98/5.27 thf(fact_2763_verit__comp__simplify1_I1_J,axiom,
% 4.98/5.27 ! [A: rat] :
% 4.98/5.27 ~ ( ord_less_rat @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(1)
% 4.98/5.27 thf(fact_2764_verit__comp__simplify1_I1_J,axiom,
% 4.98/5.27 ! [A: num] :
% 4.98/5.27 ~ ( ord_less_num @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(1)
% 4.98/5.27 thf(fact_2765_verit__comp__simplify1_I1_J,axiom,
% 4.98/5.27 ! [A: nat] :
% 4.98/5.27 ~ ( ord_less_nat @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(1)
% 4.98/5.27 thf(fact_2766_verit__comp__simplify1_I1_J,axiom,
% 4.98/5.27 ! [A: int] :
% 4.98/5.27 ~ ( ord_less_int @ A @ A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(1)
% 4.98/5.27 thf(fact_2767_verit__la__generic,axiom,
% 4.98/5.27 ! [A: int,X2: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ A @ X2 )
% 4.98/5.27 | ( A = X2 )
% 4.98/5.27 | ( ord_less_eq_int @ X2 @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_la_generic
% 4.98/5.27 thf(fact_2768_mod__pos__neg__trivial,axiom,
% 4.98/5.27 ! [K: int,L: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ K )
% 4.98/5.27 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 4.98/5.27 => ( ( modulo_modulo_int @ K @ L )
% 4.98/5.27 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % mod_pos_neg_trivial
% 4.98/5.27 thf(fact_2769_verit__le__mono__div__int,axiom,
% 4.98/5.27 ! [A3: int,B4: int,N2: int] :
% 4.98/5.27 ( ( ord_less_int @ A3 @ B4 )
% 4.98/5.27 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 4.98/5.27 => ( ord_less_eq_int
% 4.98/5.27 @ ( plus_plus_int @ ( divide_divide_int @ A3 @ N2 )
% 4.98/5.27 @ ( if_int
% 4.98/5.27 @ ( ( modulo_modulo_int @ B4 @ N2 )
% 4.98/5.27 = zero_zero_int )
% 4.98/5.27 @ one_one_int
% 4.98/5.27 @ zero_zero_int ) )
% 4.98/5.27 @ ( divide_divide_int @ B4 @ N2 ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_le_mono_div_int
% 4.98/5.27 thf(fact_2770_split__zmod,axiom,
% 4.98/5.27 ! [P: int > $o,N2: int,K: int] :
% 4.98/5.27 ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 4.98/5.27 = ( ( ( K = zero_zero_int )
% 4.98/5.27 => ( P @ N2 ) )
% 4.98/5.27 & ( ( ord_less_int @ zero_zero_int @ K )
% 4.98/5.27 => ! [I5: int,J3: int] :
% 4.98/5.27 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.98/5.27 & ( ord_less_int @ J3 @ K )
% 4.98/5.27 & ( N2
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 4.98/5.27 => ( P @ J3 ) ) )
% 4.98/5.27 & ( ( ord_less_int @ K @ zero_zero_int )
% 4.98/5.27 => ! [I5: int,J3: int] :
% 4.98/5.27 ( ( ( ord_less_int @ K @ J3 )
% 4.98/5.27 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.98/5.27 & ( N2
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 4.98/5.27 => ( P @ J3 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % split_zmod
% 4.98/5.27 thf(fact_2771_int__mod__neg__eq,axiom,
% 4.98/5.27 ! [A: int,B: int,Q2: int,R2: int] :
% 4.98/5.27 ( ( A
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 4.98/5.27 => ( ( ord_less_eq_int @ R2 @ zero_zero_int )
% 4.98/5.27 => ( ( ord_less_int @ B @ R2 )
% 4.98/5.27 => ( ( modulo_modulo_int @ A @ B )
% 4.98/5.27 = R2 ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % int_mod_neg_eq
% 4.98/5.27 thf(fact_2772_int__mod__pos__eq,axiom,
% 4.98/5.27 ! [A: int,B: int,Q2: int,R2: int] :
% 4.98/5.27 ( ( A
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R2 ) )
% 4.98/5.27 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.98/5.27 => ( ( ord_less_int @ R2 @ B )
% 4.98/5.27 => ( ( modulo_modulo_int @ A @ B )
% 4.98/5.27 = R2 ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % int_mod_pos_eq
% 4.98/5.27 thf(fact_2773_zmod__zmult2__eq,axiom,
% 4.98/5.27 ! [C: int,A: int,B: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 4.98/5.27 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % zmod_zmult2_eq
% 4.98/5.27 thf(fact_2774_split__neg__lemma,axiom,
% 4.98/5.27 ! [K: int,P: int > int > $o,N2: int] :
% 4.98/5.27 ( ( ord_less_int @ K @ zero_zero_int )
% 4.98/5.27 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 4.98/5.27 = ( ! [I5: int,J3: int] :
% 4.98/5.27 ( ( ( ord_less_int @ K @ J3 )
% 4.98/5.27 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 4.98/5.27 & ( N2
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 4.98/5.27 => ( P @ I5 @ J3 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % split_neg_lemma
% 4.98/5.27 thf(fact_2775_split__pos__lemma,axiom,
% 4.98/5.27 ! [K: int,P: int > int > $o,N2: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ K )
% 4.98/5.27 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 4.98/5.27 = ( ! [I5: int,J3: int] :
% 4.98/5.27 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 4.98/5.27 & ( ord_less_int @ J3 @ K )
% 4.98/5.27 & ( N2
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 4.98/5.27 => ( P @ I5 @ J3 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % split_pos_lemma
% 4.98/5.27 thf(fact_2776_verit__comp__simplify1_I3_J,axiom,
% 4.98/5.27 ! [B2: real,A2: real] :
% 4.98/5.27 ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 4.98/5.27 = ( ord_less_real @ A2 @ B2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(3)
% 4.98/5.27 thf(fact_2777_verit__comp__simplify1_I3_J,axiom,
% 4.98/5.27 ! [B2: rat,A2: rat] :
% 4.98/5.27 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 4.98/5.27 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(3)
% 4.98/5.27 thf(fact_2778_verit__comp__simplify1_I3_J,axiom,
% 4.98/5.27 ! [B2: num,A2: num] :
% 4.98/5.27 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 4.98/5.27 = ( ord_less_num @ A2 @ B2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(3)
% 4.98/5.27 thf(fact_2779_verit__comp__simplify1_I3_J,axiom,
% 4.98/5.27 ! [B2: nat,A2: nat] :
% 4.98/5.27 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 4.98/5.27 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(3)
% 4.98/5.27 thf(fact_2780_verit__comp__simplify1_I3_J,axiom,
% 4.98/5.27 ! [B2: int,A2: int] :
% 4.98/5.27 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 4.98/5.27 = ( ord_less_int @ A2 @ B2 ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_comp_simplify1(3)
% 4.98/5.27 thf(fact_2781_verit__sum__simplify,axiom,
% 4.98/5.27 ! [A: complex] :
% 4.98/5.27 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_sum_simplify
% 4.98/5.27 thf(fact_2782_verit__sum__simplify,axiom,
% 4.98/5.27 ! [A: real] :
% 4.98/5.27 ( ( plus_plus_real @ A @ zero_zero_real )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_sum_simplify
% 4.98/5.27 thf(fact_2783_verit__sum__simplify,axiom,
% 4.98/5.27 ! [A: rat] :
% 4.98/5.27 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_sum_simplify
% 4.98/5.27 thf(fact_2784_verit__sum__simplify,axiom,
% 4.98/5.27 ! [A: nat] :
% 4.98/5.27 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_sum_simplify
% 4.98/5.27 thf(fact_2785_verit__sum__simplify,axiom,
% 4.98/5.27 ! [A: int] :
% 4.98/5.27 ( ( plus_plus_int @ A @ zero_zero_int )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % verit_sum_simplify
% 4.98/5.27 thf(fact_2786_verit__eq__simplify_I10_J,axiom,
% 4.98/5.27 ! [X22: num] :
% 4.98/5.27 ( one
% 4.98/5.27 != ( bit0 @ X22 ) ) ).
% 4.98/5.27
% 4.98/5.27 % verit_eq_simplify(10)
% 4.98/5.27 thf(fact_2787_Euclid__induct,axiom,
% 4.98/5.27 ! [P: nat > nat > $o,A: nat,B: nat] :
% 4.98/5.27 ( ! [A4: nat,B3: nat] :
% 4.98/5.27 ( ( P @ A4 @ B3 )
% 4.98/5.27 = ( P @ B3 @ A4 ) )
% 4.98/5.27 => ( ! [A4: nat] : ( P @ A4 @ zero_zero_nat )
% 4.98/5.27 => ( ! [A4: nat,B3: nat] :
% 4.98/5.27 ( ( P @ A4 @ B3 )
% 4.98/5.27 => ( P @ A4 @ ( plus_plus_nat @ A4 @ B3 ) ) )
% 4.98/5.27 => ( P @ A @ B ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % Euclid_induct
% 4.98/5.27 thf(fact_2788_eucl__rel__int__iff,axiom,
% 4.98/5.27 ! [K: int,L: int,Q2: int,R2: int] :
% 4.98/5.27 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 4.98/5.27 = ( ( K
% 4.98/5.27 = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R2 ) )
% 4.98/5.27 & ( ( ord_less_int @ zero_zero_int @ L )
% 4.98/5.27 => ( ( ord_less_eq_int @ zero_zero_int @ R2 )
% 4.98/5.27 & ( ord_less_int @ R2 @ L ) ) )
% 4.98/5.27 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 4.98/5.27 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 4.98/5.27 => ( ( ord_less_int @ L @ R2 )
% 4.98/5.27 & ( ord_less_eq_int @ R2 @ zero_zero_int ) ) )
% 4.98/5.27 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 4.98/5.27 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % eucl_rel_int_iff
% 4.98/5.27 thf(fact_2789_pos__zmod__mult__2,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 4.98/5.27 => ( ( 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 ) )
% 4.98/5.27 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % pos_zmod_mult_2
% 4.98/5.27 thf(fact_2790_option_Osize__gen_I1_J,axiom,
% 4.98/5.27 ! [X2: product_prod_nat_nat > nat] :
% 4.98/5.27 ( ( size_o8335143837870341156at_nat @ X2 @ none_P5556105721700978146at_nat )
% 4.98/5.27 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % option.size_gen(1)
% 4.98/5.27 thf(fact_2791_option_Osize__gen_I1_J,axiom,
% 4.98/5.27 ! [X2: num > nat] :
% 4.98/5.27 ( ( size_option_num @ X2 @ none_num )
% 4.98/5.27 = ( suc @ zero_zero_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % option.size_gen(1)
% 4.98/5.27 thf(fact_2792_neg__eucl__rel__int__mult__2,axiom,
% 4.98/5.27 ! [B: int,A: int,Q2: int,R2: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 4.98/5.27 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 4.98/5.27 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R2 ) @ one_one_int ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % neg_eucl_rel_int_mult_2
% 4.98/5.27 thf(fact_2793_even__succ__mod__exp,axiom,
% 4.98/5.27 ! [A: code_integer,N2: nat] :
% 4.98/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.27 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % even_succ_mod_exp
% 4.98/5.27 thf(fact_2794_even__succ__mod__exp,axiom,
% 4.98/5.27 ! [A: nat,N2: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.27 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % even_succ_mod_exp
% 4.98/5.27 thf(fact_2795_even__succ__mod__exp,axiom,
% 4.98/5.27 ! [A: int,N2: nat] :
% 4.98/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.27 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % even_succ_mod_exp
% 4.98/5.27 thf(fact_2796_even__succ__div__exp,axiom,
% 4.98/5.27 ! [A: code_integer,N2: nat] :
% 4.98/5.27 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.27 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % even_succ_div_exp
% 4.98/5.27 thf(fact_2797_even__succ__div__exp,axiom,
% 4.98/5.27 ! [A: nat,N2: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.27 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % even_succ_div_exp
% 4.98/5.27 thf(fact_2798_even__succ__div__exp,axiom,
% 4.98/5.27 ! [A: int,N2: nat] :
% 4.98/5.27 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.27 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.27 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 4.98/5.27 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % even_succ_div_exp
% 4.98/5.27 thf(fact_2799_signed__take__bit__Suc,axiom,
% 4.98/5.27 ! [N2: nat,A: int] :
% 4.98/5.27 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 4.98/5.27 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % signed_take_bit_Suc
% 4.98/5.27 thf(fact_2800_vebt__insert_Oelims,axiom,
% 4.98/5.27 ! [X2: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 4.98/5.27 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 4.98/5.27 = Y )
% 4.98/5.27 => ( ! [A4: $o,B3: $o] :
% 4.98/5.27 ( ( X2
% 4.98/5.27 = ( vEBT_Leaf @ A4 @ B3 ) )
% 4.98/5.27 => ~ ( ( ( Xa2 = zero_zero_nat )
% 4.98/5.27 => ( Y
% 4.98/5.27 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 4.98/5.27 & ( ( Xa2 != zero_zero_nat )
% 4.98/5.27 => ( ( ( Xa2 = one_one_nat )
% 4.98/5.27 => ( Y
% 4.98/5.27 = ( vEBT_Leaf @ A4 @ $true ) ) )
% 4.98/5.27 & ( ( Xa2 != one_one_nat )
% 4.98/5.27 => ( Y
% 4.98/5.27 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ) ) )
% 4.98/5.27 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 4.98/5.27 ( ( X2
% 4.98/5.27 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 4.98/5.27 => ( Y
% 4.98/5.27 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) ) )
% 4.98/5.27 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 4.98/5.27 ( ( X2
% 4.98/5.27 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 4.98/5.27 => ( Y
% 4.98/5.27 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) ) )
% 4.98/5.27 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.98/5.27 ( ( X2
% 4.98/5.27 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 4.98/5.27 => ( Y
% 4.98/5.27 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) ) )
% 4.98/5.27 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 4.98/5.27 ( ( X2
% 4.98/5.27 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 4.98/5.27 => ( Y
% 4.98/5.27 != ( if_VEBT_VEBT
% 4.98/5.27 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 4.98/5.27 & ~ ( ( Xa2 = Mi2 )
% 4.98/5.27 | ( Xa2 = Ma2 ) ) )
% 4.98/5.27 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 4.98/5.27 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % vebt_insert.elims
% 4.98/5.27 thf(fact_2801_add__scale__eq__noteq,axiom,
% 4.98/5.27 ! [R2: complex,A: complex,B: complex,C: complex,D: complex] :
% 4.98/5.27 ( ( R2 != zero_zero_complex )
% 4.98/5.27 => ( ( ( A = B )
% 4.98/5.27 & ( C != D ) )
% 4.98/5.27 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R2 @ C ) )
% 4.98/5.27 != ( plus_plus_complex @ B @ ( times_times_complex @ R2 @ D ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_scale_eq_noteq
% 4.98/5.27 thf(fact_2802_add__scale__eq__noteq,axiom,
% 4.98/5.27 ! [R2: real,A: real,B: real,C: real,D: real] :
% 4.98/5.27 ( ( R2 != zero_zero_real )
% 4.98/5.27 => ( ( ( A = B )
% 4.98/5.27 & ( C != D ) )
% 4.98/5.27 => ( ( plus_plus_real @ A @ ( times_times_real @ R2 @ C ) )
% 4.98/5.27 != ( plus_plus_real @ B @ ( times_times_real @ R2 @ D ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_scale_eq_noteq
% 4.98/5.27 thf(fact_2803_add__scale__eq__noteq,axiom,
% 4.98/5.27 ! [R2: rat,A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.27 ( ( R2 != zero_zero_rat )
% 4.98/5.27 => ( ( ( A = B )
% 4.98/5.27 & ( C != D ) )
% 4.98/5.27 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R2 @ C ) )
% 4.98/5.27 != ( plus_plus_rat @ B @ ( times_times_rat @ R2 @ D ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_scale_eq_noteq
% 4.98/5.27 thf(fact_2804_add__scale__eq__noteq,axiom,
% 4.98/5.27 ! [R2: nat,A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.27 ( ( R2 != zero_zero_nat )
% 4.98/5.27 => ( ( ( A = B )
% 4.98/5.27 & ( C != D ) )
% 4.98/5.27 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R2 @ C ) )
% 4.98/5.27 != ( plus_plus_nat @ B @ ( times_times_nat @ R2 @ D ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_scale_eq_noteq
% 4.98/5.27 thf(fact_2805_add__scale__eq__noteq,axiom,
% 4.98/5.27 ! [R2: int,A: int,B: int,C: int,D: int] :
% 4.98/5.27 ( ( R2 != zero_zero_int )
% 4.98/5.27 => ( ( ( A = B )
% 4.98/5.27 & ( C != D ) )
% 4.98/5.27 => ( ( plus_plus_int @ A @ ( times_times_int @ R2 @ C ) )
% 4.98/5.27 != ( plus_plus_int @ B @ ( times_times_int @ R2 @ D ) ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_scale_eq_noteq
% 4.98/5.27 thf(fact_2806_num_Osize__gen_I2_J,axiom,
% 4.98/5.27 ! [X22: num] :
% 4.98/5.27 ( ( size_num @ ( bit0 @ X22 ) )
% 4.98/5.27 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % num.size_gen(2)
% 4.98/5.27 thf(fact_2807_power__numeral,axiom,
% 4.98/5.27 ! [K: num,L: num] :
% 4.98/5.27 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 4.98/5.27 = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % power_numeral
% 4.98/5.27 thf(fact_2808_power__numeral,axiom,
% 4.98/5.27 ! [K: num,L: num] :
% 4.98/5.27 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 4.98/5.27 = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % power_numeral
% 4.98/5.27 thf(fact_2809_power__numeral,axiom,
% 4.98/5.27 ! [K: num,L: num] :
% 4.98/5.27 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L ) )
% 4.98/5.27 = ( numeral_numeral_rat @ ( pow @ K @ L ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % power_numeral
% 4.98/5.27 thf(fact_2810_power__numeral,axiom,
% 4.98/5.27 ! [K: num,L: num] :
% 4.98/5.27 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 4.98/5.27 = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % power_numeral
% 4.98/5.27 thf(fact_2811_power__numeral,axiom,
% 4.98/5.27 ! [K: num,L: num] :
% 4.98/5.27 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 4.98/5.27 = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % power_numeral
% 4.98/5.27 thf(fact_2812_buildup__gives__empty,axiom,
% 4.98/5.27 ! [N2: nat] :
% 4.98/5.27 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N2 ) )
% 4.98/5.27 = bot_bot_set_nat ) ).
% 4.98/5.27
% 4.98/5.27 % buildup_gives_empty
% 4.98/5.27 thf(fact_2813_set__vebt_H__def,axiom,
% 4.98/5.27 ( vEBT_VEBT_set_vebt
% 4.98/5.27 = ( ^ [T: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % set_vebt'_def
% 4.98/5.27 thf(fact_2814_nat__dvd__1__iff__1,axiom,
% 4.98/5.27 ! [M: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 4.98/5.27 = ( M = one_one_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % nat_dvd_1_iff_1
% 4.98/5.27 thf(fact_2815_diff__self,axiom,
% 4.98/5.27 ! [A: complex] :
% 4.98/5.27 ( ( minus_minus_complex @ A @ A )
% 4.98/5.27 = zero_zero_complex ) ).
% 4.98/5.27
% 4.98/5.27 % diff_self
% 4.98/5.27 thf(fact_2816_diff__self,axiom,
% 4.98/5.27 ! [A: real] :
% 4.98/5.27 ( ( minus_minus_real @ A @ A )
% 4.98/5.27 = zero_zero_real ) ).
% 4.98/5.27
% 4.98/5.27 % diff_self
% 4.98/5.27 thf(fact_2817_diff__self,axiom,
% 4.98/5.27 ! [A: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ A @ A )
% 4.98/5.27 = zero_zero_rat ) ).
% 4.98/5.27
% 4.98/5.27 % diff_self
% 4.98/5.27 thf(fact_2818_diff__self,axiom,
% 4.98/5.27 ! [A: int] :
% 4.98/5.27 ( ( minus_minus_int @ A @ A )
% 4.98/5.27 = zero_zero_int ) ).
% 4.98/5.27
% 4.98/5.27 % diff_self
% 4.98/5.27 thf(fact_2819_diff__0__right,axiom,
% 4.98/5.27 ! [A: complex] :
% 4.98/5.27 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_0_right
% 4.98/5.27 thf(fact_2820_diff__0__right,axiom,
% 4.98/5.27 ! [A: real] :
% 4.98/5.27 ( ( minus_minus_real @ A @ zero_zero_real )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_0_right
% 4.98/5.27 thf(fact_2821_diff__0__right,axiom,
% 4.98/5.27 ! [A: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_0_right
% 4.98/5.27 thf(fact_2822_diff__0__right,axiom,
% 4.98/5.27 ! [A: int] :
% 4.98/5.27 ( ( minus_minus_int @ A @ zero_zero_int )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_0_right
% 4.98/5.27 thf(fact_2823_zero__diff,axiom,
% 4.98/5.27 ! [A: nat] :
% 4.98/5.27 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 4.98/5.27 = zero_zero_nat ) ).
% 4.98/5.27
% 4.98/5.27 % zero_diff
% 4.98/5.27 thf(fact_2824_diff__zero,axiom,
% 4.98/5.27 ! [A: complex] :
% 4.98/5.27 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_zero
% 4.98/5.27 thf(fact_2825_diff__zero,axiom,
% 4.98/5.27 ! [A: real] :
% 4.98/5.27 ( ( minus_minus_real @ A @ zero_zero_real )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_zero
% 4.98/5.27 thf(fact_2826_diff__zero,axiom,
% 4.98/5.27 ! [A: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_zero
% 4.98/5.27 thf(fact_2827_diff__zero,axiom,
% 4.98/5.27 ! [A: nat] :
% 4.98/5.27 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_zero
% 4.98/5.27 thf(fact_2828_diff__zero,axiom,
% 4.98/5.27 ! [A: int] :
% 4.98/5.27 ( ( minus_minus_int @ A @ zero_zero_int )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_zero
% 4.98/5.27 thf(fact_2829_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.98/5.27 ! [A: complex] :
% 4.98/5.27 ( ( minus_minus_complex @ A @ A )
% 4.98/5.27 = zero_zero_complex ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_comm_monoid_add_class.diff_cancel
% 4.98/5.27 thf(fact_2830_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.98/5.27 ! [A: real] :
% 4.98/5.27 ( ( minus_minus_real @ A @ A )
% 4.98/5.27 = zero_zero_real ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_comm_monoid_add_class.diff_cancel
% 4.98/5.27 thf(fact_2831_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.98/5.27 ! [A: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ A @ A )
% 4.98/5.27 = zero_zero_rat ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_comm_monoid_add_class.diff_cancel
% 4.98/5.27 thf(fact_2832_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.98/5.27 ! [A: nat] :
% 4.98/5.27 ( ( minus_minus_nat @ A @ A )
% 4.98/5.27 = zero_zero_nat ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_comm_monoid_add_class.diff_cancel
% 4.98/5.27 thf(fact_2833_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 4.98/5.27 ! [A: int] :
% 4.98/5.27 ( ( minus_minus_int @ A @ A )
% 4.98/5.27 = zero_zero_int ) ).
% 4.98/5.27
% 4.98/5.27 % cancel_comm_monoid_add_class.diff_cancel
% 4.98/5.27 thf(fact_2834_add__diff__cancel,axiom,
% 4.98/5.27 ! [A: real,B: real] :
% 4.98/5.27 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel
% 4.98/5.27 thf(fact_2835_add__diff__cancel,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel
% 4.98/5.27 thf(fact_2836_add__diff__cancel,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel
% 4.98/5.27 thf(fact_2837_diff__add__cancel,axiom,
% 4.98/5.27 ! [A: real,B: real] :
% 4.98/5.27 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_add_cancel
% 4.98/5.27 thf(fact_2838_diff__add__cancel,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_add_cancel
% 4.98/5.27 thf(fact_2839_diff__add__cancel,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % diff_add_cancel
% 4.98/5.27 thf(fact_2840_add__diff__cancel__left,axiom,
% 4.98/5.27 ! [C: real,A: real,B: real] :
% 4.98/5.27 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 4.98/5.27 = ( minus_minus_real @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_left
% 4.98/5.27 thf(fact_2841_add__diff__cancel__left,axiom,
% 4.98/5.27 ! [C: rat,A: rat,B: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 4.98/5.27 = ( minus_minus_rat @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_left
% 4.98/5.27 thf(fact_2842_add__diff__cancel__left,axiom,
% 4.98/5.27 ! [C: nat,A: nat,B: nat] :
% 4.98/5.27 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 4.98/5.27 = ( minus_minus_nat @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_left
% 4.98/5.27 thf(fact_2843_add__diff__cancel__left,axiom,
% 4.98/5.27 ! [C: int,A: int,B: int] :
% 4.98/5.27 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 4.98/5.27 = ( minus_minus_int @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_left
% 4.98/5.27 thf(fact_2844_add__diff__cancel__left_H,axiom,
% 4.98/5.27 ! [A: real,B: real] :
% 4.98/5.27 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 4.98/5.27 = B ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_left'
% 4.98/5.27 thf(fact_2845_add__diff__cancel__left_H,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 4.98/5.27 = B ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_left'
% 4.98/5.27 thf(fact_2846_add__diff__cancel__left_H,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 4.98/5.27 = B ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_left'
% 4.98/5.27 thf(fact_2847_add__diff__cancel__left_H,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 4.98/5.27 = B ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_left'
% 4.98/5.27 thf(fact_2848_add__diff__cancel__right,axiom,
% 4.98/5.27 ! [A: real,C: real,B: real] :
% 4.98/5.27 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 4.98/5.27 = ( minus_minus_real @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_right
% 4.98/5.27 thf(fact_2849_add__diff__cancel__right,axiom,
% 4.98/5.27 ! [A: rat,C: rat,B: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.27 = ( minus_minus_rat @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_right
% 4.98/5.27 thf(fact_2850_add__diff__cancel__right,axiom,
% 4.98/5.27 ! [A: nat,C: nat,B: nat] :
% 4.98/5.27 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.27 = ( minus_minus_nat @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_right
% 4.98/5.27 thf(fact_2851_add__diff__cancel__right,axiom,
% 4.98/5.27 ! [A: int,C: int,B: int] :
% 4.98/5.27 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 4.98/5.27 = ( minus_minus_int @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_right
% 4.98/5.27 thf(fact_2852_add__diff__cancel__right_H,axiom,
% 4.98/5.27 ! [A: real,B: real] :
% 4.98/5.27 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_right'
% 4.98/5.27 thf(fact_2853_add__diff__cancel__right_H,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_right'
% 4.98/5.27 thf(fact_2854_add__diff__cancel__right_H,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_right'
% 4.98/5.27 thf(fact_2855_add__diff__cancel__right_H,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 4.98/5.27 = A ) ).
% 4.98/5.27
% 4.98/5.27 % add_diff_cancel_right'
% 4.98/5.27 thf(fact_2856_dvd__0__right,axiom,
% 4.98/5.27 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_right
% 4.98/5.27 thf(fact_2857_dvd__0__right,axiom,
% 4.98/5.27 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_right
% 4.98/5.27 thf(fact_2858_dvd__0__right,axiom,
% 4.98/5.27 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_right
% 4.98/5.27 thf(fact_2859_dvd__0__right,axiom,
% 4.98/5.27 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_right
% 4.98/5.27 thf(fact_2860_dvd__0__right,axiom,
% 4.98/5.27 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_right
% 4.98/5.27 thf(fact_2861_dvd__0__right,axiom,
% 4.98/5.27 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_right
% 4.98/5.27 thf(fact_2862_dvd__0__left__iff,axiom,
% 4.98/5.27 ! [A: code_integer] :
% 4.98/5.27 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 4.98/5.27 = ( A = zero_z3403309356797280102nteger ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_left_iff
% 4.98/5.27 thf(fact_2863_dvd__0__left__iff,axiom,
% 4.98/5.27 ! [A: complex] :
% 4.98/5.27 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 4.98/5.27 = ( A = zero_zero_complex ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_left_iff
% 4.98/5.27 thf(fact_2864_dvd__0__left__iff,axiom,
% 4.98/5.27 ! [A: real] :
% 4.98/5.27 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 4.98/5.27 = ( A = zero_zero_real ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_left_iff
% 4.98/5.27 thf(fact_2865_dvd__0__left__iff,axiom,
% 4.98/5.27 ! [A: rat] :
% 4.98/5.27 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 4.98/5.27 = ( A = zero_zero_rat ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_left_iff
% 4.98/5.27 thf(fact_2866_dvd__0__left__iff,axiom,
% 4.98/5.27 ! [A: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 4.98/5.27 = ( A = zero_zero_nat ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_left_iff
% 4.98/5.27 thf(fact_2867_dvd__0__left__iff,axiom,
% 4.98/5.27 ! [A: int] :
% 4.98/5.27 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 4.98/5.27 = ( A = zero_zero_int ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_0_left_iff
% 4.98/5.27 thf(fact_2868_dvd__add__triv__left__iff,axiom,
% 4.98/5.27 ! [A: code_integer,B: code_integer] :
% 4.98/5.27 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 4.98/5.27 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_left_iff
% 4.98/5.27 thf(fact_2869_dvd__add__triv__left__iff,axiom,
% 4.98/5.27 ! [A: real,B: real] :
% 4.98/5.27 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 4.98/5.27 = ( dvd_dvd_real @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_left_iff
% 4.98/5.27 thf(fact_2870_dvd__add__triv__left__iff,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 4.98/5.27 = ( dvd_dvd_rat @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_left_iff
% 4.98/5.27 thf(fact_2871_dvd__add__triv__left__iff,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.98/5.27 = ( dvd_dvd_nat @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_left_iff
% 4.98/5.27 thf(fact_2872_dvd__add__triv__left__iff,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 4.98/5.27 = ( dvd_dvd_int @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_left_iff
% 4.98/5.27 thf(fact_2873_dvd__add__triv__right__iff,axiom,
% 4.98/5.27 ! [A: code_integer,B: code_integer] :
% 4.98/5.27 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 4.98/5.27 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_right_iff
% 4.98/5.27 thf(fact_2874_dvd__add__triv__right__iff,axiom,
% 4.98/5.27 ! [A: real,B: real] :
% 4.98/5.27 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 4.98/5.27 = ( dvd_dvd_real @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_right_iff
% 4.98/5.27 thf(fact_2875_dvd__add__triv__right__iff,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 4.98/5.27 = ( dvd_dvd_rat @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_right_iff
% 4.98/5.27 thf(fact_2876_dvd__add__triv__right__iff,axiom,
% 4.98/5.27 ! [A: nat,B: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 4.98/5.27 = ( dvd_dvd_nat @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_right_iff
% 4.98/5.27 thf(fact_2877_dvd__add__triv__right__iff,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 4.98/5.27 = ( dvd_dvd_int @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_add_triv_right_iff
% 4.98/5.27 thf(fact_2878_dvd__1__left,axiom,
% 4.98/5.27 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_1_left
% 4.98/5.27 thf(fact_2879_dvd__1__iff__1,axiom,
% 4.98/5.27 ! [M: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 4.98/5.27 = ( M
% 4.98/5.27 = ( suc @ zero_zero_nat ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % dvd_1_iff_1
% 4.98/5.27 thf(fact_2880_div__dvd__div,axiom,
% 4.98/5.27 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.27 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.27 => ( ( dvd_dvd_Code_integer @ A @ C )
% 4.98/5.27 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 4.98/5.27 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_dvd_div
% 4.98/5.27 thf(fact_2881_div__dvd__div,axiom,
% 4.98/5.27 ! [A: nat,B: nat,C: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.27 => ( ( dvd_dvd_nat @ A @ C )
% 4.98/5.27 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 4.98/5.27 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_dvd_div
% 4.98/5.27 thf(fact_2882_div__dvd__div,axiom,
% 4.98/5.27 ! [A: int,B: int,C: int] :
% 4.98/5.27 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.27 => ( ( dvd_dvd_int @ A @ C )
% 4.98/5.27 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 4.98/5.27 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % div_dvd_div
% 4.98/5.27 thf(fact_2883_minus__mod__self2,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 4.98/5.27 = ( modulo_modulo_int @ A @ B ) ) ).
% 4.98/5.27
% 4.98/5.27 % minus_mod_self2
% 4.98/5.27 thf(fact_2884_nat__mult__dvd__cancel__disj,axiom,
% 4.98/5.27 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.27 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 4.98/5.27 = ( ( K = zero_zero_nat )
% 4.98/5.27 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 4.98/5.27
% 4.98/5.27 % nat_mult_dvd_cancel_disj
% 4.98/5.27 thf(fact_2885_signed__take__bit__of__0,axiom,
% 4.98/5.27 ! [N2: nat] :
% 4.98/5.27 ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 4.98/5.27 = zero_zero_int ) ).
% 4.98/5.27
% 4.98/5.27 % signed_take_bit_of_0
% 4.98/5.27 thf(fact_2886_diff__ge__0__iff__ge,axiom,
% 4.98/5.27 ! [A: real,B: real] :
% 4.98/5.27 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 4.98/5.27 = ( ord_less_eq_real @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % diff_ge_0_iff_ge
% 4.98/5.27 thf(fact_2887_diff__ge__0__iff__ge,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 4.98/5.27 = ( ord_less_eq_rat @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % diff_ge_0_iff_ge
% 4.98/5.27 thf(fact_2888_diff__ge__0__iff__ge,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 4.98/5.27 = ( ord_less_eq_int @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % diff_ge_0_iff_ge
% 4.98/5.27 thf(fact_2889_diff__gt__0__iff__gt,axiom,
% 4.98/5.27 ! [A: real,B: real] :
% 4.98/5.27 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 4.98/5.27 = ( ord_less_real @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % diff_gt_0_iff_gt
% 4.98/5.27 thf(fact_2890_diff__gt__0__iff__gt,axiom,
% 4.98/5.27 ! [A: rat,B: rat] :
% 4.98/5.27 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 4.98/5.27 = ( ord_less_rat @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % diff_gt_0_iff_gt
% 4.98/5.27 thf(fact_2891_diff__gt__0__iff__gt,axiom,
% 4.98/5.27 ! [A: int,B: int] :
% 4.98/5.27 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 4.98/5.27 = ( ord_less_int @ B @ A ) ) ).
% 4.98/5.27
% 4.98/5.27 % diff_gt_0_iff_gt
% 4.98/5.27 thf(fact_2892_le__add__diff__inverse,axiom,
% 4.98/5.27 ! [B: real,A: real] :
% 4.98/5.27 ( ( ord_less_eq_real @ B @ A )
% 4.98/5.27 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 4.98/5.27 = A ) ) ).
% 4.98/5.27
% 4.98/5.27 % le_add_diff_inverse
% 4.98/5.27 thf(fact_2893_le__add__diff__inverse,axiom,
% 4.98/5.27 ! [B: rat,A: rat] :
% 4.98/5.27 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.27 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 4.98/5.27 = A ) ) ).
% 4.98/5.27
% 4.98/5.27 % le_add_diff_inverse
% 4.98/5.27 thf(fact_2894_le__add__diff__inverse,axiom,
% 4.98/5.27 ! [B: nat,A: nat] :
% 4.98/5.27 ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.27 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 4.98/5.27 = A ) ) ).
% 4.98/5.27
% 4.98/5.27 % le_add_diff_inverse
% 4.98/5.27 thf(fact_2895_le__add__diff__inverse,axiom,
% 4.98/5.27 ! [B: int,A: int] :
% 4.98/5.27 ( ( ord_less_eq_int @ B @ A )
% 4.98/5.27 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 4.98/5.27 = A ) ) ).
% 4.98/5.27
% 4.98/5.27 % le_add_diff_inverse
% 4.98/5.27 thf(fact_2896_le__add__diff__inverse2,axiom,
% 4.98/5.27 ! [B: real,A: real] :
% 4.98/5.27 ( ( ord_less_eq_real @ B @ A )
% 4.98/5.27 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 4.98/5.27 = A ) ) ).
% 4.98/5.27
% 4.98/5.27 % le_add_diff_inverse2
% 4.98/5.27 thf(fact_2897_le__add__diff__inverse2,axiom,
% 4.98/5.27 ! [B: rat,A: rat] :
% 4.98/5.27 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.27 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 4.98/5.27 = A ) ) ).
% 4.98/5.27
% 4.98/5.27 % le_add_diff_inverse2
% 4.98/5.27 thf(fact_2898_le__add__diff__inverse2,axiom,
% 4.98/5.27 ! [B: nat,A: nat] :
% 4.98/5.28 ( ( ord_less_eq_nat @ B @ A )
% 4.98/5.28 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 4.98/5.28 = A ) ) ).
% 4.98/5.28
% 4.98/5.28 % le_add_diff_inverse2
% 4.98/5.28 thf(fact_2899_le__add__diff__inverse2,axiom,
% 4.98/5.28 ! [B: int,A: int] :
% 4.98/5.28 ( ( ord_less_eq_int @ B @ A )
% 4.98/5.28 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 4.98/5.28 = A ) ) ).
% 4.98/5.28
% 4.98/5.28 % le_add_diff_inverse2
% 4.98/5.28 thf(fact_2900_diff__numeral__special_I9_J,axiom,
% 4.98/5.28 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 4.98/5.28 = zero_zero_complex ) ).
% 4.98/5.28
% 4.98/5.28 % diff_numeral_special(9)
% 4.98/5.28 thf(fact_2901_diff__numeral__special_I9_J,axiom,
% 4.98/5.28 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 4.98/5.28 = zero_zero_real ) ).
% 4.98/5.28
% 4.98/5.28 % diff_numeral_special(9)
% 4.98/5.28 thf(fact_2902_diff__numeral__special_I9_J,axiom,
% 4.98/5.28 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 4.98/5.28 = zero_zero_rat ) ).
% 4.98/5.28
% 4.98/5.28 % diff_numeral_special(9)
% 4.98/5.28 thf(fact_2903_diff__numeral__special_I9_J,axiom,
% 4.98/5.28 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 4.98/5.28 = zero_zero_int ) ).
% 4.98/5.28
% 4.98/5.28 % diff_numeral_special(9)
% 4.98/5.28 thf(fact_2904_diff__add__zero,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 4.98/5.28 = zero_zero_nat ) ).
% 4.98/5.28
% 4.98/5.28 % diff_add_zero
% 4.98/5.28 thf(fact_2905_right__diff__distrib__numeral,axiom,
% 4.98/5.28 ! [V: num,B: complex,C: complex] :
% 4.98/5.28 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 4.98/5.28 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib_numeral
% 4.98/5.28 thf(fact_2906_right__diff__distrib__numeral,axiom,
% 4.98/5.28 ! [V: num,B: real,C: real] :
% 4.98/5.28 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 4.98/5.28 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib_numeral
% 4.98/5.28 thf(fact_2907_right__diff__distrib__numeral,axiom,
% 4.98/5.28 ! [V: num,B: rat,C: rat] :
% 4.98/5.28 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 4.98/5.28 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib_numeral
% 4.98/5.28 thf(fact_2908_right__diff__distrib__numeral,axiom,
% 4.98/5.28 ! [V: num,B: int,C: int] :
% 4.98/5.28 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 4.98/5.28 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib_numeral
% 4.98/5.28 thf(fact_2909_left__diff__distrib__numeral,axiom,
% 4.98/5.28 ! [A: complex,B: complex,V: num] :
% 4.98/5.28 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 4.98/5.28 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib_numeral
% 4.98/5.28 thf(fact_2910_left__diff__distrib__numeral,axiom,
% 4.98/5.28 ! [A: real,B: real,V: num] :
% 4.98/5.28 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 4.98/5.28 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib_numeral
% 4.98/5.28 thf(fact_2911_left__diff__distrib__numeral,axiom,
% 4.98/5.28 ! [A: rat,B: rat,V: num] :
% 4.98/5.28 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 4.98/5.28 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib_numeral
% 4.98/5.28 thf(fact_2912_left__diff__distrib__numeral,axiom,
% 4.98/5.28 ! [A: int,B: int,V: num] :
% 4.98/5.28 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 4.98/5.28 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib_numeral
% 4.98/5.28 thf(fact_2913_dvd__mult__cancel__left,axiom,
% 4.98/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.98/5.28 = ( ( C = zero_z3403309356797280102nteger )
% 4.98/5.28 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_left
% 4.98/5.28 thf(fact_2914_dvd__mult__cancel__left,axiom,
% 4.98/5.28 ! [C: complex,A: complex,B: complex] :
% 4.98/5.28 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 4.98/5.28 = ( ( C = zero_zero_complex )
% 4.98/5.28 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_left
% 4.98/5.28 thf(fact_2915_dvd__mult__cancel__left,axiom,
% 4.98/5.28 ! [C: real,A: real,B: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 4.98/5.28 = ( ( C = zero_zero_real )
% 4.98/5.28 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_left
% 4.98/5.28 thf(fact_2916_dvd__mult__cancel__left,axiom,
% 4.98/5.28 ! [C: rat,A: rat,B: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 4.98/5.28 = ( ( C = zero_zero_rat )
% 4.98/5.28 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_left
% 4.98/5.28 thf(fact_2917_dvd__mult__cancel__left,axiom,
% 4.98/5.28 ! [C: int,A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 4.98/5.28 = ( ( C = zero_zero_int )
% 4.98/5.28 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_left
% 4.98/5.28 thf(fact_2918_dvd__mult__cancel__right,axiom,
% 4.98/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.98/5.28 = ( ( C = zero_z3403309356797280102nteger )
% 4.98/5.28 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_right
% 4.98/5.28 thf(fact_2919_dvd__mult__cancel__right,axiom,
% 4.98/5.28 ! [A: complex,C: complex,B: complex] :
% 4.98/5.28 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 4.98/5.28 = ( ( C = zero_zero_complex )
% 4.98/5.28 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_right
% 4.98/5.28 thf(fact_2920_dvd__mult__cancel__right,axiom,
% 4.98/5.28 ! [A: real,C: real,B: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 4.98/5.28 = ( ( C = zero_zero_real )
% 4.98/5.28 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_right
% 4.98/5.28 thf(fact_2921_dvd__mult__cancel__right,axiom,
% 4.98/5.28 ! [A: rat,C: rat,B: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 4.98/5.28 = ( ( C = zero_zero_rat )
% 4.98/5.28 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_right
% 4.98/5.28 thf(fact_2922_dvd__mult__cancel__right,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 4.98/5.28 = ( ( C = zero_zero_int )
% 4.98/5.28 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_cancel_right
% 4.98/5.28 thf(fact_2923_dvd__times__left__cancel__iff,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( A != zero_z3403309356797280102nteger )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_times_left_cancel_iff
% 4.98/5.28 thf(fact_2924_dvd__times__left__cancel__iff,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( A != zero_zero_nat )
% 4.98/5.28 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 4.98/5.28 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_times_left_cancel_iff
% 4.98/5.28 thf(fact_2925_dvd__times__left__cancel__iff,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( A != zero_zero_int )
% 4.98/5.28 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 4.98/5.28 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_times_left_cancel_iff
% 4.98/5.28 thf(fact_2926_dvd__times__right__cancel__iff,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( A != zero_z3403309356797280102nteger )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_times_right_cancel_iff
% 4.98/5.28 thf(fact_2927_dvd__times__right__cancel__iff,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( A != zero_zero_nat )
% 4.98/5.28 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 4.98/5.28 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_times_right_cancel_iff
% 4.98/5.28 thf(fact_2928_dvd__times__right__cancel__iff,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( A != zero_zero_int )
% 4.98/5.28 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 4.98/5.28 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_times_right_cancel_iff
% 4.98/5.28 thf(fact_2929_unit__prod,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_prod
% 4.98/5.28 thf(fact_2930_unit__prod,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.28 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.28 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_prod
% 4.98/5.28 thf(fact_2931_unit__prod,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.28 => ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.28 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_prod
% 4.98/5.28 thf(fact_2932_dvd__add__times__triv__right__iff,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_right_iff
% 4.98/5.28 thf(fact_2933_dvd__add__times__triv__right__iff,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 4.98/5.28 = ( dvd_dvd_real @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_right_iff
% 4.98/5.28 thf(fact_2934_dvd__add__times__triv__right__iff,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 4.98/5.28 = ( dvd_dvd_rat @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_right_iff
% 4.98/5.28 thf(fact_2935_dvd__add__times__triv__right__iff,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 4.98/5.28 = ( dvd_dvd_nat @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_right_iff
% 4.98/5.28 thf(fact_2936_dvd__add__times__triv__right__iff,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 4.98/5.28 = ( dvd_dvd_int @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_right_iff
% 4.98/5.28 thf(fact_2937_dvd__add__times__triv__left__iff,axiom,
% 4.98/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_left_iff
% 4.98/5.28 thf(fact_2938_dvd__add__times__triv__left__iff,axiom,
% 4.98/5.28 ! [A: real,C: real,B: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 4.98/5.28 = ( dvd_dvd_real @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_left_iff
% 4.98/5.28 thf(fact_2939_dvd__add__times__triv__left__iff,axiom,
% 4.98/5.28 ! [A: rat,C: rat,B: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 4.98/5.28 = ( dvd_dvd_rat @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_left_iff
% 4.98/5.28 thf(fact_2940_dvd__add__times__triv__left__iff,axiom,
% 4.98/5.28 ! [A: nat,C: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 4.98/5.28 = ( dvd_dvd_nat @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_left_iff
% 4.98/5.28 thf(fact_2941_dvd__add__times__triv__left__iff,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 4.98/5.28 = ( dvd_dvd_int @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_times_triv_left_iff
% 4.98/5.28 thf(fact_2942_dvd__div__mult__self,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_mult_self
% 4.98/5.28 thf(fact_2943_dvd__div__mult__self,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_mult_self
% 4.98/5.28 thf(fact_2944_dvd__div__mult__self,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_mult_self
% 4.98/5.28 thf(fact_2945_dvd__mult__div__cancel,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_div_cancel
% 4.98/5.28 thf(fact_2946_dvd__mult__div__cancel,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_div_cancel
% 4.98/5.28 thf(fact_2947_dvd__mult__div__cancel,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_div_cancel
% 4.98/5.28 thf(fact_2948_unit__div,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div
% 4.98/5.28 thf(fact_2949_unit__div,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.28 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.28 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div
% 4.98/5.28 thf(fact_2950_unit__div,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.28 => ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.28 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div
% 4.98/5.28 thf(fact_2951_unit__div__1__unit,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_1_unit
% 4.98/5.28 thf(fact_2952_unit__div__1__unit,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.28 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_1_unit
% 4.98/5.28 thf(fact_2953_unit__div__1__unit,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.28 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_1_unit
% 4.98/5.28 thf(fact_2954_unit__div__1__div__1,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.28 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 4.98/5.28 = A ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_1_div_1
% 4.98/5.28 thf(fact_2955_unit__div__1__div__1,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.28 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 4.98/5.28 = A ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_1_div_1
% 4.98/5.28 thf(fact_2956_unit__div__1__div__1,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.28 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 4.98/5.28 = A ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_1_div_1
% 4.98/5.28 thf(fact_2957_div__add,axiom,
% 4.98/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.28 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 4.98/5.28 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % div_add
% 4.98/5.28 thf(fact_2958_div__add,axiom,
% 4.98/5.28 ! [C: nat,A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.28 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.28 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % div_add
% 4.98/5.28 thf(fact_2959_div__add,axiom,
% 4.98/5.28 ! [C: int,A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_int @ C @ B )
% 4.98/5.28 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.28 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % div_add
% 4.98/5.28 thf(fact_2960_div__diff,axiom,
% 4.98/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.28 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 4.98/5.28 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % div_diff
% 4.98/5.28 thf(fact_2961_div__diff,axiom,
% 4.98/5.28 ! [C: int,A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_int @ C @ B )
% 4.98/5.28 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % div_diff
% 4.98/5.28 thf(fact_2962_dvd__imp__mod__0,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( ( modulo364778990260209775nteger @ B @ A )
% 4.98/5.28 = zero_z3403309356797280102nteger ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_imp_mod_0
% 4.98/5.28 thf(fact_2963_dvd__imp__mod__0,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( ( modulo_modulo_nat @ B @ A )
% 4.98/5.28 = zero_zero_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_imp_mod_0
% 4.98/5.28 thf(fact_2964_dvd__imp__mod__0,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( ( modulo_modulo_int @ B @ A )
% 4.98/5.28 = zero_zero_int ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_imp_mod_0
% 4.98/5.28 thf(fact_2965_signed__take__bit__Suc__1,axiom,
% 4.98/5.28 ! [N2: nat] :
% 4.98/5.28 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 4.98/5.28 = one_one_int ) ).
% 4.98/5.28
% 4.98/5.28 % signed_take_bit_Suc_1
% 4.98/5.28 thf(fact_2966_signed__take__bit__numeral__of__1,axiom,
% 4.98/5.28 ! [K: num] :
% 4.98/5.28 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 4.98/5.28 = one_one_int ) ).
% 4.98/5.28
% 4.98/5.28 % signed_take_bit_numeral_of_1
% 4.98/5.28 thf(fact_2967_unit__mult__div__div,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.28 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 4.98/5.28 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_mult_div_div
% 4.98/5.28 thf(fact_2968_unit__mult__div__div,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.28 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 4.98/5.28 = ( divide_divide_nat @ B @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_mult_div_div
% 4.98/5.28 thf(fact_2969_unit__mult__div__div,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.28 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 4.98/5.28 = ( divide_divide_int @ B @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_mult_div_div
% 4.98/5.28 thf(fact_2970_unit__div__mult__self,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.28 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_mult_self
% 4.98/5.28 thf(fact_2971_unit__div__mult__self,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.28 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_mult_self
% 4.98/5.28 thf(fact_2972_unit__div__mult__self,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.28 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 4.98/5.28 = B ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_div_mult_self
% 4.98/5.28 thf(fact_2973_even__Suc,axiom,
% 4.98/5.28 ! [N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) )
% 4.98/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_Suc
% 4.98/5.28 thf(fact_2974_even__Suc__Suc__iff,axiom,
% 4.98/5.28 ! [N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N2 ) ) )
% 4.98/5.28 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_Suc_Suc_iff
% 4.98/5.28 thf(fact_2975_pow__divides__pow__iff,axiom,
% 4.98/5.28 ! [N2: nat,A: nat,B: nat] :
% 4.98/5.28 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.28 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 4.98/5.28 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % pow_divides_pow_iff
% 4.98/5.28 thf(fact_2976_pow__divides__pow__iff,axiom,
% 4.98/5.28 ! [N2: nat,A: int,B: int] :
% 4.98/5.28 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 4.98/5.28 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 4.98/5.28 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % pow_divides_pow_iff
% 4.98/5.28 thf(fact_2977_zle__diff1__eq,axiom,
% 4.98/5.28 ! [W: int,Z: int] :
% 4.98/5.28 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 4.98/5.28 = ( ord_less_int @ W @ Z ) ) ).
% 4.98/5.28
% 4.98/5.28 % zle_diff1_eq
% 4.98/5.28 thf(fact_2978_even__mult__iff,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 4.98/5.28 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_mult_iff
% 4.98/5.28 thf(fact_2979_even__mult__iff,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 4.98/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_mult_iff
% 4.98/5.28 thf(fact_2980_even__mult__iff,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 4.98/5.28 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_mult_iff
% 4.98/5.28 thf(fact_2981_odd__add,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 4.98/5.28 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 4.98/5.28 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_add
% 4.98/5.28 thf(fact_2982_odd__add,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 4.98/5.28 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 4.98/5.28 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_add
% 4.98/5.28 thf(fact_2983_odd__add,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 4.98/5.28 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 4.98/5.28 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_add
% 4.98/5.28 thf(fact_2984_even__add,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 4.98/5.28 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_add
% 4.98/5.28 thf(fact_2985_even__add,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 4.98/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_add
% 4.98/5.28 thf(fact_2986_even__add,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 4.98/5.28 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_add
% 4.98/5.28 thf(fact_2987_even__mod__2__iff,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_mod_2_iff
% 4.98/5.28 thf(fact_2988_even__mod__2__iff,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 4.98/5.28 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_mod_2_iff
% 4.98/5.28 thf(fact_2989_even__mod__2__iff,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 4.98/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_mod_2_iff
% 4.98/5.28 thf(fact_2990_odd__Suc__div__two,axiom,
% 4.98/5.28 ! [N2: nat] :
% 4.98/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.98/5.28 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_Suc_div_two
% 4.98/5.28 thf(fact_2991_even__Suc__div__two,axiom,
% 4.98/5.28 ! [N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.98/5.28 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_Suc_div_two
% 4.98/5.28 thf(fact_2992_signed__take__bit__Suc__bit0,axiom,
% 4.98/5.28 ! [N2: nat,K: num] :
% 4.98/5.28 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 4.98/5.28 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % signed_take_bit_Suc_bit0
% 4.98/5.28 thf(fact_2993_zero__le__power__eq__numeral,axiom,
% 4.98/5.28 ! [A: real,W: num] :
% 4.98/5.28 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 4.98/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % zero_le_power_eq_numeral
% 4.98/5.28 thf(fact_2994_zero__le__power__eq__numeral,axiom,
% 4.98/5.28 ! [A: rat,W: num] :
% 4.98/5.28 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 4.98/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % zero_le_power_eq_numeral
% 4.98/5.28 thf(fact_2995_zero__le__power__eq__numeral,axiom,
% 4.98/5.28 ! [A: int,W: num] :
% 4.98/5.28 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 4.98/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % zero_le_power_eq_numeral
% 4.98/5.28 thf(fact_2996_power__less__zero__eq,axiom,
% 4.98/5.28 ! [A: real,N2: nat] :
% 4.98/5.28 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 4.98/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.98/5.28 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_less_zero_eq
% 4.98/5.28 thf(fact_2997_power__less__zero__eq,axiom,
% 4.98/5.28 ! [A: rat,N2: nat] :
% 4.98/5.28 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 4.98/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.98/5.28 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_less_zero_eq
% 4.98/5.28 thf(fact_2998_power__less__zero__eq,axiom,
% 4.98/5.28 ! [A: int,N2: nat] :
% 4.98/5.28 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 4.98/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 4.98/5.28 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_less_zero_eq
% 4.98/5.28 thf(fact_2999_power__less__zero__eq__numeral,axiom,
% 4.98/5.28 ! [A: real,W: num] :
% 4.98/5.28 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 4.98/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_less_zero_eq_numeral
% 4.98/5.28 thf(fact_3000_power__less__zero__eq__numeral,axiom,
% 4.98/5.28 ! [A: rat,W: num] :
% 4.98/5.28 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 4.98/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_less_zero_eq_numeral
% 4.98/5.28 thf(fact_3001_power__less__zero__eq__numeral,axiom,
% 4.98/5.28 ! [A: int,W: num] :
% 4.98/5.28 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 4.98/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_less_zero_eq_numeral
% 4.98/5.28 thf(fact_3002_even__plus__one__iff,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 4.98/5.28 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_plus_one_iff
% 4.98/5.28 thf(fact_3003_even__plus__one__iff,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 4.98/5.28 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_plus_one_iff
% 4.98/5.28 thf(fact_3004_even__plus__one__iff,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 4.98/5.28 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_plus_one_iff
% 4.98/5.28 thf(fact_3005_even__diff,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_diff
% 4.98/5.28 thf(fact_3006_even__diff,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 4.98/5.28 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_diff
% 4.98/5.28 thf(fact_3007_zero__less__power__eq__numeral,axiom,
% 4.98/5.28 ! [A: real,W: num] :
% 4.98/5.28 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 4.98/5.28 = ( ( ( numeral_numeral_nat @ W )
% 4.98/5.28 = zero_zero_nat )
% 4.98/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( A != zero_zero_real ) )
% 4.98/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % zero_less_power_eq_numeral
% 4.98/5.28 thf(fact_3008_zero__less__power__eq__numeral,axiom,
% 4.98/5.28 ! [A: rat,W: num] :
% 4.98/5.28 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 4.98/5.28 = ( ( ( numeral_numeral_nat @ W )
% 4.98/5.28 = zero_zero_nat )
% 4.98/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( A != zero_zero_rat ) )
% 4.98/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % zero_less_power_eq_numeral
% 4.98/5.28 thf(fact_3009_zero__less__power__eq__numeral,axiom,
% 4.98/5.28 ! [A: int,W: num] :
% 4.98/5.28 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 4.98/5.28 = ( ( ( numeral_numeral_nat @ W )
% 4.98/5.28 = zero_zero_nat )
% 4.98/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( A != zero_zero_int ) )
% 4.98/5.28 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % zero_less_power_eq_numeral
% 4.98/5.28 thf(fact_3010_odd__succ__div__two,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_succ_div_two
% 4.98/5.28 thf(fact_3011_odd__succ__div__two,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_succ_div_two
% 4.98/5.28 thf(fact_3012_odd__succ__div__two,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_succ_div_two
% 4.98/5.28 thf(fact_3013_even__succ__div__two,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_succ_div_two
% 4.98/5.28 thf(fact_3014_even__succ__div__two,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_succ_div_two
% 4.98/5.28 thf(fact_3015_even__succ__div__two,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_succ_div_two
% 4.98/5.28 thf(fact_3016_even__succ__div__2,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_succ_div_2
% 4.98/5.28 thf(fact_3017_even__succ__div__2,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_succ_div_2
% 4.98/5.28 thf(fact_3018_even__succ__div__2,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 4.98/5.28 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_succ_div_2
% 4.98/5.28 thf(fact_3019_even__power,axiom,
% 4.98/5.28 ! [A: code_integer,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 4.98/5.28 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_power
% 4.98/5.28 thf(fact_3020_even__power,axiom,
% 4.98/5.28 ! [A: nat,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 4.98/5.28 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_power
% 4.98/5.28 thf(fact_3021_even__power,axiom,
% 4.98/5.28 ! [A: int,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 4.98/5.28 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % even_power
% 4.98/5.28 thf(fact_3022_odd__two__times__div__two__succ,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 4.98/5.28 = A ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_two_times_div_two_succ
% 4.98/5.28 thf(fact_3023_odd__two__times__div__two__succ,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 4.98/5.28 = A ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_two_times_div_two_succ
% 4.98/5.28 thf(fact_3024_odd__two__times__div__two__succ,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 4.98/5.28 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 4.98/5.28 = A ) ) ).
% 4.98/5.28
% 4.98/5.28 % odd_two_times_div_two_succ
% 4.98/5.28 thf(fact_3025_power__le__zero__eq__numeral,axiom,
% 4.98/5.28 ! [A: real,W: num] :
% 4.98/5.28 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 4.98/5.28 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 4.98/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( A = zero_zero_real ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_le_zero_eq_numeral
% 4.98/5.28 thf(fact_3026_power__le__zero__eq__numeral,axiom,
% 4.98/5.28 ! [A: rat,W: num] :
% 4.98/5.28 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 4.98/5.28 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 4.98/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( A = zero_zero_rat ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_le_zero_eq_numeral
% 4.98/5.28 thf(fact_3027_power__le__zero__eq__numeral,axiom,
% 4.98/5.28 ! [A: int,W: num] :
% 4.98/5.28 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 4.98/5.28 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 4.98/5.28 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 4.98/5.28 & ( A = zero_zero_int ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % power_le_zero_eq_numeral
% 4.98/5.28 thf(fact_3028_semiring__parity__class_Oeven__mask__iff,axiom,
% 4.98/5.28 ! [N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 4.98/5.28 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % semiring_parity_class.even_mask_iff
% 4.98/5.28 thf(fact_3029_semiring__parity__class_Oeven__mask__iff,axiom,
% 4.98/5.28 ! [N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 4.98/5.28 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % semiring_parity_class.even_mask_iff
% 4.98/5.28 thf(fact_3030_semiring__parity__class_Oeven__mask__iff,axiom,
% 4.98/5.28 ! [N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 4.98/5.28 = ( N2 = zero_zero_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % semiring_parity_class.even_mask_iff
% 4.98/5.28 thf(fact_3031_dvd__minus__mod,axiom,
% 4.98/5.28 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_minus_mod
% 4.98/5.28 thf(fact_3032_dvd__minus__mod,axiom,
% 4.98/5.28 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_minus_mod
% 4.98/5.28 thf(fact_3033_dvd__minus__mod,axiom,
% 4.98/5.28 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_minus_mod
% 4.98/5.28 thf(fact_3034_mod__eq__dvd__iff,axiom,
% 4.98/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.98/5.28 ( ( ( modulo364778990260209775nteger @ A @ C )
% 4.98/5.28 = ( modulo364778990260209775nteger @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_eq_dvd_iff
% 4.98/5.28 thf(fact_3035_mod__eq__dvd__iff,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( ( modulo_modulo_int @ A @ C )
% 4.98/5.28 = ( modulo_modulo_int @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_eq_dvd_iff
% 4.98/5.28 thf(fact_3036_subset__divisors__dvd,axiom,
% 4.98/5.28 ! [A: real,B: real] :
% 4.98/5.28 ( ( ord_less_eq_set_real
% 4.98/5.28 @ ( collect_real
% 4.98/5.28 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 4.98/5.28 @ ( collect_real
% 4.98/5.28 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 4.98/5.28 = ( dvd_dvd_real @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % subset_divisors_dvd
% 4.98/5.28 thf(fact_3037_subset__divisors__dvd,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( ord_less_eq_set_int
% 4.98/5.28 @ ( collect_int
% 4.98/5.28 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 4.98/5.28 @ ( collect_int
% 4.98/5.28 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 4.98/5.28 = ( dvd_dvd_int @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % subset_divisors_dvd
% 4.98/5.28 thf(fact_3038_subset__divisors__dvd,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( ord_le7084787975880047091nteger
% 4.98/5.28 @ ( collect_Code_integer
% 4.98/5.28 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 4.98/5.28 @ ( collect_Code_integer
% 4.98/5.28 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % subset_divisors_dvd
% 4.98/5.28 thf(fact_3039_subset__divisors__dvd,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( ord_less_eq_set_nat
% 4.98/5.28 @ ( collect_nat
% 4.98/5.28 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 4.98/5.28 @ ( collect_nat
% 4.98/5.28 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 4.98/5.28 = ( dvd_dvd_nat @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % subset_divisors_dvd
% 4.98/5.28 thf(fact_3040_diff__right__commute,axiom,
% 4.98/5.28 ! [A: real,C: real,B: real] :
% 4.98/5.28 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 4.98/5.28 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_right_commute
% 4.98/5.28 thf(fact_3041_diff__right__commute,axiom,
% 4.98/5.28 ! [A: rat,C: rat,B: rat] :
% 4.98/5.28 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 4.98/5.28 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_right_commute
% 4.98/5.28 thf(fact_3042_diff__right__commute,axiom,
% 4.98/5.28 ! [A: nat,C: nat,B: nat] :
% 4.98/5.28 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 4.98/5.28 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_right_commute
% 4.98/5.28 thf(fact_3043_diff__right__commute,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 4.98/5.28 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_right_commute
% 4.98/5.28 thf(fact_3044_dvd__trans,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_nat @ B @ C )
% 4.98/5.28 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_trans
% 4.98/5.28 thf(fact_3045_dvd__trans,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_int @ B @ C )
% 4.98/5.28 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_trans
% 4.98/5.28 thf(fact_3046_dvd__trans,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ B @ C )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_trans
% 4.98/5.28 thf(fact_3047_diff__eq__diff__eq,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.28 ( ( ( minus_minus_real @ A @ B )
% 4.98/5.28 = ( minus_minus_real @ C @ D ) )
% 4.98/5.28 => ( ( A = B )
% 4.98/5.28 = ( C = D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_eq
% 4.98/5.28 thf(fact_3048_diff__eq__diff__eq,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.28 ( ( ( minus_minus_rat @ A @ B )
% 4.98/5.28 = ( minus_minus_rat @ C @ D ) )
% 4.98/5.28 => ( ( A = B )
% 4.98/5.28 = ( C = D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_eq
% 4.98/5.28 thf(fact_3049_diff__eq__diff__eq,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.28 ( ( ( minus_minus_int @ A @ B )
% 4.98/5.28 = ( minus_minus_int @ C @ D ) )
% 4.98/5.28 => ( ( A = B )
% 4.98/5.28 = ( C = D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_eq
% 4.98/5.28 thf(fact_3050_dvd__refl,axiom,
% 4.98/5.28 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_refl
% 4.98/5.28 thf(fact_3051_dvd__refl,axiom,
% 4.98/5.28 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_refl
% 4.98/5.28 thf(fact_3052_dvd__refl,axiom,
% 4.98/5.28 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_refl
% 4.98/5.28 thf(fact_3053_dvd__diff,axiom,
% 4.98/5.28 ! [X2: code_integer,Y: code_integer,Z: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ X2 @ Y )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ X2 @ Z )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ X2 @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_diff
% 4.98/5.28 thf(fact_3054_dvd__diff,axiom,
% 4.98/5.28 ! [X2: real,Y: real,Z: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ X2 @ Y )
% 4.98/5.28 => ( ( dvd_dvd_real @ X2 @ Z )
% 4.98/5.28 => ( dvd_dvd_real @ X2 @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_diff
% 4.98/5.28 thf(fact_3055_dvd__diff,axiom,
% 4.98/5.28 ! [X2: rat,Y: rat,Z: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ X2 @ Y )
% 4.98/5.28 => ( ( dvd_dvd_rat @ X2 @ Z )
% 4.98/5.28 => ( dvd_dvd_rat @ X2 @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_diff
% 4.98/5.28 thf(fact_3056_dvd__diff,axiom,
% 4.98/5.28 ! [X2: int,Y: int,Z: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ X2 @ Y )
% 4.98/5.28 => ( ( dvd_dvd_int @ X2 @ Z )
% 4.98/5.28 => ( dvd_dvd_int @ X2 @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_diff
% 4.98/5.28 thf(fact_3057_signed__take__bit__diff,axiom,
% 4.98/5.28 ! [N2: nat,K: int,L: int] :
% 4.98/5.28 ( ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 4.98/5.28 = ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % signed_take_bit_diff
% 4.98/5.28 thf(fact_3058_dvd__diff__commute,axiom,
% 4.98/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_diff_commute
% 4.98/5.28 thf(fact_3059_dvd__diff__commute,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 4.98/5.28 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_diff_commute
% 4.98/5.28 thf(fact_3060_zdvd__zdiffD,axiom,
% 4.98/5.28 ! [K: int,M: int,N2: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N2 ) )
% 4.98/5.28 => ( ( dvd_dvd_int @ K @ N2 )
% 4.98/5.28 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % zdvd_zdiffD
% 4.98/5.28 thf(fact_3061_strict__subset__divisors__dvd,axiom,
% 4.98/5.28 ! [A: real,B: real] :
% 4.98/5.28 ( ( ord_less_set_real
% 4.98/5.28 @ ( collect_real
% 4.98/5.28 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 4.98/5.28 @ ( collect_real
% 4.98/5.28 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 4.98/5.28 = ( ( dvd_dvd_real @ A @ B )
% 4.98/5.28 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % strict_subset_divisors_dvd
% 4.98/5.28 thf(fact_3062_strict__subset__divisors__dvd,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( ord_less_set_nat
% 4.98/5.28 @ ( collect_nat
% 4.98/5.28 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 4.98/5.28 @ ( collect_nat
% 4.98/5.28 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 4.98/5.28 = ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % strict_subset_divisors_dvd
% 4.98/5.28 thf(fact_3063_strict__subset__divisors__dvd,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( ord_less_set_int
% 4.98/5.28 @ ( collect_int
% 4.98/5.28 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 4.98/5.28 @ ( collect_int
% 4.98/5.28 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 4.98/5.28 = ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % strict_subset_divisors_dvd
% 4.98/5.28 thf(fact_3064_strict__subset__divisors__dvd,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( ord_le1307284697595431911nteger
% 4.98/5.28 @ ( collect_Code_integer
% 4.98/5.28 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 4.98/5.28 @ ( collect_Code_integer
% 4.98/5.28 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 4.98/5.28 = ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % strict_subset_divisors_dvd
% 4.98/5.28 thf(fact_3065_lambda__zero,axiom,
% 4.98/5.28 ( ( ^ [H: complex] : zero_zero_complex )
% 4.98/5.28 = ( times_times_complex @ zero_zero_complex ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_zero
% 4.98/5.28 thf(fact_3066_lambda__zero,axiom,
% 4.98/5.28 ( ( ^ [H: real] : zero_zero_real )
% 4.98/5.28 = ( times_times_real @ zero_zero_real ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_zero
% 4.98/5.28 thf(fact_3067_lambda__zero,axiom,
% 4.98/5.28 ( ( ^ [H: rat] : zero_zero_rat )
% 4.98/5.28 = ( times_times_rat @ zero_zero_rat ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_zero
% 4.98/5.28 thf(fact_3068_lambda__zero,axiom,
% 4.98/5.28 ( ( ^ [H: nat] : zero_zero_nat )
% 4.98/5.28 = ( times_times_nat @ zero_zero_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_zero
% 4.98/5.28 thf(fact_3069_lambda__zero,axiom,
% 4.98/5.28 ( ( ^ [H: int] : zero_zero_int )
% 4.98/5.28 = ( times_times_int @ zero_zero_int ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_zero
% 4.98/5.28 thf(fact_3070_lambda__one,axiom,
% 4.98/5.28 ( ( ^ [X: complex] : X )
% 4.98/5.28 = ( times_times_complex @ one_one_complex ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_one
% 4.98/5.28 thf(fact_3071_lambda__one,axiom,
% 4.98/5.28 ( ( ^ [X: real] : X )
% 4.98/5.28 = ( times_times_real @ one_one_real ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_one
% 4.98/5.28 thf(fact_3072_lambda__one,axiom,
% 4.98/5.28 ( ( ^ [X: rat] : X )
% 4.98/5.28 = ( times_times_rat @ one_one_rat ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_one
% 4.98/5.28 thf(fact_3073_lambda__one,axiom,
% 4.98/5.28 ( ( ^ [X: nat] : X )
% 4.98/5.28 = ( times_times_nat @ one_one_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_one
% 4.98/5.28 thf(fact_3074_lambda__one,axiom,
% 4.98/5.28 ( ( ^ [X: int] : X )
% 4.98/5.28 = ( times_times_int @ one_one_int ) ) ).
% 4.98/5.28
% 4.98/5.28 % lambda_one
% 4.98/5.28 thf(fact_3075_max__def__raw,axiom,
% 4.98/5.28 ( ord_max_set_nat
% 4.98/5.28 = ( ^ [A5: set_nat,B5: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % max_def_raw
% 4.98/5.28 thf(fact_3076_max__def__raw,axiom,
% 4.98/5.28 ( ord_max_rat
% 4.98/5.28 = ( ^ [A5: rat,B5: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % max_def_raw
% 4.98/5.28 thf(fact_3077_max__def__raw,axiom,
% 4.98/5.28 ( ord_max_num
% 4.98/5.28 = ( ^ [A5: num,B5: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % max_def_raw
% 4.98/5.28 thf(fact_3078_max__def__raw,axiom,
% 4.98/5.28 ( ord_max_nat
% 4.98/5.28 = ( ^ [A5: nat,B5: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % max_def_raw
% 4.98/5.28 thf(fact_3079_max__def__raw,axiom,
% 4.98/5.28 ( ord_max_int
% 4.98/5.28 = ( ^ [A5: int,B5: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % max_def_raw
% 4.98/5.28 thf(fact_3080_inf__period_I3_J,axiom,
% 4.98/5.28 ! [D: code_integer,D4: code_integer,T2: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 4.98/5.28 => ! [X3: code_integer,K4: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ T2 ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(3)
% 4.98/5.28 thf(fact_3081_inf__period_I3_J,axiom,
% 4.98/5.28 ! [D: real,D4: real,T2: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ D @ D4 )
% 4.98/5.28 => ! [X3: real,K4: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ T2 ) )
% 4.98/5.28 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(3)
% 4.98/5.28 thf(fact_3082_inf__period_I3_J,axiom,
% 4.98/5.28 ! [D: rat,D4: rat,T2: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ D @ D4 )
% 4.98/5.28 => ! [X3: rat,K4: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ T2 ) )
% 4.98/5.28 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(3)
% 4.98/5.28 thf(fact_3083_inf__period_I3_J,axiom,
% 4.98/5.28 ! [D: int,D4: int,T2: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ D @ D4 )
% 4.98/5.28 => ! [X3: int,K4: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T2 ) )
% 4.98/5.28 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(3)
% 4.98/5.28 thf(fact_3084_inf__period_I4_J,axiom,
% 4.98/5.28 ! [D: code_integer,D4: code_integer,T2: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 4.98/5.28 => ! [X3: code_integer,K4: code_integer] :
% 4.98/5.28 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ T2 ) ) )
% 4.98/5.28 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(4)
% 4.98/5.28 thf(fact_3085_inf__period_I4_J,axiom,
% 4.98/5.28 ! [D: real,D4: real,T2: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ D @ D4 )
% 4.98/5.28 => ! [X3: real,K4: real] :
% 4.98/5.28 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ T2 ) ) )
% 4.98/5.28 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(4)
% 4.98/5.28 thf(fact_3086_inf__period_I4_J,axiom,
% 4.98/5.28 ! [D: rat,D4: rat,T2: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ D @ D4 )
% 4.98/5.28 => ! [X3: rat,K4: rat] :
% 4.98/5.28 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ T2 ) ) )
% 4.98/5.28 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(4)
% 4.98/5.28 thf(fact_3087_inf__period_I4_J,axiom,
% 4.98/5.28 ! [D: int,D4: int,T2: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ D @ D4 )
% 4.98/5.28 => ! [X3: int,K4: int] :
% 4.98/5.28 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T2 ) ) )
% 4.98/5.28 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(4)
% 4.98/5.28 thf(fact_3088_dvd__field__iff,axiom,
% 4.98/5.28 ( dvd_dvd_complex
% 4.98/5.28 = ( ^ [A5: complex,B5: complex] :
% 4.98/5.28 ( ( A5 = zero_zero_complex )
% 4.98/5.28 => ( B5 = zero_zero_complex ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_field_iff
% 4.98/5.28 thf(fact_3089_dvd__field__iff,axiom,
% 4.98/5.28 ( dvd_dvd_real
% 4.98/5.28 = ( ^ [A5: real,B5: real] :
% 4.98/5.28 ( ( A5 = zero_zero_real )
% 4.98/5.28 => ( B5 = zero_zero_real ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_field_iff
% 4.98/5.28 thf(fact_3090_dvd__field__iff,axiom,
% 4.98/5.28 ( dvd_dvd_rat
% 4.98/5.28 = ( ^ [A5: rat,B5: rat] :
% 4.98/5.28 ( ( A5 = zero_zero_rat )
% 4.98/5.28 => ( B5 = zero_zero_rat ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_field_iff
% 4.98/5.28 thf(fact_3091_dvd__0__left,axiom,
% 4.98/5.28 ! [A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 4.98/5.28 => ( A = zero_z3403309356797280102nteger ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_0_left
% 4.98/5.28 thf(fact_3092_dvd__0__left,axiom,
% 4.98/5.28 ! [A: complex] :
% 4.98/5.28 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 4.98/5.28 => ( A = zero_zero_complex ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_0_left
% 4.98/5.28 thf(fact_3093_dvd__0__left,axiom,
% 4.98/5.28 ! [A: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 4.98/5.28 => ( A = zero_zero_real ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_0_left
% 4.98/5.28 thf(fact_3094_dvd__0__left,axiom,
% 4.98/5.28 ! [A: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 4.98/5.28 => ( A = zero_zero_rat ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_0_left
% 4.98/5.28 thf(fact_3095_dvd__0__left,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 4.98/5.28 => ( A = zero_zero_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_0_left
% 4.98/5.28 thf(fact_3096_dvd__0__left,axiom,
% 4.98/5.28 ! [A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 4.98/5.28 => ( A = zero_zero_int ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_0_left
% 4.98/5.28 thf(fact_3097_diff__mono,axiom,
% 4.98/5.28 ! [A: real,B: real,D: real,C: real] :
% 4.98/5.28 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.28 => ( ( ord_less_eq_real @ D @ C )
% 4.98/5.28 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_mono
% 4.98/5.28 thf(fact_3098_diff__mono,axiom,
% 4.98/5.28 ! [A: rat,B: rat,D: rat,C: rat] :
% 4.98/5.28 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.28 => ( ( ord_less_eq_rat @ D @ C )
% 4.98/5.28 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_mono
% 4.98/5.28 thf(fact_3099_diff__mono,axiom,
% 4.98/5.28 ! [A: int,B: int,D: int,C: int] :
% 4.98/5.28 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.28 => ( ( ord_less_eq_int @ D @ C )
% 4.98/5.28 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_mono
% 4.98/5.28 thf(fact_3100_diff__left__mono,axiom,
% 4.98/5.28 ! [B: real,A: real,C: real] :
% 4.98/5.28 ( ( ord_less_eq_real @ B @ A )
% 4.98/5.28 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_left_mono
% 4.98/5.28 thf(fact_3101_diff__left__mono,axiom,
% 4.98/5.28 ! [B: rat,A: rat,C: rat] :
% 4.98/5.28 ( ( ord_less_eq_rat @ B @ A )
% 4.98/5.28 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_left_mono
% 4.98/5.28 thf(fact_3102_diff__left__mono,axiom,
% 4.98/5.28 ! [B: int,A: int,C: int] :
% 4.98/5.28 ( ( ord_less_eq_int @ B @ A )
% 4.98/5.28 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_left_mono
% 4.98/5.28 thf(fact_3103_diff__right__mono,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( ord_less_eq_real @ A @ B )
% 4.98/5.28 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_right_mono
% 4.98/5.28 thf(fact_3104_diff__right__mono,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.28 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_right_mono
% 4.98/5.28 thf(fact_3105_diff__right__mono,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( ord_less_eq_int @ A @ B )
% 4.98/5.28 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_right_mono
% 4.98/5.28 thf(fact_3106_diff__eq__diff__less__eq,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.28 ( ( ( minus_minus_real @ A @ B )
% 4.98/5.28 = ( minus_minus_real @ C @ D ) )
% 4.98/5.28 => ( ( ord_less_eq_real @ A @ B )
% 4.98/5.28 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_less_eq
% 4.98/5.28 thf(fact_3107_diff__eq__diff__less__eq,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.28 ( ( ( minus_minus_rat @ A @ B )
% 4.98/5.28 = ( minus_minus_rat @ C @ D ) )
% 4.98/5.28 => ( ( ord_less_eq_rat @ A @ B )
% 4.98/5.28 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_less_eq
% 4.98/5.28 thf(fact_3108_diff__eq__diff__less__eq,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.28 ( ( ( minus_minus_int @ A @ B )
% 4.98/5.28 = ( minus_minus_int @ C @ D ) )
% 4.98/5.28 => ( ( ord_less_eq_int @ A @ B )
% 4.98/5.28 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_less_eq
% 4.98/5.28 thf(fact_3109_eq__iff__diff__eq__0,axiom,
% 4.98/5.28 ( ( ^ [Y4: complex,Z2: complex] : ( Y4 = Z2 ) )
% 4.98/5.28 = ( ^ [A5: complex,B5: complex] :
% 4.98/5.28 ( ( minus_minus_complex @ A5 @ B5 )
% 4.98/5.28 = zero_zero_complex ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % eq_iff_diff_eq_0
% 4.98/5.28 thf(fact_3110_eq__iff__diff__eq__0,axiom,
% 4.98/5.28 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 4.98/5.28 = ( ^ [A5: real,B5: real] :
% 4.98/5.28 ( ( minus_minus_real @ A5 @ B5 )
% 4.98/5.28 = zero_zero_real ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % eq_iff_diff_eq_0
% 4.98/5.28 thf(fact_3111_eq__iff__diff__eq__0,axiom,
% 4.98/5.28 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 4.98/5.28 = ( ^ [A5: rat,B5: rat] :
% 4.98/5.28 ( ( minus_minus_rat @ A5 @ B5 )
% 4.98/5.28 = zero_zero_rat ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % eq_iff_diff_eq_0
% 4.98/5.28 thf(fact_3112_eq__iff__diff__eq__0,axiom,
% 4.98/5.28 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 4.98/5.28 = ( ^ [A5: int,B5: int] :
% 4.98/5.28 ( ( minus_minus_int @ A5 @ B5 )
% 4.98/5.28 = zero_zero_int ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % eq_iff_diff_eq_0
% 4.98/5.28 thf(fact_3113_dvd__triv__right,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_right
% 4.98/5.28 thf(fact_3114_dvd__triv__right,axiom,
% 4.98/5.28 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_right
% 4.98/5.28 thf(fact_3115_dvd__triv__right,axiom,
% 4.98/5.28 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_right
% 4.98/5.28 thf(fact_3116_dvd__triv__right,axiom,
% 4.98/5.28 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_right
% 4.98/5.28 thf(fact_3117_dvd__triv__right,axiom,
% 4.98/5.28 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_right
% 4.98/5.28 thf(fact_3118_dvd__mult__right,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_right
% 4.98/5.28 thf(fact_3119_dvd__mult__right,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_real @ B @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_right
% 4.98/5.28 thf(fact_3120_dvd__mult__right,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_rat @ B @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_right
% 4.98/5.28 thf(fact_3121_dvd__mult__right,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_nat @ B @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_right
% 4.98/5.28 thf(fact_3122_dvd__mult__right,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_int @ B @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_right
% 4.98/5.28 thf(fact_3123_mult__dvd__mono,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ C @ D )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mult_dvd_mono
% 4.98/5.28 thf(fact_3124_mult__dvd__mono,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_real @ C @ D )
% 4.98/5.28 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mult_dvd_mono
% 4.98/5.28 thf(fact_3125_mult__dvd__mono,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_rat @ C @ D )
% 4.98/5.28 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mult_dvd_mono
% 4.98/5.28 thf(fact_3126_mult__dvd__mono,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat,D: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_nat @ C @ D )
% 4.98/5.28 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mult_dvd_mono
% 4.98/5.28 thf(fact_3127_mult__dvd__mono,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_int @ C @ D )
% 4.98/5.28 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mult_dvd_mono
% 4.98/5.28 thf(fact_3128_dvd__triv__left,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_left
% 4.98/5.28 thf(fact_3129_dvd__triv__left,axiom,
% 4.98/5.28 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_left
% 4.98/5.28 thf(fact_3130_dvd__triv__left,axiom,
% 4.98/5.28 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_left
% 4.98/5.28 thf(fact_3131_dvd__triv__left,axiom,
% 4.98/5.28 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_left
% 4.98/5.28 thf(fact_3132_dvd__triv__left,axiom,
% 4.98/5.28 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_triv_left
% 4.98/5.28 thf(fact_3133_dvd__mult__left,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_left
% 4.98/5.28 thf(fact_3134_dvd__mult__left,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_real @ A @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_left
% 4.98/5.28 thf(fact_3135_dvd__mult__left,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_rat @ A @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_left
% 4.98/5.28 thf(fact_3136_dvd__mult__left,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_nat @ A @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_left
% 4.98/5.28 thf(fact_3137_dvd__mult__left,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 4.98/5.28 => ( dvd_dvd_int @ A @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult_left
% 4.98/5.28 thf(fact_3138_dvd__mult2,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult2
% 4.98/5.28 thf(fact_3139_dvd__mult2,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ A @ B )
% 4.98/5.28 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult2
% 4.98/5.28 thf(fact_3140_dvd__mult2,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ A @ B )
% 4.98/5.28 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult2
% 4.98/5.28 thf(fact_3141_dvd__mult2,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult2
% 4.98/5.28 thf(fact_3142_dvd__mult2,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult2
% 4.98/5.28 thf(fact_3143_dvd__mult,axiom,
% 4.98/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ C )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult
% 4.98/5.28 thf(fact_3144_dvd__mult,axiom,
% 4.98/5.28 ! [A: real,C: real,B: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ A @ C )
% 4.98/5.28 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult
% 4.98/5.28 thf(fact_3145_dvd__mult,axiom,
% 4.98/5.28 ! [A: rat,C: rat,B: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ A @ C )
% 4.98/5.28 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult
% 4.98/5.28 thf(fact_3146_dvd__mult,axiom,
% 4.98/5.28 ! [A: nat,C: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ C )
% 4.98/5.28 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult
% 4.98/5.28 thf(fact_3147_dvd__mult,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ C )
% 4.98/5.28 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mult
% 4.98/5.28 thf(fact_3148_dvd__def,axiom,
% 4.98/5.28 ( dvd_dvd_Code_integer
% 4.98/5.28 = ( ^ [B5: code_integer,A5: code_integer] :
% 4.98/5.28 ? [K3: code_integer] :
% 4.98/5.28 ( A5
% 4.98/5.28 = ( times_3573771949741848930nteger @ B5 @ K3 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_def
% 4.98/5.28 thf(fact_3149_dvd__def,axiom,
% 4.98/5.28 ( dvd_dvd_real
% 4.98/5.28 = ( ^ [B5: real,A5: real] :
% 4.98/5.28 ? [K3: real] :
% 4.98/5.28 ( A5
% 4.98/5.28 = ( times_times_real @ B5 @ K3 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_def
% 4.98/5.28 thf(fact_3150_dvd__def,axiom,
% 4.98/5.28 ( dvd_dvd_rat
% 4.98/5.28 = ( ^ [B5: rat,A5: rat] :
% 4.98/5.28 ? [K3: rat] :
% 4.98/5.28 ( A5
% 4.98/5.28 = ( times_times_rat @ B5 @ K3 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_def
% 4.98/5.28 thf(fact_3151_dvd__def,axiom,
% 4.98/5.28 ( dvd_dvd_nat
% 4.98/5.28 = ( ^ [B5: nat,A5: nat] :
% 4.98/5.28 ? [K3: nat] :
% 4.98/5.28 ( A5
% 4.98/5.28 = ( times_times_nat @ B5 @ K3 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_def
% 4.98/5.28 thf(fact_3152_dvd__def,axiom,
% 4.98/5.28 ( dvd_dvd_int
% 4.98/5.28 = ( ^ [B5: int,A5: int] :
% 4.98/5.28 ? [K3: int] :
% 4.98/5.28 ( A5
% 4.98/5.28 = ( times_times_int @ B5 @ K3 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_def
% 4.98/5.28 thf(fact_3153_dvdI,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,K: code_integer] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( times_3573771949741848930nteger @ B @ K ) )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdI
% 4.98/5.28 thf(fact_3154_dvdI,axiom,
% 4.98/5.28 ! [A: real,B: real,K: real] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( times_times_real @ B @ K ) )
% 4.98/5.28 => ( dvd_dvd_real @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdI
% 4.98/5.28 thf(fact_3155_dvdI,axiom,
% 4.98/5.28 ! [A: rat,B: rat,K: rat] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( times_times_rat @ B @ K ) )
% 4.98/5.28 => ( dvd_dvd_rat @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdI
% 4.98/5.28 thf(fact_3156_dvdI,axiom,
% 4.98/5.28 ! [A: nat,B: nat,K: nat] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( times_times_nat @ B @ K ) )
% 4.98/5.28 => ( dvd_dvd_nat @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdI
% 4.98/5.28 thf(fact_3157_dvdI,axiom,
% 4.98/5.28 ! [A: int,B: int,K: int] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( times_times_int @ B @ K ) )
% 4.98/5.28 => ( dvd_dvd_int @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdI
% 4.98/5.28 thf(fact_3158_dvdE,axiom,
% 4.98/5.28 ! [B: code_integer,A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ B @ A )
% 4.98/5.28 => ~ ! [K2: code_integer] :
% 4.98/5.28 ( A
% 4.98/5.28 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdE
% 4.98/5.28 thf(fact_3159_dvdE,axiom,
% 4.98/5.28 ! [B: real,A: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ B @ A )
% 4.98/5.28 => ~ ! [K2: real] :
% 4.98/5.28 ( A
% 4.98/5.28 != ( times_times_real @ B @ K2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdE
% 4.98/5.28 thf(fact_3160_dvdE,axiom,
% 4.98/5.28 ! [B: rat,A: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ B @ A )
% 4.98/5.28 => ~ ! [K2: rat] :
% 4.98/5.28 ( A
% 4.98/5.28 != ( times_times_rat @ B @ K2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdE
% 4.98/5.28 thf(fact_3161_dvdE,axiom,
% 4.98/5.28 ! [B: nat,A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ B @ A )
% 4.98/5.28 => ~ ! [K2: nat] :
% 4.98/5.28 ( A
% 4.98/5.28 != ( times_times_nat @ B @ K2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdE
% 4.98/5.28 thf(fact_3162_dvdE,axiom,
% 4.98/5.28 ! [B: int,A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ B @ A )
% 4.98/5.28 => ~ ! [K2: int] :
% 4.98/5.28 ( A
% 4.98/5.28 != ( times_times_int @ B @ K2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvdE
% 4.98/5.28 thf(fact_3163_dvd__productE,axiom,
% 4.98/5.28 ! [P2: nat,A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ P2 @ ( times_times_nat @ A @ B ) )
% 4.98/5.28 => ~ ! [X5: nat,Y3: nat] :
% 4.98/5.28 ( ( P2
% 4.98/5.28 = ( times_times_nat @ X5 @ Y3 ) )
% 4.98/5.28 => ( ( dvd_dvd_nat @ X5 @ A )
% 4.98/5.28 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_productE
% 4.98/5.28 thf(fact_3164_dvd__productE,axiom,
% 4.98/5.28 ! [P2: int,A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ P2 @ ( times_times_int @ A @ B ) )
% 4.98/5.28 => ~ ! [X5: int,Y3: int] :
% 4.98/5.28 ( ( P2
% 4.98/5.28 = ( times_times_int @ X5 @ Y3 ) )
% 4.98/5.28 => ( ( dvd_dvd_int @ X5 @ A )
% 4.98/5.28 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_productE
% 4.98/5.28 thf(fact_3165_division__decomp,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 4.98/5.28 => ? [B6: nat,C4: nat] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( times_times_nat @ B6 @ C4 ) )
% 4.98/5.28 & ( dvd_dvd_nat @ B6 @ B )
% 4.98/5.28 & ( dvd_dvd_nat @ C4 @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % division_decomp
% 4.98/5.28 thf(fact_3166_division__decomp,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 4.98/5.28 => ? [B6: int,C4: int] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( times_times_int @ B6 @ C4 ) )
% 4.98/5.28 & ( dvd_dvd_int @ B6 @ B )
% 4.98/5.28 & ( dvd_dvd_int @ C4 @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % division_decomp
% 4.98/5.28 thf(fact_3167_diff__strict__mono,axiom,
% 4.98/5.28 ! [A: real,B: real,D: real,C: real] :
% 4.98/5.28 ( ( ord_less_real @ A @ B )
% 4.98/5.28 => ( ( ord_less_real @ D @ C )
% 4.98/5.28 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_mono
% 4.98/5.28 thf(fact_3168_diff__strict__mono,axiom,
% 4.98/5.28 ! [A: rat,B: rat,D: rat,C: rat] :
% 4.98/5.28 ( ( ord_less_rat @ A @ B )
% 4.98/5.28 => ( ( ord_less_rat @ D @ C )
% 4.98/5.28 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_mono
% 4.98/5.28 thf(fact_3169_diff__strict__mono,axiom,
% 4.98/5.28 ! [A: int,B: int,D: int,C: int] :
% 4.98/5.28 ( ( ord_less_int @ A @ B )
% 4.98/5.28 => ( ( ord_less_int @ D @ C )
% 4.98/5.28 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_mono
% 4.98/5.28 thf(fact_3170_diff__eq__diff__less,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real,D: real] :
% 4.98/5.28 ( ( ( minus_minus_real @ A @ B )
% 4.98/5.28 = ( minus_minus_real @ C @ D ) )
% 4.98/5.28 => ( ( ord_less_real @ A @ B )
% 4.98/5.28 = ( ord_less_real @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_less
% 4.98/5.28 thf(fact_3171_diff__eq__diff__less,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat,D: rat] :
% 4.98/5.28 ( ( ( minus_minus_rat @ A @ B )
% 4.98/5.28 = ( minus_minus_rat @ C @ D ) )
% 4.98/5.28 => ( ( ord_less_rat @ A @ B )
% 4.98/5.28 = ( ord_less_rat @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_less
% 4.98/5.28 thf(fact_3172_diff__eq__diff__less,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int,D: int] :
% 4.98/5.28 ( ( ( minus_minus_int @ A @ B )
% 4.98/5.28 = ( minus_minus_int @ C @ D ) )
% 4.98/5.28 => ( ( ord_less_int @ A @ B )
% 4.98/5.28 = ( ord_less_int @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_diff_less
% 4.98/5.28 thf(fact_3173_diff__strict__left__mono,axiom,
% 4.98/5.28 ! [B: real,A: real,C: real] :
% 4.98/5.28 ( ( ord_less_real @ B @ A )
% 4.98/5.28 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_left_mono
% 4.98/5.28 thf(fact_3174_diff__strict__left__mono,axiom,
% 4.98/5.28 ! [B: rat,A: rat,C: rat] :
% 4.98/5.28 ( ( ord_less_rat @ B @ A )
% 4.98/5.28 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_left_mono
% 4.98/5.28 thf(fact_3175_diff__strict__left__mono,axiom,
% 4.98/5.28 ! [B: int,A: int,C: int] :
% 4.98/5.28 ( ( ord_less_int @ B @ A )
% 4.98/5.28 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_left_mono
% 4.98/5.28 thf(fact_3176_diff__strict__right__mono,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( ord_less_real @ A @ B )
% 4.98/5.28 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_right_mono
% 4.98/5.28 thf(fact_3177_diff__strict__right__mono,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( ord_less_rat @ A @ B )
% 4.98/5.28 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_right_mono
% 4.98/5.28 thf(fact_3178_diff__strict__right__mono,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( ord_less_int @ A @ B )
% 4.98/5.28 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_strict_right_mono
% 4.98/5.28 thf(fact_3179_one__dvd,axiom,
% 4.98/5.28 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 4.98/5.28
% 4.98/5.28 % one_dvd
% 4.98/5.28 thf(fact_3180_one__dvd,axiom,
% 4.98/5.28 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 4.98/5.28
% 4.98/5.28 % one_dvd
% 4.98/5.28 thf(fact_3181_one__dvd,axiom,
% 4.98/5.28 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 4.98/5.28
% 4.98/5.28 % one_dvd
% 4.98/5.28 thf(fact_3182_one__dvd,axiom,
% 4.98/5.28 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 4.98/5.28
% 4.98/5.28 % one_dvd
% 4.98/5.28 thf(fact_3183_one__dvd,axiom,
% 4.98/5.28 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 4.98/5.28
% 4.98/5.28 % one_dvd
% 4.98/5.28 thf(fact_3184_one__dvd,axiom,
% 4.98/5.28 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 4.98/5.28
% 4.98/5.28 % one_dvd
% 4.98/5.28 thf(fact_3185_unit__imp__dvd,axiom,
% 4.98/5.28 ! [B: code_integer,A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_imp_dvd
% 4.98/5.28 thf(fact_3186_unit__imp__dvd,axiom,
% 4.98/5.28 ! [B: nat,A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.28 => ( dvd_dvd_nat @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_imp_dvd
% 4.98/5.28 thf(fact_3187_unit__imp__dvd,axiom,
% 4.98/5.28 ! [B: int,A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.28 => ( dvd_dvd_int @ B @ A ) ) ).
% 4.98/5.28
% 4.98/5.28 % unit_imp_dvd
% 4.98/5.28 thf(fact_3188_dvd__unit__imp__unit,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_unit_imp_unit
% 4.98/5.28 thf(fact_3189_dvd__unit__imp__unit,axiom,
% 4.98/5.28 ! [A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.28 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_unit_imp_unit
% 4.98/5.28 thf(fact_3190_dvd__unit__imp__unit,axiom,
% 4.98/5.28 ! [A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.28 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_unit_imp_unit
% 4.98/5.28 thf(fact_3191_dvd__add,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ A @ C )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add
% 4.98/5.28 thf(fact_3192_dvd__add,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_real @ A @ C )
% 4.98/5.28 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add
% 4.98/5.28 thf(fact_3193_dvd__add,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_rat @ A @ C )
% 4.98/5.28 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add
% 4.98/5.28 thf(fact_3194_dvd__add,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_nat @ A @ C )
% 4.98/5.28 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add
% 4.98/5.28 thf(fact_3195_dvd__add,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_int @ A @ C )
% 4.98/5.28 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add
% 4.98/5.28 thf(fact_3196_dvd__add__left__iff,axiom,
% 4.98/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ C )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_left_iff
% 4.98/5.28 thf(fact_3197_dvd__add__left__iff,axiom,
% 4.98/5.28 ! [A: real,C: real,B: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ A @ C )
% 4.98/5.28 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_left_iff
% 4.98/5.28 thf(fact_3198_dvd__add__left__iff,axiom,
% 4.98/5.28 ! [A: rat,C: rat,B: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ A @ C )
% 4.98/5.28 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_left_iff
% 4.98/5.28 thf(fact_3199_dvd__add__left__iff,axiom,
% 4.98/5.28 ! [A: nat,C: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ C )
% 4.98/5.28 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_left_iff
% 4.98/5.28 thf(fact_3200_dvd__add__left__iff,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ C )
% 4.98/5.28 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_left_iff
% 4.98/5.28 thf(fact_3201_dvd__add__right__iff,axiom,
% 4.98/5.28 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_right_iff
% 4.98/5.28 thf(fact_3202_dvd__add__right__iff,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_right_iff
% 4.98/5.28 thf(fact_3203_dvd__add__right__iff,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_right_iff
% 4.98/5.28 thf(fact_3204_dvd__add__right__iff,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_right_iff
% 4.98/5.28 thf(fact_3205_dvd__add__right__iff,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ A @ B )
% 4.98/5.28 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.98/5.28 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_add_right_iff
% 4.98/5.28 thf(fact_3206_inf__period_I1_J,axiom,
% 4.98/5.28 ! [P: real > $o,D4: real,Q: real > $o] :
% 4.98/5.28 ( ! [X5: real,K2: real] :
% 4.98/5.28 ( ( P @ X5 )
% 4.98/5.28 = ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ( ! [X5: real,K2: real] :
% 4.98/5.28 ( ( Q @ X5 )
% 4.98/5.28 = ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ! [X3: real,K4: real] :
% 4.98/5.28 ( ( ( P @ X3 )
% 4.98/5.28 & ( Q @ X3 ) )
% 4.98/5.28 = ( ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) )
% 4.98/5.28 & ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(1)
% 4.98/5.28 thf(fact_3207_inf__period_I1_J,axiom,
% 4.98/5.28 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 4.98/5.28 ( ! [X5: rat,K2: rat] :
% 4.98/5.28 ( ( P @ X5 )
% 4.98/5.28 = ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ( ! [X5: rat,K2: rat] :
% 4.98/5.28 ( ( Q @ X5 )
% 4.98/5.28 = ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ! [X3: rat,K4: rat] :
% 4.98/5.28 ( ( ( P @ X3 )
% 4.98/5.28 & ( Q @ X3 ) )
% 4.98/5.28 = ( ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) )
% 4.98/5.28 & ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(1)
% 4.98/5.28 thf(fact_3208_inf__period_I1_J,axiom,
% 4.98/5.28 ! [P: int > $o,D4: int,Q: int > $o] :
% 4.98/5.28 ( ! [X5: int,K2: int] :
% 4.98/5.28 ( ( P @ X5 )
% 4.98/5.28 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ( ! [X5: int,K2: int] :
% 4.98/5.28 ( ( Q @ X5 )
% 4.98/5.28 = ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ! [X3: int,K4: int] :
% 4.98/5.28 ( ( ( P @ X3 )
% 4.98/5.28 & ( Q @ X3 ) )
% 4.98/5.28 = ( ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) )
% 4.98/5.28 & ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(1)
% 4.98/5.28 thf(fact_3209_inf__period_I2_J,axiom,
% 4.98/5.28 ! [P: real > $o,D4: real,Q: real > $o] :
% 4.98/5.28 ( ! [X5: real,K2: real] :
% 4.98/5.28 ( ( P @ X5 )
% 4.98/5.28 = ( P @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ( ! [X5: real,K2: real] :
% 4.98/5.28 ( ( Q @ X5 )
% 4.98/5.28 = ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ! [X3: real,K4: real] :
% 4.98/5.28 ( ( ( P @ X3 )
% 4.98/5.28 | ( Q @ X3 ) )
% 4.98/5.28 = ( ( P @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) )
% 4.98/5.28 | ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(2)
% 4.98/5.28 thf(fact_3210_inf__period_I2_J,axiom,
% 4.98/5.28 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 4.98/5.28 ( ! [X5: rat,K2: rat] :
% 4.98/5.28 ( ( P @ X5 )
% 4.98/5.28 = ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ( ! [X5: rat,K2: rat] :
% 4.98/5.28 ( ( Q @ X5 )
% 4.98/5.28 = ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ! [X3: rat,K4: rat] :
% 4.98/5.28 ( ( ( P @ X3 )
% 4.98/5.28 | ( Q @ X3 ) )
% 4.98/5.28 = ( ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) )
% 4.98/5.28 | ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(2)
% 4.98/5.28 thf(fact_3211_inf__period_I2_J,axiom,
% 4.98/5.28 ! [P: int > $o,D4: int,Q: int > $o] :
% 4.98/5.28 ( ! [X5: int,K2: int] :
% 4.98/5.28 ( ( P @ X5 )
% 4.98/5.28 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ( ! [X5: int,K2: int] :
% 4.98/5.28 ( ( Q @ X5 )
% 4.98/5.28 = ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 4.98/5.28 => ! [X3: int,K4: int] :
% 4.98/5.28 ( ( ( P @ X3 )
% 4.98/5.28 | ( Q @ X3 ) )
% 4.98/5.28 = ( ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) )
% 4.98/5.28 | ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % inf_period(2)
% 4.98/5.28 thf(fact_3212_right__diff__distrib_H,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.98/5.28 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib'
% 4.98/5.28 thf(fact_3213_right__diff__distrib_H,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.98/5.28 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib'
% 4.98/5.28 thf(fact_3214_right__diff__distrib_H,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 4.98/5.28 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib'
% 4.98/5.28 thf(fact_3215_right__diff__distrib_H,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.98/5.28 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib'
% 4.98/5.28 thf(fact_3216_left__diff__distrib_H,axiom,
% 4.98/5.28 ! [B: real,C: real,A: real] :
% 4.98/5.28 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 4.98/5.28 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib'
% 4.98/5.28 thf(fact_3217_left__diff__distrib_H,axiom,
% 4.98/5.28 ! [B: rat,C: rat,A: rat] :
% 4.98/5.28 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 4.98/5.28 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib'
% 4.98/5.28 thf(fact_3218_left__diff__distrib_H,axiom,
% 4.98/5.28 ! [B: nat,C: nat,A: nat] :
% 4.98/5.28 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 4.98/5.28 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib'
% 4.98/5.28 thf(fact_3219_left__diff__distrib_H,axiom,
% 4.98/5.28 ! [B: int,C: int,A: int] :
% 4.98/5.28 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 4.98/5.28 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib'
% 4.98/5.28 thf(fact_3220_right__diff__distrib,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.98/5.28 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib
% 4.98/5.28 thf(fact_3221_right__diff__distrib,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.98/5.28 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib
% 4.98/5.28 thf(fact_3222_right__diff__distrib,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.98/5.28 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % right_diff_distrib
% 4.98/5.28 thf(fact_3223_left__diff__distrib,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib
% 4.98/5.28 thf(fact_3224_left__diff__distrib,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib
% 4.98/5.28 thf(fact_3225_left__diff__distrib,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % left_diff_distrib
% 4.98/5.28 thf(fact_3226_dvd__div__eq__iff,axiom,
% 4.98/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.28 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 4.98/5.28 = ( divide6298287555418463151nteger @ B @ C ) )
% 4.98/5.28 = ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_iff
% 4.98/5.28 thf(fact_3227_dvd__div__eq__iff,axiom,
% 4.98/5.28 ! [C: complex,A: complex,B: complex] :
% 4.98/5.28 ( ( dvd_dvd_complex @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_complex @ C @ B )
% 4.98/5.28 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 4.98/5.28 = ( divide1717551699836669952omplex @ B @ C ) )
% 4.98/5.28 = ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_iff
% 4.98/5.28 thf(fact_3228_dvd__div__eq__iff,axiom,
% 4.98/5.28 ! [C: real,A: real,B: real] :
% 4.98/5.28 ( ( dvd_dvd_real @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_real @ C @ B )
% 4.98/5.28 => ( ( ( divide_divide_real @ A @ C )
% 4.98/5.28 = ( divide_divide_real @ B @ C ) )
% 4.98/5.28 = ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_iff
% 4.98/5.28 thf(fact_3229_dvd__div__eq__iff,axiom,
% 4.98/5.28 ! [C: rat,A: rat,B: rat] :
% 4.98/5.28 ( ( dvd_dvd_rat @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_rat @ C @ B )
% 4.98/5.28 => ( ( ( divide_divide_rat @ A @ C )
% 4.98/5.28 = ( divide_divide_rat @ B @ C ) )
% 4.98/5.28 = ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_iff
% 4.98/5.28 thf(fact_3230_dvd__div__eq__iff,axiom,
% 4.98/5.28 ! [C: nat,A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.28 => ( ( ( divide_divide_nat @ A @ C )
% 4.98/5.28 = ( divide_divide_nat @ B @ C ) )
% 4.98/5.28 = ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_iff
% 4.98/5.28 thf(fact_3231_dvd__div__eq__iff,axiom,
% 4.98/5.28 ! [C: int,A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_int @ C @ B )
% 4.98/5.28 => ( ( ( divide_divide_int @ A @ C )
% 4.98/5.28 = ( divide_divide_int @ B @ C ) )
% 4.98/5.28 = ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_iff
% 4.98/5.28 thf(fact_3232_dvd__div__eq__cancel,axiom,
% 4.98/5.28 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.98/5.28 ( ( ( divide6298287555418463151nteger @ A @ C )
% 4.98/5.28 = ( divide6298287555418463151nteger @ B @ C ) )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.28 => ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_cancel
% 4.98/5.28 thf(fact_3233_dvd__div__eq__cancel,axiom,
% 4.98/5.28 ! [A: complex,C: complex,B: complex] :
% 4.98/5.28 ( ( ( divide1717551699836669952omplex @ A @ C )
% 4.98/5.28 = ( divide1717551699836669952omplex @ B @ C ) )
% 4.98/5.28 => ( ( dvd_dvd_complex @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_complex @ C @ B )
% 4.98/5.28 => ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_cancel
% 4.98/5.28 thf(fact_3234_dvd__div__eq__cancel,axiom,
% 4.98/5.28 ! [A: real,C: real,B: real] :
% 4.98/5.28 ( ( ( divide_divide_real @ A @ C )
% 4.98/5.28 = ( divide_divide_real @ B @ C ) )
% 4.98/5.28 => ( ( dvd_dvd_real @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_real @ C @ B )
% 4.98/5.28 => ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_cancel
% 4.98/5.28 thf(fact_3235_dvd__div__eq__cancel,axiom,
% 4.98/5.28 ! [A: rat,C: rat,B: rat] :
% 4.98/5.28 ( ( ( divide_divide_rat @ A @ C )
% 4.98/5.28 = ( divide_divide_rat @ B @ C ) )
% 4.98/5.28 => ( ( dvd_dvd_rat @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_rat @ C @ B )
% 4.98/5.28 => ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_cancel
% 4.98/5.28 thf(fact_3236_dvd__div__eq__cancel,axiom,
% 4.98/5.28 ! [A: nat,C: nat,B: nat] :
% 4.98/5.28 ( ( ( divide_divide_nat @ A @ C )
% 4.98/5.28 = ( divide_divide_nat @ B @ C ) )
% 4.98/5.28 => ( ( dvd_dvd_nat @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.28 => ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_cancel
% 4.98/5.28 thf(fact_3237_dvd__div__eq__cancel,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( ( divide_divide_int @ A @ C )
% 4.98/5.28 = ( divide_divide_int @ B @ C ) )
% 4.98/5.28 => ( ( dvd_dvd_int @ C @ A )
% 4.98/5.28 => ( ( dvd_dvd_int @ C @ B )
% 4.98/5.28 => ( A = B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_div_eq_cancel
% 4.98/5.28 thf(fact_3238_div__div__div__same,axiom,
% 4.98/5.28 ! [D: code_integer,B: code_integer,A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ D @ B )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ B @ A )
% 4.98/5.28 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 4.98/5.28 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % div_div_div_same
% 4.98/5.28 thf(fact_3239_div__div__div__same,axiom,
% 4.98/5.28 ! [D: nat,B: nat,A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ D @ B )
% 4.98/5.28 => ( ( dvd_dvd_nat @ B @ A )
% 4.98/5.28 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 4.98/5.28 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % div_div_div_same
% 4.98/5.28 thf(fact_3240_div__div__div__same,axiom,
% 4.98/5.28 ! [D: int,B: int,A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ D @ B )
% 4.98/5.28 => ( ( dvd_dvd_int @ B @ A )
% 4.98/5.28 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 4.98/5.28 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % div_div_div_same
% 4.98/5.28 thf(fact_3241_add__diff__add,axiom,
% 4.98/5.28 ! [A: real,C: real,B: real,D: real] :
% 4.98/5.28 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 4.98/5.28 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_diff_add
% 4.98/5.28 thf(fact_3242_add__diff__add,axiom,
% 4.98/5.28 ! [A: rat,C: rat,B: rat,D: rat] :
% 4.98/5.28 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 4.98/5.28 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_diff_add
% 4.98/5.28 thf(fact_3243_add__diff__add,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int,D: int] :
% 4.98/5.28 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 4.98/5.28 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_diff_add
% 4.98/5.28 thf(fact_3244_group__cancel_Osub1,axiom,
% 4.98/5.28 ! [A3: real,K: real,A: real,B: real] :
% 4.98/5.28 ( ( A3
% 4.98/5.28 = ( plus_plus_real @ K @ A ) )
% 4.98/5.28 => ( ( minus_minus_real @ A3 @ B )
% 4.98/5.28 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % group_cancel.sub1
% 4.98/5.28 thf(fact_3245_group__cancel_Osub1,axiom,
% 4.98/5.28 ! [A3: rat,K: rat,A: rat,B: rat] :
% 4.98/5.28 ( ( A3
% 4.98/5.28 = ( plus_plus_rat @ K @ A ) )
% 4.98/5.28 => ( ( minus_minus_rat @ A3 @ B )
% 4.98/5.28 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % group_cancel.sub1
% 4.98/5.28 thf(fact_3246_group__cancel_Osub1,axiom,
% 4.98/5.28 ! [A3: int,K: int,A: int,B: int] :
% 4.98/5.28 ( ( A3
% 4.98/5.28 = ( plus_plus_int @ K @ A ) )
% 4.98/5.28 => ( ( minus_minus_int @ A3 @ B )
% 4.98/5.28 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % group_cancel.sub1
% 4.98/5.28 thf(fact_3247_diff__eq__eq,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( ( minus_minus_real @ A @ B )
% 4.98/5.28 = C )
% 4.98/5.28 = ( A
% 4.98/5.28 = ( plus_plus_real @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_eq
% 4.98/5.28 thf(fact_3248_diff__eq__eq,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( ( minus_minus_rat @ A @ B )
% 4.98/5.28 = C )
% 4.98/5.28 = ( A
% 4.98/5.28 = ( plus_plus_rat @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_eq
% 4.98/5.28 thf(fact_3249_diff__eq__eq,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( ( minus_minus_int @ A @ B )
% 4.98/5.28 = C )
% 4.98/5.28 = ( A
% 4.98/5.28 = ( plus_plus_int @ C @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_eq_eq
% 4.98/5.28 thf(fact_3250_eq__diff__eq,axiom,
% 4.98/5.28 ! [A: real,C: real,B: real] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( minus_minus_real @ C @ B ) )
% 4.98/5.28 = ( ( plus_plus_real @ A @ B )
% 4.98/5.28 = C ) ) ).
% 4.98/5.28
% 4.98/5.28 % eq_diff_eq
% 4.98/5.28 thf(fact_3251_eq__diff__eq,axiom,
% 4.98/5.28 ! [A: rat,C: rat,B: rat] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( minus_minus_rat @ C @ B ) )
% 4.98/5.28 = ( ( plus_plus_rat @ A @ B )
% 4.98/5.28 = C ) ) ).
% 4.98/5.28
% 4.98/5.28 % eq_diff_eq
% 4.98/5.28 thf(fact_3252_eq__diff__eq,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( A
% 4.98/5.28 = ( minus_minus_int @ C @ B ) )
% 4.98/5.28 = ( ( plus_plus_int @ A @ B )
% 4.98/5.28 = C ) ) ).
% 4.98/5.28
% 4.98/5.28 % eq_diff_eq
% 4.98/5.28 thf(fact_3253_add__diff__eq,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.98/5.28 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_diff_eq
% 4.98/5.28 thf(fact_3254_add__diff__eq,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.98/5.28 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_diff_eq
% 4.98/5.28 thf(fact_3255_add__diff__eq,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.98/5.28 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_diff_eq
% 4.98/5.28 thf(fact_3256_diff__diff__eq2,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 4.98/5.28 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_diff_eq2
% 4.98/5.28 thf(fact_3257_diff__diff__eq2,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 4.98/5.28 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_diff_eq2
% 4.98/5.28 thf(fact_3258_diff__diff__eq2,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 4.98/5.28 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_diff_eq2
% 4.98/5.28 thf(fact_3259_diff__add__eq,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_add_eq
% 4.98/5.28 thf(fact_3260_diff__add__eq,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_add_eq
% 4.98/5.28 thf(fact_3261_diff__add__eq,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_add_eq
% 4.98/5.28 thf(fact_3262_diff__add__eq__diff__diff__swap,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 4.98/5.28 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_add_eq_diff_diff_swap
% 4.98/5.28 thf(fact_3263_diff__add__eq__diff__diff__swap,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 4.98/5.28 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_add_eq_diff_diff_swap
% 4.98/5.28 thf(fact_3264_diff__add__eq__diff__diff__swap,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 4.98/5.28 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_add_eq_diff_diff_swap
% 4.98/5.28 thf(fact_3265_add__implies__diff,axiom,
% 4.98/5.28 ! [C: real,B: real,A: real] :
% 4.98/5.28 ( ( ( plus_plus_real @ C @ B )
% 4.98/5.28 = A )
% 4.98/5.28 => ( C
% 4.98/5.28 = ( minus_minus_real @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_implies_diff
% 4.98/5.28 thf(fact_3266_add__implies__diff,axiom,
% 4.98/5.28 ! [C: rat,B: rat,A: rat] :
% 4.98/5.28 ( ( ( plus_plus_rat @ C @ B )
% 4.98/5.28 = A )
% 4.98/5.28 => ( C
% 4.98/5.28 = ( minus_minus_rat @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_implies_diff
% 4.98/5.28 thf(fact_3267_add__implies__diff,axiom,
% 4.98/5.28 ! [C: nat,B: nat,A: nat] :
% 4.98/5.28 ( ( ( plus_plus_nat @ C @ B )
% 4.98/5.28 = A )
% 4.98/5.28 => ( C
% 4.98/5.28 = ( minus_minus_nat @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_implies_diff
% 4.98/5.28 thf(fact_3268_add__implies__diff,axiom,
% 4.98/5.28 ! [C: int,B: int,A: int] :
% 4.98/5.28 ( ( ( plus_plus_int @ C @ B )
% 4.98/5.28 = A )
% 4.98/5.28 => ( C
% 4.98/5.28 = ( minus_minus_int @ A @ B ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % add_implies_diff
% 4.98/5.28 thf(fact_3269_diff__diff__eq,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_diff_eq
% 4.98/5.28 thf(fact_3270_diff__diff__eq,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_diff_eq
% 4.98/5.28 thf(fact_3271_diff__diff__eq,axiom,
% 4.98/5.28 ! [A: nat,B: nat,C: nat] :
% 4.98/5.28 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_diff_eq
% 4.98/5.28 thf(fact_3272_diff__diff__eq,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_diff_eq
% 4.98/5.28 thf(fact_3273_dvd__power__same,axiom,
% 4.98/5.28 ! [X2: code_integer,Y: code_integer,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ X2 @ Y )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_power_same
% 4.98/5.28 thf(fact_3274_dvd__power__same,axiom,
% 4.98/5.28 ! [X2: nat,Y: nat,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ X2 @ Y )
% 4.98/5.28 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_power_same
% 4.98/5.28 thf(fact_3275_dvd__power__same,axiom,
% 4.98/5.28 ! [X2: int,Y: int,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_int @ X2 @ Y )
% 4.98/5.28 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N2 ) @ ( power_power_int @ Y @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_power_same
% 4.98/5.28 thf(fact_3276_dvd__power__same,axiom,
% 4.98/5.28 ! [X2: real,Y: real,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_real @ X2 @ Y )
% 4.98/5.28 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_power_same
% 4.98/5.28 thf(fact_3277_dvd__power__same,axiom,
% 4.98/5.28 ! [X2: complex,Y: complex,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_complex @ X2 @ Y )
% 4.98/5.28 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_power_same
% 4.98/5.28 thf(fact_3278_diff__divide__distrib,axiom,
% 4.98/5.28 ! [A: complex,B: complex,C: complex] :
% 4.98/5.28 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_divide_distrib
% 4.98/5.28 thf(fact_3279_diff__divide__distrib,axiom,
% 4.98/5.28 ! [A: real,B: real,C: real] :
% 4.98/5.28 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_divide_distrib
% 4.98/5.28 thf(fact_3280_diff__divide__distrib,axiom,
% 4.98/5.28 ! [A: rat,B: rat,C: rat] :
% 4.98/5.28 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.98/5.28 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % diff_divide_distrib
% 4.98/5.28 thf(fact_3281_gcd__nat_Oextremum,axiom,
% 4.98/5.28 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 4.98/5.28
% 4.98/5.28 % gcd_nat.extremum
% 4.98/5.28 thf(fact_3282_gcd__nat_Oextremum__strict,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 4.98/5.28 & ( zero_zero_nat != A ) ) ).
% 4.98/5.28
% 4.98/5.28 % gcd_nat.extremum_strict
% 4.98/5.28 thf(fact_3283_gcd__nat_Oextremum__unique,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 4.98/5.28 = ( A = zero_zero_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % gcd_nat.extremum_unique
% 4.98/5.28 thf(fact_3284_gcd__nat_Onot__eq__extremum,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( A != zero_zero_nat )
% 4.98/5.28 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 4.98/5.28 & ( A != zero_zero_nat ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % gcd_nat.not_eq_extremum
% 4.98/5.28 thf(fact_3285_gcd__nat_Oextremum__uniqueI,axiom,
% 4.98/5.28 ! [A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 4.98/5.28 => ( A = zero_zero_nat ) ) ).
% 4.98/5.28
% 4.98/5.28 % gcd_nat.extremum_uniqueI
% 4.98/5.28 thf(fact_3286_dvd__mod__imp__dvd,axiom,
% 4.98/5.28 ! [C: code_integer,A: code_integer,B: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod_imp_dvd
% 4.98/5.28 thf(fact_3287_dvd__mod__imp__dvd,axiom,
% 4.98/5.28 ! [C: nat,A: nat,B: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 4.98/5.28 => ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.28 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod_imp_dvd
% 4.98/5.28 thf(fact_3288_dvd__mod__imp__dvd,axiom,
% 4.98/5.28 ! [C: int,A: int,B: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 4.98/5.28 => ( ( dvd_dvd_int @ C @ B )
% 4.98/5.28 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod_imp_dvd
% 4.98/5.28 thf(fact_3289_dvd__mod__iff,axiom,
% 4.98/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 4.98/5.28 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod_iff
% 4.98/5.28 thf(fact_3290_dvd__mod__iff,axiom,
% 4.98/5.28 ! [C: nat,B: nat,A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.28 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 4.98/5.28 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod_iff
% 4.98/5.28 thf(fact_3291_dvd__mod__iff,axiom,
% 4.98/5.28 ! [C: int,B: int,A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ C @ B )
% 4.98/5.28 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 4.98/5.28 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod_iff
% 4.98/5.28 thf(fact_3292_mod__mod__cancel,axiom,
% 4.98/5.28 ! [C: code_integer,B: code_integer,A: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.28 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 4.98/5.28 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_mod_cancel
% 4.98/5.28 thf(fact_3293_mod__mod__cancel,axiom,
% 4.98/5.28 ! [C: nat,B: nat,A: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.28 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 4.98/5.28 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_mod_cancel
% 4.98/5.28 thf(fact_3294_mod__mod__cancel,axiom,
% 4.98/5.28 ! [C: int,B: int,A: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ C @ B )
% 4.98/5.28 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 4.98/5.28 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_mod_cancel
% 4.98/5.28 thf(fact_3295_dvd__mod,axiom,
% 4.98/5.28 ! [K: code_integer,M: code_integer,N2: code_integer] :
% 4.98/5.28 ( ( dvd_dvd_Code_integer @ K @ M )
% 4.98/5.28 => ( ( dvd_dvd_Code_integer @ K @ N2 )
% 4.98/5.28 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N2 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod
% 4.98/5.28 thf(fact_3296_dvd__mod,axiom,
% 4.98/5.28 ! [K: nat,M: nat,N2: nat] :
% 4.98/5.28 ( ( dvd_dvd_nat @ K @ M )
% 4.98/5.28 => ( ( dvd_dvd_nat @ K @ N2 )
% 4.98/5.28 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod
% 4.98/5.28 thf(fact_3297_dvd__mod,axiom,
% 4.98/5.28 ! [K: int,M: int,N2: int] :
% 4.98/5.28 ( ( dvd_dvd_int @ K @ M )
% 4.98/5.28 => ( ( dvd_dvd_int @ K @ N2 )
% 4.98/5.28 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N2 ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % dvd_mod
% 4.98/5.28 thf(fact_3298_mod__diff__right__eq,axiom,
% 4.98/5.28 ! [A: int,B: int,C: int] :
% 4.98/5.28 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 4.98/5.28 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_diff_right_eq
% 4.98/5.28 thf(fact_3299_mod__diff__left__eq,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 4.98/5.28 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_diff_left_eq
% 4.98/5.28 thf(fact_3300_mod__diff__cong,axiom,
% 4.98/5.28 ! [A: int,C: int,A2: int,B: int,B2: int] :
% 4.98/5.28 ( ( ( modulo_modulo_int @ A @ C )
% 4.98/5.28 = ( modulo_modulo_int @ A2 @ C ) )
% 4.98/5.28 => ( ( ( modulo_modulo_int @ B @ C )
% 4.98/5.28 = ( modulo_modulo_int @ B2 @ C ) )
% 4.98/5.28 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.98/5.28 = ( modulo_modulo_int @ ( minus_minus_int @ A2 @ B2 ) @ C ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_diff_cong
% 4.98/5.28 thf(fact_3301_mod__diff__eq,axiom,
% 4.98/5.28 ! [A: int,C: int,B: int] :
% 4.98/5.28 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 4.98/5.28 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 4.98/5.28
% 4.98/5.28 % mod_diff_eq
% 4.98/5.28 thf(fact_3302_minus__int__code_I1_J,axiom,
% 4.98/5.28 ! [K: int] :
% 4.98/5.28 ( ( minus_minus_int @ K @ zero_zero_int )
% 4.98/5.28 = K ) ).
% 4.98/5.28
% 4.98/5.28 % minus_int_code(1)
% 4.98/5.28 thf(fact_3303_signed__take__bit__mult,axiom,
% 4.98/5.28 ! [N2: nat,K: int,L: int] :
% 4.98/5.28 ( ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 4.98/5.28 = ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % signed_take_bit_mult
% 4.98/5.28 thf(fact_3304_signed__take__bit__add,axiom,
% 4.98/5.28 ! [N2: nat,K: int,L: int] :
% 4.98/5.28 ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 4.98/5.28 = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % signed_take_bit_add
% 4.98/5.28 thf(fact_3305_int__distrib_I4_J,axiom,
% 4.98/5.28 ! [W: int,Z1: int,Z22: int] :
% 4.98/5.28 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 4.98/5.28 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % int_distrib(4)
% 4.98/5.28 thf(fact_3306_int__distrib_I3_J,axiom,
% 4.98/5.28 ! [Z1: int,Z22: int,W: int] :
% 4.98/5.28 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 4.98/5.28 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % int_distrib(3)
% 4.98/5.28 thf(fact_3307_max__diff__distrib__left,axiom,
% 4.98/5.28 ! [X2: real,Y: real,Z: real] :
% 4.98/5.28 ( ( minus_minus_real @ ( ord_max_real @ X2 @ Y ) @ Z )
% 4.98/5.28 = ( ord_max_real @ ( minus_minus_real @ X2 @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % max_diff_distrib_left
% 4.98/5.28 thf(fact_3308_max__diff__distrib__left,axiom,
% 4.98/5.28 ! [X2: rat,Y: rat,Z: rat] :
% 4.98/5.28 ( ( minus_minus_rat @ ( ord_max_rat @ X2 @ Y ) @ Z )
% 4.98/5.28 = ( ord_max_rat @ ( minus_minus_rat @ X2 @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % max_diff_distrib_left
% 4.98/5.28 thf(fact_3309_max__diff__distrib__left,axiom,
% 4.98/5.28 ! [X2: int,Y: int,Z: int] :
% 4.98/5.28 ( ( minus_minus_int @ ( ord_max_int @ X2 @ Y ) @ Z )
% 4.98/5.28 = ( ord_max_int @ ( minus_minus_int @ X2 @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % max_diff_distrib_left
% 4.98/5.28 thf(fact_3310_numeral__code_I2_J,axiom,
% 4.98/5.28 ! [N2: num] :
% 4.98/5.28 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 4.98/5.28 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % numeral_code(2)
% 4.98/5.28 thf(fact_3311_numeral__code_I2_J,axiom,
% 4.98/5.28 ! [N2: num] :
% 4.98/5.28 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 4.98/5.28 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % numeral_code(2)
% 4.98/5.28 thf(fact_3312_numeral__code_I2_J,axiom,
% 4.98/5.28 ! [N2: num] :
% 4.98/5.28 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 4.98/5.28 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % numeral_code(2)
% 4.98/5.28 thf(fact_3313_numeral__code_I2_J,axiom,
% 4.98/5.28 ! [N2: num] :
% 4.98/5.28 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 4.98/5.28 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % numeral_code(2)
% 4.98/5.28 thf(fact_3314_numeral__code_I2_J,axiom,
% 4.98/5.28 ! [N2: num] :
% 4.98/5.28 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 4.98/5.28 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % numeral_code(2)
% 4.98/5.28 thf(fact_3315_set__vebt__def,axiom,
% 4.98/5.28 ( vEBT_set_vebt
% 4.98/5.28 = ( ^ [T: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T ) ) ) ) ).
% 4.98/5.28
% 4.98/5.28 % set_vebt_def
% 4.98/5.28 thf(fact_3316_even__signed__take__bit__iff,axiom,
% 4.98/5.29 ! [M: nat,A: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 4.98/5.29
% 4.98/5.29 % even_signed_take_bit_iff
% 4.98/5.29 thf(fact_3317_even__signed__take__bit__iff,axiom,
% 4.98/5.29 ! [M: nat,A: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 4.98/5.29 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 4.98/5.29
% 4.98/5.29 % even_signed_take_bit_iff
% 4.98/5.29 thf(fact_3318_power__numeral__even,axiom,
% 4.98/5.29 ! [Z: complex,W: num] :
% 4.98/5.29 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 4.98/5.29 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % power_numeral_even
% 4.98/5.29 thf(fact_3319_power__numeral__even,axiom,
% 4.98/5.29 ! [Z: real,W: num] :
% 4.98/5.29 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 4.98/5.29 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % power_numeral_even
% 4.98/5.29 thf(fact_3320_power__numeral__even,axiom,
% 4.98/5.29 ! [Z: rat,W: num] :
% 4.98/5.29 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 4.98/5.29 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % power_numeral_even
% 4.98/5.29 thf(fact_3321_power__numeral__even,axiom,
% 4.98/5.29 ! [Z: nat,W: num] :
% 4.98/5.29 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 4.98/5.29 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % power_numeral_even
% 4.98/5.29 thf(fact_3322_power__numeral__even,axiom,
% 4.98/5.29 ! [Z: int,W: num] :
% 4.98/5.29 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 4.98/5.29 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % power_numeral_even
% 4.98/5.29 thf(fact_3323_even__diff__iff,axiom,
% 4.98/5.29 ! [K: int,L: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 4.98/5.29 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % even_diff_iff
% 4.98/5.29 thf(fact_3324_le__iff__diff__le__0,axiom,
% 4.98/5.29 ( ord_less_eq_real
% 4.98/5.29 = ( ^ [A5: real,B5: real] : ( ord_less_eq_real @ ( minus_minus_real @ A5 @ B5 ) @ zero_zero_real ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % le_iff_diff_le_0
% 4.98/5.29 thf(fact_3325_le__iff__diff__le__0,axiom,
% 4.98/5.29 ( ord_less_eq_rat
% 4.98/5.29 = ( ^ [A5: rat,B5: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B5 ) @ zero_zero_rat ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % le_iff_diff_le_0
% 4.98/5.29 thf(fact_3326_le__iff__diff__le__0,axiom,
% 4.98/5.29 ( ord_less_eq_int
% 4.98/5.29 = ( ^ [A5: int,B5: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B5 ) @ zero_zero_int ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % le_iff_diff_le_0
% 4.98/5.29 thf(fact_3327_not__is__unit__0,axiom,
% 4.98/5.29 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 4.98/5.29
% 4.98/5.29 % not_is_unit_0
% 4.98/5.29 thf(fact_3328_not__is__unit__0,axiom,
% 4.98/5.29 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 4.98/5.29
% 4.98/5.29 % not_is_unit_0
% 4.98/5.29 thf(fact_3329_not__is__unit__0,axiom,
% 4.98/5.29 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 4.98/5.29
% 4.98/5.29 % not_is_unit_0
% 4.98/5.29 thf(fact_3330_less__iff__diff__less__0,axiom,
% 4.98/5.29 ( ord_less_real
% 4.98/5.29 = ( ^ [A5: real,B5: real] : ( ord_less_real @ ( minus_minus_real @ A5 @ B5 ) @ zero_zero_real ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % less_iff_diff_less_0
% 4.98/5.29 thf(fact_3331_less__iff__diff__less__0,axiom,
% 4.98/5.29 ( ord_less_rat
% 4.98/5.29 = ( ^ [A5: rat,B5: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B5 ) @ zero_zero_rat ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % less_iff_diff_less_0
% 4.98/5.29 thf(fact_3332_less__iff__diff__less__0,axiom,
% 4.98/5.29 ( ord_less_int
% 4.98/5.29 = ( ^ [A5: int,B5: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B5 ) @ zero_zero_int ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % less_iff_diff_less_0
% 4.98/5.29 thf(fact_3333_minf_I10_J,axiom,
% 4.98/5.29 ! [D: code_integer,S2: code_integer] :
% 4.98/5.29 ? [Z3: code_integer] :
% 4.98/5.29 ! [X3: code_integer] :
% 4.98/5.29 ( ( ord_le6747313008572928689nteger @ X3 @ Z3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(10)
% 4.98/5.29 thf(fact_3334_minf_I10_J,axiom,
% 4.98/5.29 ! [D: real,S2: real] :
% 4.98/5.29 ? [Z3: real] :
% 4.98/5.29 ! [X3: real] :
% 4.98/5.29 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(10)
% 4.98/5.29 thf(fact_3335_minf_I10_J,axiom,
% 4.98/5.29 ! [D: rat,S2: rat] :
% 4.98/5.29 ? [Z3: rat] :
% 4.98/5.29 ! [X3: rat] :
% 4.98/5.29 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(10)
% 4.98/5.29 thf(fact_3336_minf_I10_J,axiom,
% 4.98/5.29 ! [D: nat,S2: nat] :
% 4.98/5.29 ? [Z3: nat] :
% 4.98/5.29 ! [X3: nat] :
% 4.98/5.29 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(10)
% 4.98/5.29 thf(fact_3337_minf_I10_J,axiom,
% 4.98/5.29 ! [D: int,S2: int] :
% 4.98/5.29 ? [Z3: int] :
% 4.98/5.29 ! [X3: int] :
% 4.98/5.29 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(10)
% 4.98/5.29 thf(fact_3338_minf_I9_J,axiom,
% 4.98/5.29 ! [D: code_integer,S2: code_integer] :
% 4.98/5.29 ? [Z3: code_integer] :
% 4.98/5.29 ! [X3: code_integer] :
% 4.98/5.29 ( ( ord_le6747313008572928689nteger @ X3 @ Z3 )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(9)
% 4.98/5.29 thf(fact_3339_minf_I9_J,axiom,
% 4.98/5.29 ! [D: real,S2: real] :
% 4.98/5.29 ? [Z3: real] :
% 4.98/5.29 ! [X3: real] :
% 4.98/5.29 ( ( ord_less_real @ X3 @ Z3 )
% 4.98/5.29 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(9)
% 4.98/5.29 thf(fact_3340_minf_I9_J,axiom,
% 4.98/5.29 ! [D: rat,S2: rat] :
% 4.98/5.29 ? [Z3: rat] :
% 4.98/5.29 ! [X3: rat] :
% 4.98/5.29 ( ( ord_less_rat @ X3 @ Z3 )
% 4.98/5.29 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(9)
% 4.98/5.29 thf(fact_3341_minf_I9_J,axiom,
% 4.98/5.29 ! [D: nat,S2: nat] :
% 4.98/5.29 ? [Z3: nat] :
% 4.98/5.29 ! [X3: nat] :
% 4.98/5.29 ( ( ord_less_nat @ X3 @ Z3 )
% 4.98/5.29 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(9)
% 4.98/5.29 thf(fact_3342_minf_I9_J,axiom,
% 4.98/5.29 ! [D: int,S2: int] :
% 4.98/5.29 ? [Z3: int] :
% 4.98/5.29 ! [X3: int] :
% 4.98/5.29 ( ( ord_less_int @ X3 @ Z3 )
% 4.98/5.29 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % minf(9)
% 4.98/5.29 thf(fact_3343_pinf_I10_J,axiom,
% 4.98/5.29 ! [D: code_integer,S2: code_integer] :
% 4.98/5.29 ? [Z3: code_integer] :
% 4.98/5.29 ! [X3: code_integer] :
% 4.98/5.29 ( ( ord_le6747313008572928689nteger @ Z3 @ X3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(10)
% 4.98/5.29 thf(fact_3344_pinf_I10_J,axiom,
% 4.98/5.29 ! [D: real,S2: real] :
% 4.98/5.29 ? [Z3: real] :
% 4.98/5.29 ! [X3: real] :
% 4.98/5.29 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(10)
% 4.98/5.29 thf(fact_3345_pinf_I10_J,axiom,
% 4.98/5.29 ! [D: rat,S2: rat] :
% 4.98/5.29 ? [Z3: rat] :
% 4.98/5.29 ! [X3: rat] :
% 4.98/5.29 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(10)
% 4.98/5.29 thf(fact_3346_pinf_I10_J,axiom,
% 4.98/5.29 ! [D: nat,S2: nat] :
% 4.98/5.29 ? [Z3: nat] :
% 4.98/5.29 ! [X3: nat] :
% 4.98/5.29 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(10)
% 4.98/5.29 thf(fact_3347_pinf_I10_J,axiom,
% 4.98/5.29 ! [D: int,S2: int] :
% 4.98/5.29 ? [Z3: int] :
% 4.98/5.29 ! [X3: int] :
% 4.98/5.29 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.29 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) )
% 4.98/5.29 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(10)
% 4.98/5.29 thf(fact_3348_pinf_I9_J,axiom,
% 4.98/5.29 ! [D: code_integer,S2: code_integer] :
% 4.98/5.29 ? [Z3: code_integer] :
% 4.98/5.29 ! [X3: code_integer] :
% 4.98/5.29 ( ( ord_le6747313008572928689nteger @ Z3 @ X3 )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(9)
% 4.98/5.29 thf(fact_3349_pinf_I9_J,axiom,
% 4.98/5.29 ! [D: real,S2: real] :
% 4.98/5.29 ? [Z3: real] :
% 4.98/5.29 ! [X3: real] :
% 4.98/5.29 ( ( ord_less_real @ Z3 @ X3 )
% 4.98/5.29 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(9)
% 4.98/5.29 thf(fact_3350_pinf_I9_J,axiom,
% 4.98/5.29 ! [D: rat,S2: rat] :
% 4.98/5.29 ? [Z3: rat] :
% 4.98/5.29 ! [X3: rat] :
% 4.98/5.29 ( ( ord_less_rat @ Z3 @ X3 )
% 4.98/5.29 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(9)
% 4.98/5.29 thf(fact_3351_pinf_I9_J,axiom,
% 4.98/5.29 ! [D: nat,S2: nat] :
% 4.98/5.29 ? [Z3: nat] :
% 4.98/5.29 ! [X3: nat] :
% 4.98/5.29 ( ( ord_less_nat @ Z3 @ X3 )
% 4.98/5.29 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(9)
% 4.98/5.29 thf(fact_3352_pinf_I9_J,axiom,
% 4.98/5.29 ! [D: int,S2: int] :
% 4.98/5.29 ? [Z3: int] :
% 4.98/5.29 ! [X3: int] :
% 4.98/5.29 ( ( ord_less_int @ Z3 @ X3 )
% 4.98/5.29 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) )
% 4.98/5.29 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ S2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % pinf(9)
% 4.98/5.29 thf(fact_3353_dvd__div__eq__0__iff,axiom,
% 4.98/5.29 ! [B: code_integer,A: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ B @ A )
% 4.98/5.29 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 4.98/5.29 = zero_z3403309356797280102nteger )
% 4.98/5.29 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_eq_0_iff
% 4.98/5.29 thf(fact_3354_dvd__div__eq__0__iff,axiom,
% 4.98/5.29 ! [B: complex,A: complex] :
% 4.98/5.29 ( ( dvd_dvd_complex @ B @ A )
% 4.98/5.29 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 4.98/5.29 = zero_zero_complex )
% 4.98/5.29 = ( A = zero_zero_complex ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_eq_0_iff
% 4.98/5.29 thf(fact_3355_dvd__div__eq__0__iff,axiom,
% 4.98/5.29 ! [B: real,A: real] :
% 4.98/5.29 ( ( dvd_dvd_real @ B @ A )
% 4.98/5.29 => ( ( ( divide_divide_real @ A @ B )
% 4.98/5.29 = zero_zero_real )
% 4.98/5.29 = ( A = zero_zero_real ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_eq_0_iff
% 4.98/5.29 thf(fact_3356_dvd__div__eq__0__iff,axiom,
% 4.98/5.29 ! [B: rat,A: rat] :
% 4.98/5.29 ( ( dvd_dvd_rat @ B @ A )
% 4.98/5.29 => ( ( ( divide_divide_rat @ A @ B )
% 4.98/5.29 = zero_zero_rat )
% 4.98/5.29 = ( A = zero_zero_rat ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_eq_0_iff
% 4.98/5.29 thf(fact_3357_dvd__div__eq__0__iff,axiom,
% 4.98/5.29 ! [B: nat,A: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ B @ A )
% 4.98/5.29 => ( ( ( divide_divide_nat @ A @ B )
% 4.98/5.29 = zero_zero_nat )
% 4.98/5.29 = ( A = zero_zero_nat ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_eq_0_iff
% 4.98/5.29 thf(fact_3358_dvd__div__eq__0__iff,axiom,
% 4.98/5.29 ! [B: int,A: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ B @ A )
% 4.98/5.29 => ( ( ( divide_divide_int @ A @ B )
% 4.98/5.29 = zero_zero_int )
% 4.98/5.29 = ( A = zero_zero_int ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_eq_0_iff
% 4.98/5.29 thf(fact_3359_is__unit__mult__iff,axiom,
% 4.98/5.29 ! [A: code_integer,B: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 4.98/5.29 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.29 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % is_unit_mult_iff
% 4.98/5.29 thf(fact_3360_is__unit__mult__iff,axiom,
% 4.98/5.29 ! [A: nat,B: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 4.98/5.29 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.29 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % is_unit_mult_iff
% 4.98/5.29 thf(fact_3361_is__unit__mult__iff,axiom,
% 4.98/5.29 ! [A: int,B: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 4.98/5.29 = ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.29 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % is_unit_mult_iff
% 4.98/5.29 thf(fact_3362_dvd__mult__unit__iff,axiom,
% 4.98/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_unit_iff
% 4.98/5.29 thf(fact_3363_dvd__mult__unit__iff,axiom,
% 4.98/5.29 ! [B: nat,A: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.29 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 4.98/5.29 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_unit_iff
% 4.98/5.29 thf(fact_3364_dvd__mult__unit__iff,axiom,
% 4.98/5.29 ! [B: int,A: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.29 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 4.98/5.29 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_unit_iff
% 4.98/5.29 thf(fact_3365_mult__unit__dvd__iff,axiom,
% 4.98/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_unit_dvd_iff
% 4.98/5.29 thf(fact_3366_mult__unit__dvd__iff,axiom,
% 4.98/5.29 ! [B: nat,A: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.29 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_unit_dvd_iff
% 4.98/5.29 thf(fact_3367_mult__unit__dvd__iff,axiom,
% 4.98/5.29 ! [B: int,A: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.29 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_unit_dvd_iff
% 4.98/5.29 thf(fact_3368_dvd__mult__unit__iff_H,axiom,
% 4.98/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_unit_iff'
% 4.98/5.29 thf(fact_3369_dvd__mult__unit__iff_H,axiom,
% 4.98/5.29 ! [B: nat,A: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.29 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 4.98/5.29 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_unit_iff'
% 4.98/5.29 thf(fact_3370_dvd__mult__unit__iff_H,axiom,
% 4.98/5.29 ! [B: int,A: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.29 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 4.98/5.29 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_unit_iff'
% 4.98/5.29 thf(fact_3371_mult__unit__dvd__iff_H,axiom,
% 4.98/5.29 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_unit_dvd_iff'
% 4.98/5.29 thf(fact_3372_mult__unit__dvd__iff_H,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.29 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_unit_dvd_iff'
% 4.98/5.29 thf(fact_3373_mult__unit__dvd__iff_H,axiom,
% 4.98/5.29 ! [A: int,B: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.29 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_unit_dvd_iff'
% 4.98/5.29 thf(fact_3374_unit__mult__left__cancel,axiom,
% 4.98/5.29 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.29 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 4.98/5.29 = ( times_3573771949741848930nteger @ A @ C ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_mult_left_cancel
% 4.98/5.29 thf(fact_3375_unit__mult__left__cancel,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.29 => ( ( ( times_times_nat @ A @ B )
% 4.98/5.29 = ( times_times_nat @ A @ C ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_mult_left_cancel
% 4.98/5.29 thf(fact_3376_unit__mult__left__cancel,axiom,
% 4.98/5.29 ! [A: int,B: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.29 => ( ( ( times_times_int @ A @ B )
% 4.98/5.29 = ( times_times_int @ A @ C ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_mult_left_cancel
% 4.98/5.29 thf(fact_3377_unit__mult__right__cancel,axiom,
% 4.98/5.29 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.29 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 4.98/5.29 = ( times_3573771949741848930nteger @ C @ A ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_mult_right_cancel
% 4.98/5.29 thf(fact_3378_unit__mult__right__cancel,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.29 => ( ( ( times_times_nat @ B @ A )
% 4.98/5.29 = ( times_times_nat @ C @ A ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_mult_right_cancel
% 4.98/5.29 thf(fact_3379_unit__mult__right__cancel,axiom,
% 4.98/5.29 ! [A: int,B: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.29 => ( ( ( times_times_int @ B @ A )
% 4.98/5.29 = ( times_times_int @ C @ A ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_mult_right_cancel
% 4.98/5.29 thf(fact_3380_diff__le__eq,axiom,
% 4.98/5.29 ! [A: real,B: real,C: real] :
% 4.98/5.29 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.98/5.29 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % diff_le_eq
% 4.98/5.29 thf(fact_3381_diff__le__eq,axiom,
% 4.98/5.29 ! [A: rat,B: rat,C: rat] :
% 4.98/5.29 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.98/5.29 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % diff_le_eq
% 4.98/5.29 thf(fact_3382_diff__le__eq,axiom,
% 4.98/5.29 ! [A: int,B: int,C: int] :
% 4.98/5.29 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.98/5.29 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % diff_le_eq
% 4.98/5.29 thf(fact_3383_le__diff__eq,axiom,
% 4.98/5.29 ! [A: real,C: real,B: real] :
% 4.98/5.29 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 4.98/5.29 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.98/5.29
% 4.98/5.29 % le_diff_eq
% 4.98/5.29 thf(fact_3384_le__diff__eq,axiom,
% 4.98/5.29 ! [A: rat,C: rat,B: rat] :
% 4.98/5.29 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 4.98/5.29 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.98/5.29
% 4.98/5.29 % le_diff_eq
% 4.98/5.29 thf(fact_3385_le__diff__eq,axiom,
% 4.98/5.29 ! [A: int,C: int,B: int] :
% 4.98/5.29 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 4.98/5.29 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.98/5.29
% 4.98/5.29 % le_diff_eq
% 4.98/5.29 thf(fact_3386_add__le__imp__le__diff,axiom,
% 4.98/5.29 ! [I3: real,K: real,N2: real] :
% 4.98/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ord_less_eq_real @ I3 @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % add_le_imp_le_diff
% 4.98/5.29 thf(fact_3387_add__le__imp__le__diff,axiom,
% 4.98/5.29 ! [I3: rat,K: rat,N2: rat] :
% 4.98/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ord_less_eq_rat @ I3 @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % add_le_imp_le_diff
% 4.98/5.29 thf(fact_3388_add__le__imp__le__diff,axiom,
% 4.98/5.29 ! [I3: nat,K: nat,N2: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ord_less_eq_nat @ I3 @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % add_le_imp_le_diff
% 4.98/5.29 thf(fact_3389_add__le__imp__le__diff,axiom,
% 4.98/5.29 ! [I3: int,K: int,N2: int] :
% 4.98/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ord_less_eq_int @ I3 @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % add_le_imp_le_diff
% 4.98/5.29 thf(fact_3390_diff__add,axiom,
% 4.98/5.29 ! [A: nat,B: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 4.98/5.29 = B ) ) ).
% 4.98/5.29
% 4.98/5.29 % diff_add
% 4.98/5.29 thf(fact_3391_add__le__add__imp__diff__le,axiom,
% 4.98/5.29 ! [I3: real,K: real,N2: real,J: real] :
% 4.98/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 4.98/5.29 => ( ( ord_less_eq_real @ ( plus_plus_real @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 4.98/5.29 => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % add_le_add_imp_diff_le
% 4.98/5.29 thf(fact_3392_add__le__add__imp__diff__le,axiom,
% 4.98/5.29 ! [I3: rat,K: rat,N2: rat,J: rat] :
% 4.98/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 4.98/5.29 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 4.98/5.29 => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % add_le_add_imp_diff_le
% 4.98/5.29 thf(fact_3393_add__le__add__imp__diff__le,axiom,
% 4.98/5.29 ! [I3: nat,K: nat,N2: nat,J: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 4.98/5.29 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 4.98/5.29 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % add_le_add_imp_diff_le
% 4.98/5.29 thf(fact_3394_add__le__add__imp__diff__le,axiom,
% 4.98/5.29 ! [I3: int,K: int,N2: int,J: int] :
% 4.98/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 4.98/5.29 => ( ( ord_less_eq_int @ ( plus_plus_int @ I3 @ K ) @ N2 )
% 4.98/5.29 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 4.98/5.29 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % add_le_add_imp_diff_le
% 4.98/5.29 thf(fact_3395_le__add__diff,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % le_add_diff
% 4.98/5.29 thf(fact_3396_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.98/5.29 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 4.98/5.29 thf(fact_3397_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.98/5.29 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 4.98/5.29 thf(fact_3398_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 4.98/5.29 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 4.98/5.29 thf(fact_3399_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 4.98/5.29 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 4.98/5.29 thf(fact_3400_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 4.98/5.29 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 4.98/5.29 thf(fact_3401_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 4.98/5.29 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 4.98/5.29 thf(fact_3402_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 4.98/5.29 ! [A: nat,B: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 4.98/5.29 = B ) ) ).
% 4.98/5.29
% 4.98/5.29 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 4.98/5.29 thf(fact_3403_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( ord_less_eq_nat @ A @ B )
% 4.98/5.29 => ( ( ( minus_minus_nat @ B @ A )
% 4.98/5.29 = C )
% 4.98/5.29 = ( B
% 4.98/5.29 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 4.98/5.29 thf(fact_3404_diff__less__eq,axiom,
% 4.98/5.29 ! [A: real,B: real,C: real] :
% 4.98/5.29 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 4.98/5.29 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % diff_less_eq
% 4.98/5.29 thf(fact_3405_diff__less__eq,axiom,
% 4.98/5.29 ! [A: rat,B: rat,C: rat] :
% 4.98/5.29 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 4.98/5.29 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % diff_less_eq
% 4.98/5.29 thf(fact_3406_diff__less__eq,axiom,
% 4.98/5.29 ! [A: int,B: int,C: int] :
% 4.98/5.29 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 4.98/5.29 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % diff_less_eq
% 4.98/5.29 thf(fact_3407_less__diff__eq,axiom,
% 4.98/5.29 ! [A: real,C: real,B: real] :
% 4.98/5.29 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 4.98/5.29 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 4.98/5.29
% 4.98/5.29 % less_diff_eq
% 4.98/5.29 thf(fact_3408_less__diff__eq,axiom,
% 4.98/5.29 ! [A: rat,C: rat,B: rat] :
% 4.98/5.29 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 4.98/5.29 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 4.98/5.29
% 4.98/5.29 % less_diff_eq
% 4.98/5.29 thf(fact_3409_less__diff__eq,axiom,
% 4.98/5.29 ! [A: int,C: int,B: int] :
% 4.98/5.29 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 4.98/5.29 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 4.98/5.29
% 4.98/5.29 % less_diff_eq
% 4.98/5.29 thf(fact_3410_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.98/5.29 ! [A: real,B: real] :
% 4.98/5.29 ( ~ ( ord_less_real @ A @ B )
% 4.98/5.29 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 4.98/5.29 = A ) ) ).
% 4.98/5.29
% 4.98/5.29 % linordered_semidom_class.add_diff_inverse
% 4.98/5.29 thf(fact_3411_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.98/5.29 ! [A: rat,B: rat] :
% 4.98/5.29 ( ~ ( ord_less_rat @ A @ B )
% 4.98/5.29 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 4.98/5.29 = A ) ) ).
% 4.98/5.29
% 4.98/5.29 % linordered_semidom_class.add_diff_inverse
% 4.98/5.29 thf(fact_3412_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.98/5.29 ! [A: nat,B: nat] :
% 4.98/5.29 ( ~ ( ord_less_nat @ A @ B )
% 4.98/5.29 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 4.98/5.29 = A ) ) ).
% 4.98/5.29
% 4.98/5.29 % linordered_semidom_class.add_diff_inverse
% 4.98/5.29 thf(fact_3413_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 4.98/5.29 ! [A: int,B: int] :
% 4.98/5.29 ( ~ ( ord_less_int @ A @ B )
% 4.98/5.29 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 4.98/5.29 = A ) ) ).
% 4.98/5.29
% 4.98/5.29 % linordered_semidom_class.add_diff_inverse
% 4.98/5.29 thf(fact_3414_dvd__div__mult,axiom,
% 4.98/5.29 ! [C: code_integer,B: code_integer,A: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.29 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 4.98/5.29 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_mult
% 4.98/5.29 thf(fact_3415_dvd__div__mult,axiom,
% 4.98/5.29 ! [C: nat,B: nat,A: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.29 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 4.98/5.29 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_mult
% 4.98/5.29 thf(fact_3416_dvd__div__mult,axiom,
% 4.98/5.29 ! [C: int,B: int,A: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ C @ B )
% 4.98/5.29 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 4.98/5.29 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_mult
% 4.98/5.29 thf(fact_3417_div__mult__swap,axiom,
% 4.98/5.29 ! [C: code_integer,B: code_integer,A: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.29 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 4.98/5.29 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_mult_swap
% 4.98/5.29 thf(fact_3418_div__mult__swap,axiom,
% 4.98/5.29 ! [C: nat,B: nat,A: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.29 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 4.98/5.29 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_mult_swap
% 4.98/5.29 thf(fact_3419_div__mult__swap,axiom,
% 4.98/5.29 ! [C: int,B: int,A: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ C @ B )
% 4.98/5.29 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 4.98/5.29 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_mult_swap
% 4.98/5.29 thf(fact_3420_div__div__eq__right,axiom,
% 4.98/5.29 ! [C: code_integer,B: code_integer,A: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ B @ A )
% 4.98/5.29 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 4.98/5.29 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_div_eq_right
% 4.98/5.29 thf(fact_3421_div__div__eq__right,axiom,
% 4.98/5.29 ! [C: nat,B: nat,A: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.29 => ( ( dvd_dvd_nat @ B @ A )
% 4.98/5.29 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 4.98/5.29 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_div_eq_right
% 4.98/5.29 thf(fact_3422_div__div__eq__right,axiom,
% 4.98/5.29 ! [C: int,B: int,A: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ C @ B )
% 4.98/5.29 => ( ( dvd_dvd_int @ B @ A )
% 4.98/5.29 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 4.98/5.29 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_div_eq_right
% 4.98/5.29 thf(fact_3423_dvd__div__mult2__eq,axiom,
% 4.98/5.29 ! [B: code_integer,C: code_integer,A: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 4.98/5.29 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 4.98/5.29 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_mult2_eq
% 4.98/5.29 thf(fact_3424_dvd__div__mult2__eq,axiom,
% 4.98/5.29 ! [B: nat,C: nat,A: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 4.98/5.29 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 4.98/5.29 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_mult2_eq
% 4.98/5.29 thf(fact_3425_dvd__div__mult2__eq,axiom,
% 4.98/5.29 ! [B: int,C: int,A: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 4.98/5.29 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 4.98/5.29 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_mult2_eq
% 4.98/5.29 thf(fact_3426_dvd__mult__imp__div,axiom,
% 4.98/5.29 ! [A: code_integer,C: code_integer,B: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 4.98/5.29 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_imp_div
% 4.98/5.29 thf(fact_3427_dvd__mult__imp__div,axiom,
% 4.98/5.29 ! [A: nat,C: nat,B: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 4.98/5.29 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_imp_div
% 4.98/5.29 thf(fact_3428_dvd__mult__imp__div,axiom,
% 4.98/5.29 ! [A: int,C: int,B: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 4.98/5.29 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_mult_imp_div
% 4.98/5.29 thf(fact_3429_div__mult__div__if__dvd,axiom,
% 4.98/5.29 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ B @ A )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ D @ C )
% 4.98/5.29 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 4.98/5.29 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_mult_div_if_dvd
% 4.98/5.29 thf(fact_3430_div__mult__div__if__dvd,axiom,
% 4.98/5.29 ! [B: nat,A: nat,D: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ B @ A )
% 4.98/5.29 => ( ( dvd_dvd_nat @ D @ C )
% 4.98/5.29 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 4.98/5.29 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_mult_div_if_dvd
% 4.98/5.29 thf(fact_3431_div__mult__div__if__dvd,axiom,
% 4.98/5.29 ! [B: int,A: int,D: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ B @ A )
% 4.98/5.29 => ( ( dvd_dvd_int @ D @ C )
% 4.98/5.29 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 4.98/5.29 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_mult_div_if_dvd
% 4.98/5.29 thf(fact_3432_unit__div__cancel,axiom,
% 4.98/5.29 ! [A: code_integer,B: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 4.98/5.29 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 4.98/5.29 = ( divide6298287555418463151nteger @ C @ A ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_div_cancel
% 4.98/5.29 thf(fact_3433_unit__div__cancel,axiom,
% 4.98/5.29 ! [A: nat,B: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 4.98/5.29 => ( ( ( divide_divide_nat @ B @ A )
% 4.98/5.29 = ( divide_divide_nat @ C @ A ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_div_cancel
% 4.98/5.29 thf(fact_3434_unit__div__cancel,axiom,
% 4.98/5.29 ! [A: int,B: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ A @ one_one_int )
% 4.98/5.29 => ( ( ( divide_divide_int @ B @ A )
% 4.98/5.29 = ( divide_divide_int @ C @ A ) )
% 4.98/5.29 = ( B = C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % unit_div_cancel
% 4.98/5.29 thf(fact_3435_div__unit__dvd__iff,axiom,
% 4.98/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_unit_dvd_iff
% 4.98/5.29 thf(fact_3436_div__unit__dvd__iff,axiom,
% 4.98/5.29 ! [B: nat,A: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.29 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_unit_dvd_iff
% 4.98/5.29 thf(fact_3437_div__unit__dvd__iff,axiom,
% 4.98/5.29 ! [B: int,A: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.29 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 4.98/5.29 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_unit_dvd_iff
% 4.98/5.29 thf(fact_3438_dvd__div__unit__iff,axiom,
% 4.98/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 4.98/5.29 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 4.98/5.29 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_unit_iff
% 4.98/5.29 thf(fact_3439_dvd__div__unit__iff,axiom,
% 4.98/5.29 ! [B: nat,A: nat,C: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 4.98/5.29 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 4.98/5.29 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_unit_iff
% 4.98/5.29 thf(fact_3440_dvd__div__unit__iff,axiom,
% 4.98/5.29 ! [B: int,A: int,C: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 4.98/5.29 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 4.98/5.29 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % dvd_div_unit_iff
% 4.98/5.29 thf(fact_3441_div__plus__div__distrib__dvd__right,axiom,
% 4.98/5.29 ! [C: code_integer,B: code_integer,A: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ C @ B )
% 4.98/5.29 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 4.98/5.29 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_plus_div_distrib_dvd_right
% 4.98/5.29 thf(fact_3442_div__plus__div__distrib__dvd__right,axiom,
% 4.98/5.29 ! [C: nat,B: nat,A: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ C @ B )
% 4.98/5.29 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.29 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_plus_div_distrib_dvd_right
% 4.98/5.29 thf(fact_3443_div__plus__div__distrib__dvd__right,axiom,
% 4.98/5.29 ! [C: int,B: int,A: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ C @ B )
% 4.98/5.29 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.29 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_plus_div_distrib_dvd_right
% 4.98/5.29 thf(fact_3444_div__plus__div__distrib__dvd__left,axiom,
% 4.98/5.29 ! [C: code_integer,A: code_integer,B: code_integer] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ C @ A )
% 4.98/5.29 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 4.98/5.29 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_plus_div_distrib_dvd_left
% 4.98/5.29 thf(fact_3445_div__plus__div__distrib__dvd__left,axiom,
% 4.98/5.29 ! [C: nat,A: nat,B: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ C @ A )
% 4.98/5.29 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 4.98/5.29 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_plus_div_distrib_dvd_left
% 4.98/5.29 thf(fact_3446_div__plus__div__distrib__dvd__left,axiom,
% 4.98/5.29 ! [C: int,A: int,B: int] :
% 4.98/5.29 ( ( dvd_dvd_int @ C @ A )
% 4.98/5.29 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 4.98/5.29 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_plus_div_distrib_dvd_left
% 4.98/5.29 thf(fact_3447_mult__diff__mult,axiom,
% 4.98/5.29 ! [X2: real,Y: real,A: real,B: real] :
% 4.98/5.29 ( ( minus_minus_real @ ( times_times_real @ X2 @ Y ) @ ( times_times_real @ A @ B ) )
% 4.98/5.29 = ( plus_plus_real @ ( times_times_real @ X2 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X2 @ A ) @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_diff_mult
% 4.98/5.29 thf(fact_3448_mult__diff__mult,axiom,
% 4.98/5.29 ! [X2: rat,Y: rat,A: rat,B: rat] :
% 4.98/5.29 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ Y ) @ ( times_times_rat @ A @ B ) )
% 4.98/5.29 = ( plus_plus_rat @ ( times_times_rat @ X2 @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X2 @ A ) @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_diff_mult
% 4.98/5.29 thf(fact_3449_mult__diff__mult,axiom,
% 4.98/5.29 ! [X2: int,Y: int,A: int,B: int] :
% 4.98/5.29 ( ( minus_minus_int @ ( times_times_int @ X2 @ Y ) @ ( times_times_int @ A @ B ) )
% 4.98/5.29 = ( plus_plus_int @ ( times_times_int @ X2 @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X2 @ A ) @ B ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % mult_diff_mult
% 4.98/5.29 thf(fact_3450_square__diff__square__factored,axiom,
% 4.98/5.29 ! [X2: real,Y: real] :
% 4.98/5.29 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) )
% 4.98/5.29 = ( times_times_real @ ( plus_plus_real @ X2 @ Y ) @ ( minus_minus_real @ X2 @ Y ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % square_diff_square_factored
% 4.98/5.29 thf(fact_3451_square__diff__square__factored,axiom,
% 4.98/5.29 ! [X2: rat,Y: rat] :
% 4.98/5.29 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ ( times_times_rat @ Y @ Y ) )
% 4.98/5.29 = ( times_times_rat @ ( plus_plus_rat @ X2 @ Y ) @ ( minus_minus_rat @ X2 @ Y ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % square_diff_square_factored
% 4.98/5.29 thf(fact_3452_square__diff__square__factored,axiom,
% 4.98/5.29 ! [X2: int,Y: int] :
% 4.98/5.29 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ ( times_times_int @ Y @ Y ) )
% 4.98/5.29 = ( times_times_int @ ( plus_plus_int @ X2 @ Y ) @ ( minus_minus_int @ X2 @ Y ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % square_diff_square_factored
% 4.98/5.29 thf(fact_3453_eq__add__iff2,axiom,
% 4.98/5.29 ! [A: real,E2: real,C: real,B: real,D: real] :
% 4.98/5.29 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 4.98/5.29 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 4.98/5.29 = ( C
% 4.98/5.29 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % eq_add_iff2
% 4.98/5.29 thf(fact_3454_eq__add__iff2,axiom,
% 4.98/5.29 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 4.98/5.29 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 4.98/5.29 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 4.98/5.29 = ( C
% 4.98/5.29 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % eq_add_iff2
% 4.98/5.29 thf(fact_3455_eq__add__iff2,axiom,
% 4.98/5.29 ! [A: int,E2: int,C: int,B: int,D: int] :
% 4.98/5.29 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 4.98/5.29 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 4.98/5.29 = ( C
% 4.98/5.29 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % eq_add_iff2
% 4.98/5.29 thf(fact_3456_eq__add__iff1,axiom,
% 4.98/5.29 ! [A: real,E2: real,C: real,B: real,D: real] :
% 4.98/5.29 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 4.98/5.29 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 4.98/5.29 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 4.98/5.29 = D ) ) ).
% 4.98/5.29
% 4.98/5.29 % eq_add_iff1
% 4.98/5.29 thf(fact_3457_eq__add__iff1,axiom,
% 4.98/5.29 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 4.98/5.29 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 4.98/5.29 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 4.98/5.29 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 4.98/5.29 = D ) ) ).
% 4.98/5.29
% 4.98/5.29 % eq_add_iff1
% 4.98/5.29 thf(fact_3458_eq__add__iff1,axiom,
% 4.98/5.29 ! [A: int,E2: int,C: int,B: int,D: int] :
% 4.98/5.29 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 4.98/5.29 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 4.98/5.29 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 4.98/5.29 = D ) ) ).
% 4.98/5.29
% 4.98/5.29 % eq_add_iff1
% 4.98/5.29 thf(fact_3459_div__power,axiom,
% 4.98/5.29 ! [B: code_integer,A: code_integer,N2: nat] :
% 4.98/5.29 ( ( dvd_dvd_Code_integer @ B @ A )
% 4.98/5.29 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N2 )
% 4.98/5.29 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 4.98/5.29
% 4.98/5.29 % div_power
% 4.98/5.29 thf(fact_3460_div__power,axiom,
% 4.98/5.29 ! [B: nat,A: nat,N2: nat] :
% 4.98/5.29 ( ( dvd_dvd_nat @ B @ A )
% 5.02/5.29 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
% 5.02/5.29 = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_power
% 5.02/5.29 thf(fact_3461_div__power,axiom,
% 5.02/5.29 ! [B: int,A: int,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_int @ B @ A )
% 5.02/5.29 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N2 )
% 5.02/5.29 = ( divide_divide_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_power
% 5.02/5.29 thf(fact_3462_mod__eq__0__iff__dvd,axiom,
% 5.02/5.29 ! [A: code_integer,B: code_integer] :
% 5.02/5.29 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.02/5.29 = zero_z3403309356797280102nteger )
% 5.02/5.29 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_eq_0_iff_dvd
% 5.02/5.29 thf(fact_3463_mod__eq__0__iff__dvd,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( ( modulo_modulo_nat @ A @ B )
% 5.02/5.29 = zero_zero_nat )
% 5.02/5.29 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_eq_0_iff_dvd
% 5.02/5.29 thf(fact_3464_mod__eq__0__iff__dvd,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.29 = zero_zero_int )
% 5.02/5.29 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_eq_0_iff_dvd
% 5.02/5.29 thf(fact_3465_dvd__eq__mod__eq__0,axiom,
% 5.02/5.29 ( dvd_dvd_Code_integer
% 5.02/5.29 = ( ^ [A5: code_integer,B5: code_integer] :
% 5.02/5.29 ( ( modulo364778990260209775nteger @ B5 @ A5 )
% 5.02/5.29 = zero_z3403309356797280102nteger ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_eq_mod_eq_0
% 5.02/5.29 thf(fact_3466_dvd__eq__mod__eq__0,axiom,
% 5.02/5.29 ( dvd_dvd_nat
% 5.02/5.29 = ( ^ [A5: nat,B5: nat] :
% 5.02/5.29 ( ( modulo_modulo_nat @ B5 @ A5 )
% 5.02/5.29 = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_eq_mod_eq_0
% 5.02/5.29 thf(fact_3467_dvd__eq__mod__eq__0,axiom,
% 5.02/5.29 ( dvd_dvd_int
% 5.02/5.29 = ( ^ [A5: int,B5: int] :
% 5.02/5.29 ( ( modulo_modulo_int @ B5 @ A5 )
% 5.02/5.29 = zero_zero_int ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_eq_mod_eq_0
% 5.02/5.29 thf(fact_3468_mod__0__imp__dvd,axiom,
% 5.02/5.29 ! [A: code_integer,B: code_integer] :
% 5.02/5.29 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.02/5.29 = zero_z3403309356797280102nteger )
% 5.02/5.29 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_0_imp_dvd
% 5.02/5.29 thf(fact_3469_mod__0__imp__dvd,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( ( modulo_modulo_nat @ A @ B )
% 5.02/5.29 = zero_zero_nat )
% 5.02/5.29 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_0_imp_dvd
% 5.02/5.29 thf(fact_3470_mod__0__imp__dvd,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.29 = zero_zero_int )
% 5.02/5.29 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_0_imp_dvd
% 5.02/5.29 thf(fact_3471_dvd__power__le,axiom,
% 5.02/5.29 ! [X2: code_integer,Y: code_integer,N2: nat,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ X2 @ Y )
% 5.02/5.29 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.29 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ N2 ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_le
% 5.02/5.29 thf(fact_3472_dvd__power__le,axiom,
% 5.02/5.29 ! [X2: nat,Y: nat,N2: nat,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ X2 @ Y )
% 5.02/5.29 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.29 => ( dvd_dvd_nat @ ( power_power_nat @ X2 @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_le
% 5.02/5.29 thf(fact_3473_dvd__power__le,axiom,
% 5.02/5.29 ! [X2: int,Y: int,N2: nat,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_int @ X2 @ Y )
% 5.02/5.29 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.29 => ( dvd_dvd_int @ ( power_power_int @ X2 @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_le
% 5.02/5.29 thf(fact_3474_dvd__power__le,axiom,
% 5.02/5.29 ! [X2: real,Y: real,N2: nat,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_real @ X2 @ Y )
% 5.02/5.29 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.29 => ( dvd_dvd_real @ ( power_power_real @ X2 @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_le
% 5.02/5.29 thf(fact_3475_dvd__power__le,axiom,
% 5.02/5.29 ! [X2: complex,Y: complex,N2: nat,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_complex @ X2 @ Y )
% 5.02/5.29 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.29 => ( dvd_dvd_complex @ ( power_power_complex @ X2 @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_le
% 5.02/5.29 thf(fact_3476_power__le__dvd,axiom,
% 5.02/5.29 ! [A: code_integer,N2: nat,B: code_integer,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ B )
% 5.02/5.29 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_le_dvd
% 5.02/5.29 thf(fact_3477_power__le__dvd,axiom,
% 5.02/5.29 ! [A: nat,N2: nat,B: nat,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 5.02/5.29 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_le_dvd
% 5.02/5.29 thf(fact_3478_power__le__dvd,axiom,
% 5.02/5.29 ! [A: int,N2: nat,B: int,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 5.02/5.29 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_le_dvd
% 5.02/5.29 thf(fact_3479_power__le__dvd,axiom,
% 5.02/5.29 ! [A: real,N2: nat,B: real,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 5.02/5.29 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_le_dvd
% 5.02/5.29 thf(fact_3480_power__le__dvd,axiom,
% 5.02/5.29 ! [A: complex,N2: nat,B: complex,M: nat] :
% 5.02/5.29 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 5.02/5.29 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_le_dvd
% 5.02/5.29 thf(fact_3481_le__imp__power__dvd,axiom,
% 5.02/5.29 ! [M: nat,N2: nat,A: code_integer] :
% 5.02/5.29 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % le_imp_power_dvd
% 5.02/5.29 thf(fact_3482_le__imp__power__dvd,axiom,
% 5.02/5.29 ! [M: nat,N2: nat,A: nat] :
% 5.02/5.29 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % le_imp_power_dvd
% 5.02/5.29 thf(fact_3483_le__imp__power__dvd,axiom,
% 5.02/5.29 ! [M: nat,N2: nat,A: int] :
% 5.02/5.29 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % le_imp_power_dvd
% 5.02/5.29 thf(fact_3484_le__imp__power__dvd,axiom,
% 5.02/5.29 ! [M: nat,N2: nat,A: real] :
% 5.02/5.29 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % le_imp_power_dvd
% 5.02/5.29 thf(fact_3485_le__imp__power__dvd,axiom,
% 5.02/5.29 ! [M: nat,N2: nat,A: complex] :
% 5.02/5.29 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.29 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % le_imp_power_dvd
% 5.02/5.29 thf(fact_3486_nat__dvd__not__less,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.29 => ( ( ord_less_nat @ M @ N2 )
% 5.02/5.29 => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % nat_dvd_not_less
% 5.02/5.29 thf(fact_3487_dvd__pos__nat,axiom,
% 5.02/5.29 ! [N2: nat,M: nat] :
% 5.02/5.29 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.02/5.29 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_pos_nat
% 5.02/5.29 thf(fact_3488_zdvd__antisym__nonneg,axiom,
% 5.02/5.29 ! [M: int,N2: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.02/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.02/5.29 => ( ( dvd_dvd_int @ M @ N2 )
% 5.02/5.29 => ( ( dvd_dvd_int @ N2 @ M )
% 5.02/5.29 => ( M = N2 ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zdvd_antisym_nonneg
% 5.02/5.29 thf(fact_3489_zdvd__not__zless,axiom,
% 5.02/5.29 ! [M: int,N2: int] :
% 5.02/5.29 ( ( ord_less_int @ zero_zero_int @ M )
% 5.02/5.29 => ( ( ord_less_int @ M @ N2 )
% 5.02/5.29 => ~ ( dvd_dvd_int @ N2 @ M ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zdvd_not_zless
% 5.02/5.29 thf(fact_3490_zdvd__mono,axiom,
% 5.02/5.29 ! [K: int,M: int,T2: int] :
% 5.02/5.29 ( ( K != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ M @ T2 )
% 5.02/5.29 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zdvd_mono
% 5.02/5.29 thf(fact_3491_zdvd__mult__cancel,axiom,
% 5.02/5.29 ! [K: int,M: int,N2: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N2 ) )
% 5.02/5.29 => ( ( K != zero_zero_int )
% 5.02/5.29 => ( dvd_dvd_int @ M @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zdvd_mult_cancel
% 5.02/5.29 thf(fact_3492_bezout__lemma__nat,axiom,
% 5.02/5.29 ! [D: nat,A: nat,B: nat,X2: nat,Y: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ D @ A )
% 5.02/5.29 => ( ( dvd_dvd_nat @ D @ B )
% 5.02/5.29 => ( ( ( ( times_times_nat @ A @ X2 )
% 5.02/5.29 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.02/5.29 | ( ( times_times_nat @ B @ X2 )
% 5.02/5.29 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.02/5.29 => ? [X5: nat,Y3: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ D @ A )
% 5.02/5.29 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.02/5.29 & ( ( ( times_times_nat @ A @ X5 )
% 5.02/5.29 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.02/5.29 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X5 )
% 5.02/5.29 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % bezout_lemma_nat
% 5.02/5.29 thf(fact_3493_bezout__add__nat,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ? [D3: nat,X5: nat,Y3: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ D3 @ A )
% 5.02/5.29 & ( dvd_dvd_nat @ D3 @ B )
% 5.02/5.29 & ( ( ( times_times_nat @ A @ X5 )
% 5.02/5.29 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.02/5.29 | ( ( times_times_nat @ B @ X5 )
% 5.02/5.29 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % bezout_add_nat
% 5.02/5.29 thf(fact_3494_int__le__induct,axiom,
% 5.02/5.29 ! [I3: int,K: int,P: int > $o] :
% 5.02/5.29 ( ( ord_less_eq_int @ I3 @ K )
% 5.02/5.29 => ( ( P @ K )
% 5.02/5.29 => ( ! [I2: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ I2 @ K )
% 5.02/5.29 => ( ( P @ I2 )
% 5.02/5.29 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.02/5.29 => ( P @ I3 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % int_le_induct
% 5.02/5.29 thf(fact_3495_int__less__induct,axiom,
% 5.02/5.29 ! [I3: int,K: int,P: int > $o] :
% 5.02/5.29 ( ( ord_less_int @ I3 @ K )
% 5.02/5.29 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.02/5.29 => ( ! [I2: int] :
% 5.02/5.29 ( ( ord_less_int @ I2 @ K )
% 5.02/5.29 => ( ( P @ I2 )
% 5.02/5.29 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.02/5.29 => ( P @ I3 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % int_less_induct
% 5.02/5.29 thf(fact_3496_zdvd__reduce,axiom,
% 5.02/5.29 ! [K: int,N2: int,M: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N2 @ ( times_times_int @ K @ M ) ) )
% 5.02/5.29 = ( dvd_dvd_int @ K @ N2 ) ) ).
% 5.02/5.29
% 5.02/5.29 % zdvd_reduce
% 5.02/5.29 thf(fact_3497_zdvd__period,axiom,
% 5.02/5.29 ! [A: int,D: int,X2: int,T2: int,C: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ A @ D )
% 5.02/5.29 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X2 @ T2 ) )
% 5.02/5.29 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X2 @ ( times_times_int @ C @ D ) ) @ T2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zdvd_period
% 5.02/5.29 thf(fact_3498_pow_Osimps_I1_J,axiom,
% 5.02/5.29 ! [X2: num] :
% 5.02/5.29 ( ( pow @ X2 @ one )
% 5.02/5.29 = X2 ) ).
% 5.02/5.29
% 5.02/5.29 % pow.simps(1)
% 5.02/5.29 thf(fact_3499_signed__take__bit__int__less__eq,axiom,
% 5.02/5.29 ! [N2: nat,K: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.02/5.29 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % signed_take_bit_int_less_eq
% 5.02/5.29 thf(fact_3500_unit__dvdE,axiom,
% 5.02/5.29 ! [A: code_integer,B: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.02/5.29 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.02/5.29 => ! [C3: code_integer] :
% 5.02/5.29 ( B
% 5.02/5.29 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_dvdE
% 5.02/5.29 thf(fact_3501_unit__dvdE,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.02/5.29 => ~ ( ( A != zero_zero_nat )
% 5.02/5.29 => ! [C3: nat] :
% 5.02/5.29 ( B
% 5.02/5.29 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_dvdE
% 5.02/5.29 thf(fact_3502_unit__dvdE,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.02/5.29 => ~ ( ( A != zero_zero_int )
% 5.02/5.29 => ! [C3: int] :
% 5.02/5.29 ( B
% 5.02/5.29 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_dvdE
% 5.02/5.29 thf(fact_3503_unity__coeff__ex,axiom,
% 5.02/5.29 ! [P: code_integer > $o,L: code_integer] :
% 5.02/5.29 ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X ) ) )
% 5.02/5.29 = ( ? [X: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 5.02/5.29 & ( P @ X ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unity_coeff_ex
% 5.02/5.29 thf(fact_3504_unity__coeff__ex,axiom,
% 5.02/5.29 ! [P: complex > $o,L: complex] :
% 5.02/5.29 ( ( ? [X: complex] : ( P @ ( times_times_complex @ L @ X ) ) )
% 5.02/5.29 = ( ? [X: complex] :
% 5.02/5.29 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X @ zero_zero_complex ) )
% 5.02/5.29 & ( P @ X ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unity_coeff_ex
% 5.02/5.29 thf(fact_3505_unity__coeff__ex,axiom,
% 5.02/5.29 ! [P: real > $o,L: real] :
% 5.02/5.29 ( ( ? [X: real] : ( P @ ( times_times_real @ L @ X ) ) )
% 5.02/5.29 = ( ? [X: real] :
% 5.02/5.29 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X @ zero_zero_real ) )
% 5.02/5.29 & ( P @ X ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unity_coeff_ex
% 5.02/5.29 thf(fact_3506_unity__coeff__ex,axiom,
% 5.02/5.29 ! [P: rat > $o,L: rat] :
% 5.02/5.29 ( ( ? [X: rat] : ( P @ ( times_times_rat @ L @ X ) ) )
% 5.02/5.29 = ( ? [X: rat] :
% 5.02/5.29 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 5.02/5.29 & ( P @ X ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unity_coeff_ex
% 5.02/5.29 thf(fact_3507_unity__coeff__ex,axiom,
% 5.02/5.29 ! [P: nat > $o,L: nat] :
% 5.02/5.29 ( ( ? [X: nat] : ( P @ ( times_times_nat @ L @ X ) ) )
% 5.02/5.29 = ( ? [X: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 5.02/5.29 & ( P @ X ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unity_coeff_ex
% 5.02/5.29 thf(fact_3508_unity__coeff__ex,axiom,
% 5.02/5.29 ! [P: int > $o,L: int] :
% 5.02/5.29 ( ( ? [X: int] : ( P @ ( times_times_int @ L @ X ) ) )
% 5.02/5.29 = ( ? [X: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X @ zero_zero_int ) )
% 5.02/5.29 & ( P @ X ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unity_coeff_ex
% 5.02/5.29 thf(fact_3509_dvd__div__div__eq__mult,axiom,
% 5.02/5.29 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.02/5.29 ( ( A != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( C != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.02/5.29 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.02/5.29 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.02/5.29 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.02/5.29 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_div_eq_mult
% 5.02/5.29 thf(fact_3510_dvd__div__div__eq__mult,axiom,
% 5.02/5.29 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.02/5.29 ( ( A != zero_zero_nat )
% 5.02/5.29 => ( ( C != zero_zero_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ A @ B )
% 5.02/5.29 => ( ( dvd_dvd_nat @ C @ D )
% 5.02/5.29 => ( ( ( divide_divide_nat @ B @ A )
% 5.02/5.29 = ( divide_divide_nat @ D @ C ) )
% 5.02/5.29 = ( ( times_times_nat @ B @ C )
% 5.02/5.29 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_div_eq_mult
% 5.02/5.29 thf(fact_3511_dvd__div__div__eq__mult,axiom,
% 5.02/5.29 ! [A: int,C: int,B: int,D: int] :
% 5.02/5.29 ( ( A != zero_zero_int )
% 5.02/5.29 => ( ( C != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ A @ B )
% 5.02/5.29 => ( ( dvd_dvd_int @ C @ D )
% 5.02/5.29 => ( ( ( divide_divide_int @ B @ A )
% 5.02/5.29 = ( divide_divide_int @ D @ C ) )
% 5.02/5.29 = ( ( times_times_int @ B @ C )
% 5.02/5.29 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_div_eq_mult
% 5.02/5.29 thf(fact_3512_dvd__div__iff__mult,axiom,
% 5.02/5.29 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.02/5.29 ( ( C != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.02/5.29 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_iff_mult
% 5.02/5.29 thf(fact_3513_dvd__div__iff__mult,axiom,
% 5.02/5.29 ! [C: nat,B: nat,A: nat] :
% 5.02/5.29 ( ( C != zero_zero_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ C @ B )
% 5.02/5.29 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.02/5.29 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_iff_mult
% 5.02/5.29 thf(fact_3514_dvd__div__iff__mult,axiom,
% 5.02/5.29 ! [C: int,B: int,A: int] :
% 5.02/5.29 ( ( C != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ C @ B )
% 5.02/5.29 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.02/5.29 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_iff_mult
% 5.02/5.29 thf(fact_3515_div__dvd__iff__mult,axiom,
% 5.02/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.02/5.29 ( ( B != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.02/5.29 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_dvd_iff_mult
% 5.02/5.29 thf(fact_3516_div__dvd__iff__mult,axiom,
% 5.02/5.29 ! [B: nat,A: nat,C: nat] :
% 5.02/5.29 ( ( B != zero_zero_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ B @ A )
% 5.02/5.29 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.02/5.29 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_dvd_iff_mult
% 5.02/5.29 thf(fact_3517_div__dvd__iff__mult,axiom,
% 5.02/5.29 ! [B: int,A: int,C: int] :
% 5.02/5.29 ( ( B != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ B @ A )
% 5.02/5.29 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.02/5.29 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_dvd_iff_mult
% 5.02/5.29 thf(fact_3518_dvd__div__eq__mult,axiom,
% 5.02/5.29 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.02/5.29 ( ( A != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.02/5.29 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.02/5.29 = C )
% 5.02/5.29 = ( B
% 5.02/5.29 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_eq_mult
% 5.02/5.29 thf(fact_3519_dvd__div__eq__mult,axiom,
% 5.02/5.29 ! [A: nat,B: nat,C: nat] :
% 5.02/5.29 ( ( A != zero_zero_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ A @ B )
% 5.02/5.29 => ( ( ( divide_divide_nat @ B @ A )
% 5.02/5.29 = C )
% 5.02/5.29 = ( B
% 5.02/5.29 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_eq_mult
% 5.02/5.29 thf(fact_3520_dvd__div__eq__mult,axiom,
% 5.02/5.29 ! [A: int,B: int,C: int] :
% 5.02/5.29 ( ( A != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ A @ B )
% 5.02/5.29 => ( ( ( divide_divide_int @ B @ A )
% 5.02/5.29 = C )
% 5.02/5.29 = ( B
% 5.02/5.29 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_div_eq_mult
% 5.02/5.29 thf(fact_3521_unit__div__eq__0__iff,axiom,
% 5.02/5.29 ! [B: code_integer,A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.02/5.29 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.02/5.29 = zero_z3403309356797280102nteger )
% 5.02/5.29 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_eq_0_iff
% 5.02/5.29 thf(fact_3522_unit__div__eq__0__iff,axiom,
% 5.02/5.29 ! [B: nat,A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.02/5.29 => ( ( ( divide_divide_nat @ A @ B )
% 5.02/5.29 = zero_zero_nat )
% 5.02/5.29 = ( A = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_eq_0_iff
% 5.02/5.29 thf(fact_3523_unit__div__eq__0__iff,axiom,
% 5.02/5.29 ! [B: int,A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.02/5.29 => ( ( ( divide_divide_int @ A @ B )
% 5.02/5.29 = zero_zero_int )
% 5.02/5.29 = ( A = zero_zero_int ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_eq_0_iff
% 5.02/5.29 thf(fact_3524_even__numeral,axiom,
% 5.02/5.29 ! [N2: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_numeral
% 5.02/5.29 thf(fact_3525_even__numeral,axiom,
% 5.02/5.29 ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_numeral
% 5.02/5.29 thf(fact_3526_even__numeral,axiom,
% 5.02/5.29 ! [N2: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_numeral
% 5.02/5.29 thf(fact_3527_ordered__ring__class_Ole__add__iff1,axiom,
% 5.02/5.29 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.02/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.02/5.29
% 5.02/5.29 % ordered_ring_class.le_add_iff1
% 5.02/5.29 thf(fact_3528_ordered__ring__class_Ole__add__iff1,axiom,
% 5.02/5.29 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.02/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.02/5.29
% 5.02/5.29 % ordered_ring_class.le_add_iff1
% 5.02/5.29 thf(fact_3529_ordered__ring__class_Ole__add__iff1,axiom,
% 5.02/5.29 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.02/5.29
% 5.02/5.29 % ordered_ring_class.le_add_iff1
% 5.02/5.29 thf(fact_3530_ordered__ring__class_Ole__add__iff2,axiom,
% 5.02/5.29 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.02/5.29 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % ordered_ring_class.le_add_iff2
% 5.02/5.29 thf(fact_3531_ordered__ring__class_Ole__add__iff2,axiom,
% 5.02/5.29 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.02/5.29 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % ordered_ring_class.le_add_iff2
% 5.02/5.29 thf(fact_3532_ordered__ring__class_Ole__add__iff2,axiom,
% 5.02/5.29 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % ordered_ring_class.le_add_iff2
% 5.02/5.29 thf(fact_3533_unit__eq__div1,axiom,
% 5.02/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.02/5.29 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.02/5.29 = C )
% 5.02/5.29 = ( A
% 5.02/5.29 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_eq_div1
% 5.02/5.29 thf(fact_3534_unit__eq__div1,axiom,
% 5.02/5.29 ! [B: nat,A: nat,C: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.02/5.29 => ( ( ( divide_divide_nat @ A @ B )
% 5.02/5.29 = C )
% 5.02/5.29 = ( A
% 5.02/5.29 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_eq_div1
% 5.02/5.29 thf(fact_3535_unit__eq__div1,axiom,
% 5.02/5.29 ! [B: int,A: int,C: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.02/5.29 => ( ( ( divide_divide_int @ A @ B )
% 5.02/5.29 = C )
% 5.02/5.29 = ( A
% 5.02/5.29 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_eq_div1
% 5.02/5.29 thf(fact_3536_unit__eq__div2,axiom,
% 5.02/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.02/5.29 => ( ( A
% 5.02/5.29 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.02/5.29 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.02/5.29 = C ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_eq_div2
% 5.02/5.29 thf(fact_3537_unit__eq__div2,axiom,
% 5.02/5.29 ! [B: nat,A: nat,C: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.02/5.29 => ( ( A
% 5.02/5.29 = ( divide_divide_nat @ C @ B ) )
% 5.02/5.29 = ( ( times_times_nat @ A @ B )
% 5.02/5.29 = C ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_eq_div2
% 5.02/5.29 thf(fact_3538_unit__eq__div2,axiom,
% 5.02/5.29 ! [B: int,A: int,C: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.02/5.29 => ( ( A
% 5.02/5.29 = ( divide_divide_int @ C @ B ) )
% 5.02/5.29 = ( ( times_times_int @ A @ B )
% 5.02/5.29 = C ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_eq_div2
% 5.02/5.29 thf(fact_3539_div__mult__unit2,axiom,
% 5.02/5.29 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.02/5.29 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.02/5.29 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_mult_unit2
% 5.02/5.29 thf(fact_3540_div__mult__unit2,axiom,
% 5.02/5.29 ! [C: nat,B: nat,A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ B @ A )
% 5.02/5.29 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.02/5.29 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_mult_unit2
% 5.02/5.29 thf(fact_3541_div__mult__unit2,axiom,
% 5.02/5.29 ! [C: int,B: int,A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ B @ A )
% 5.02/5.29 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.02/5.29 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_mult_unit2
% 5.02/5.29 thf(fact_3542_unit__div__commute,axiom,
% 5.02/5.29 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.02/5.29 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.02/5.29 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_commute
% 5.02/5.29 thf(fact_3543_unit__div__commute,axiom,
% 5.02/5.29 ! [B: nat,A: nat,C: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.02/5.29 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.02/5.29 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_commute
% 5.02/5.29 thf(fact_3544_unit__div__commute,axiom,
% 5.02/5.29 ! [B: int,A: int,C: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.02/5.29 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.02/5.29 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_commute
% 5.02/5.29 thf(fact_3545_unit__div__mult__swap,axiom,
% 5.02/5.29 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.02/5.29 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.02/5.29 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_mult_swap
% 5.02/5.29 thf(fact_3546_unit__div__mult__swap,axiom,
% 5.02/5.29 ! [C: nat,A: nat,B: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.02/5.29 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.02/5.29 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_mult_swap
% 5.02/5.29 thf(fact_3547_unit__div__mult__swap,axiom,
% 5.02/5.29 ! [C: int,A: int,B: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.02/5.29 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.02/5.29 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_div_mult_swap
% 5.02/5.29 thf(fact_3548_is__unit__div__mult2__eq,axiom,
% 5.02/5.29 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.02/5.29 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.02/5.29 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult2_eq
% 5.02/5.29 thf(fact_3549_is__unit__div__mult2__eq,axiom,
% 5.02/5.29 ! [B: nat,C: nat,A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.02/5.29 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.02/5.29 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult2_eq
% 5.02/5.29 thf(fact_3550_is__unit__div__mult2__eq,axiom,
% 5.02/5.29 ! [B: int,C: int,A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.02/5.29 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.02/5.29 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult2_eq
% 5.02/5.29 thf(fact_3551_less__add__iff1,axiom,
% 5.02/5.29 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.02/5.29 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.02/5.29
% 5.02/5.29 % less_add_iff1
% 5.02/5.29 thf(fact_3552_less__add__iff1,axiom,
% 5.02/5.29 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.02/5.29 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.02/5.29
% 5.02/5.29 % less_add_iff1
% 5.02/5.29 thf(fact_3553_less__add__iff1,axiom,
% 5.02/5.29 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.02/5.29 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.02/5.29
% 5.02/5.29 % less_add_iff1
% 5.02/5.29 thf(fact_3554_less__add__iff2,axiom,
% 5.02/5.29 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.02/5.29 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % less_add_iff2
% 5.02/5.29 thf(fact_3555_less__add__iff2,axiom,
% 5.02/5.29 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.02/5.29 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % less_add_iff2
% 5.02/5.29 thf(fact_3556_less__add__iff2,axiom,
% 5.02/5.29 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.02/5.29 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.02/5.29 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % less_add_iff2
% 5.02/5.29 thf(fact_3557_divide__diff__eq__iff,axiom,
% 5.02/5.29 ! [Z: complex,X2: complex,Y: complex] :
% 5.02/5.29 ( ( Z != zero_zero_complex )
% 5.02/5.29 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Z ) @ Y )
% 5.02/5.29 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % divide_diff_eq_iff
% 5.02/5.29 thf(fact_3558_divide__diff__eq__iff,axiom,
% 5.02/5.29 ! [Z: real,X2: real,Y: real] :
% 5.02/5.29 ( ( Z != zero_zero_real )
% 5.02/5.29 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Z ) @ Y )
% 5.02/5.29 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % divide_diff_eq_iff
% 5.02/5.29 thf(fact_3559_divide__diff__eq__iff,axiom,
% 5.02/5.29 ! [Z: rat,X2: rat,Y: rat] :
% 5.02/5.29 ( ( Z != zero_zero_rat )
% 5.02/5.29 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Z ) @ Y )
% 5.02/5.29 = ( divide_divide_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % divide_diff_eq_iff
% 5.02/5.29 thf(fact_3560_diff__divide__eq__iff,axiom,
% 5.02/5.29 ! [Z: complex,X2: complex,Y: complex] :
% 5.02/5.29 ( ( Z != zero_zero_complex )
% 5.02/5.29 => ( ( minus_minus_complex @ X2 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.02/5.29 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % diff_divide_eq_iff
% 5.02/5.29 thf(fact_3561_diff__divide__eq__iff,axiom,
% 5.02/5.29 ! [Z: real,X2: real,Y: real] :
% 5.02/5.29 ( ( Z != zero_zero_real )
% 5.02/5.29 => ( ( minus_minus_real @ X2 @ ( divide_divide_real @ Y @ Z ) )
% 5.02/5.29 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % diff_divide_eq_iff
% 5.02/5.29 thf(fact_3562_diff__divide__eq__iff,axiom,
% 5.02/5.29 ! [Z: rat,X2: rat,Y: rat] :
% 5.02/5.29 ( ( Z != zero_zero_rat )
% 5.02/5.29 => ( ( minus_minus_rat @ X2 @ ( divide_divide_rat @ Y @ Z ) )
% 5.02/5.29 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % diff_divide_eq_iff
% 5.02/5.29 thf(fact_3563_diff__frac__eq,axiom,
% 5.02/5.29 ! [Y: complex,Z: complex,X2: complex,W: complex] :
% 5.02/5.29 ( ( Y != zero_zero_complex )
% 5.02/5.29 => ( ( Z != zero_zero_complex )
% 5.02/5.29 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X2 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.02/5.29 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X2 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % diff_frac_eq
% 5.02/5.29 thf(fact_3564_diff__frac__eq,axiom,
% 5.02/5.29 ! [Y: real,Z: real,X2: real,W: real] :
% 5.02/5.29 ( ( Y != zero_zero_real )
% 5.02/5.29 => ( ( Z != zero_zero_real )
% 5.02/5.29 => ( ( minus_minus_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.02/5.29 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % diff_frac_eq
% 5.02/5.29 thf(fact_3565_diff__frac__eq,axiom,
% 5.02/5.29 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 5.02/5.29 ( ( Y != zero_zero_rat )
% 5.02/5.29 => ( ( Z != zero_zero_rat )
% 5.02/5.29 => ( ( minus_minus_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.02/5.29 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % diff_frac_eq
% 5.02/5.29 thf(fact_3566_add__divide__eq__if__simps_I4_J,axiom,
% 5.02/5.29 ! [Z: complex,A: complex,B: complex] :
% 5.02/5.29 ( ( ( Z = zero_zero_complex )
% 5.02/5.29 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.02/5.29 = A ) )
% 5.02/5.29 & ( ( Z != zero_zero_complex )
% 5.02/5.29 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.02/5.29 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % add_divide_eq_if_simps(4)
% 5.02/5.29 thf(fact_3567_add__divide__eq__if__simps_I4_J,axiom,
% 5.02/5.29 ! [Z: real,A: real,B: real] :
% 5.02/5.29 ( ( ( Z = zero_zero_real )
% 5.02/5.29 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.02/5.29 = A ) )
% 5.02/5.29 & ( ( Z != zero_zero_real )
% 5.02/5.29 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.02/5.29 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % add_divide_eq_if_simps(4)
% 5.02/5.29 thf(fact_3568_add__divide__eq__if__simps_I4_J,axiom,
% 5.02/5.29 ! [Z: rat,A: rat,B: rat] :
% 5.02/5.29 ( ( ( Z = zero_zero_rat )
% 5.02/5.29 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.02/5.29 = A ) )
% 5.02/5.29 & ( ( Z != zero_zero_rat )
% 5.02/5.29 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.02/5.29 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % add_divide_eq_if_simps(4)
% 5.02/5.29 thf(fact_3569_square__diff__one__factored,axiom,
% 5.02/5.29 ! [X2: complex] :
% 5.02/5.29 ( ( minus_minus_complex @ ( times_times_complex @ X2 @ X2 ) @ one_one_complex )
% 5.02/5.29 = ( times_times_complex @ ( plus_plus_complex @ X2 @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % square_diff_one_factored
% 5.02/5.29 thf(fact_3570_square__diff__one__factored,axiom,
% 5.02/5.29 ! [X2: real] :
% 5.02/5.29 ( ( minus_minus_real @ ( times_times_real @ X2 @ X2 ) @ one_one_real )
% 5.02/5.29 = ( times_times_real @ ( plus_plus_real @ X2 @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % square_diff_one_factored
% 5.02/5.29 thf(fact_3571_square__diff__one__factored,axiom,
% 5.02/5.29 ! [X2: rat] :
% 5.02/5.29 ( ( minus_minus_rat @ ( times_times_rat @ X2 @ X2 ) @ one_one_rat )
% 5.02/5.29 = ( times_times_rat @ ( plus_plus_rat @ X2 @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % square_diff_one_factored
% 5.02/5.29 thf(fact_3572_square__diff__one__factored,axiom,
% 5.02/5.29 ! [X2: int] :
% 5.02/5.29 ( ( minus_minus_int @ ( times_times_int @ X2 @ X2 ) @ one_one_int )
% 5.02/5.29 = ( times_times_int @ ( plus_plus_int @ X2 @ one_one_int ) @ ( minus_minus_int @ X2 @ one_one_int ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % square_diff_one_factored
% 5.02/5.29 thf(fact_3573_unit__imp__mod__eq__0,axiom,
% 5.02/5.29 ! [B: code_integer,A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.02/5.29 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.02/5.29 = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_imp_mod_eq_0
% 5.02/5.29 thf(fact_3574_unit__imp__mod__eq__0,axiom,
% 5.02/5.29 ! [B: nat,A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.02/5.29 => ( ( modulo_modulo_nat @ A @ B )
% 5.02/5.29 = zero_zero_nat ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_imp_mod_eq_0
% 5.02/5.29 thf(fact_3575_unit__imp__mod__eq__0,axiom,
% 5.02/5.29 ! [B: int,A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.02/5.29 => ( ( modulo_modulo_int @ A @ B )
% 5.02/5.29 = zero_zero_int ) ) ).
% 5.02/5.29
% 5.02/5.29 % unit_imp_mod_eq_0
% 5.02/5.29 thf(fact_3576_is__unit__power__iff,axiom,
% 5.02/5.29 ! [A: code_integer,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 5.02/5.29 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.02/5.29 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_power_iff
% 5.02/5.29 thf(fact_3577_is__unit__power__iff,axiom,
% 5.02/5.29 ! [A: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 5.02/5.29 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.02/5.29 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_power_iff
% 5.02/5.29 thf(fact_3578_is__unit__power__iff,axiom,
% 5.02/5.29 ! [A: int,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 5.02/5.29 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.02/5.29 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_power_iff
% 5.02/5.29 thf(fact_3579_minus__mult__div__eq__mod,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.02/5.29 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.02/5.29
% 5.02/5.29 % minus_mult_div_eq_mod
% 5.02/5.29 thf(fact_3580_minus__mult__div__eq__mod,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.02/5.29 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.02/5.29
% 5.02/5.29 % minus_mult_div_eq_mod
% 5.02/5.29 thf(fact_3581_minus__mod__eq__mult__div,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.02/5.29 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % minus_mod_eq_mult_div
% 5.02/5.29 thf(fact_3582_minus__mod__eq__mult__div,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.02/5.29 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % minus_mod_eq_mult_div
% 5.02/5.29 thf(fact_3583_minus__mod__eq__div__mult,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.02/5.29 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.02/5.29
% 5.02/5.29 % minus_mod_eq_div_mult
% 5.02/5.29 thf(fact_3584_minus__mod__eq__div__mult,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.02/5.29 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.02/5.29
% 5.02/5.29 % minus_mod_eq_div_mult
% 5.02/5.29 thf(fact_3585_minus__div__mult__eq__mod,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.02/5.29 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.02/5.29
% 5.02/5.29 % minus_div_mult_eq_mod
% 5.02/5.29 thf(fact_3586_minus__div__mult__eq__mod,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.02/5.29 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.02/5.29
% 5.02/5.29 % minus_div_mult_eq_mod
% 5.02/5.29 thf(fact_3587_dvd__imp__le,axiom,
% 5.02/5.29 ! [K: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ K @ N2 )
% 5.02/5.29 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_imp_le
% 5.02/5.29 thf(fact_3588_dvd__mult__cancel,axiom,
% 5.02/5.29 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.02/5.29 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.29 => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_mult_cancel
% 5.02/5.29 thf(fact_3589_nat__mult__dvd__cancel1,axiom,
% 5.02/5.29 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.29 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.29 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.02/5.29 = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % nat_mult_dvd_cancel1
% 5.02/5.29 thf(fact_3590_bezout__add__strong__nat,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( A != zero_zero_nat )
% 5.02/5.29 => ? [D3: nat,X5: nat,Y3: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ D3 @ A )
% 5.02/5.29 & ( dvd_dvd_nat @ D3 @ B )
% 5.02/5.29 & ( ( times_times_nat @ A @ X5 )
% 5.02/5.29 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % bezout_add_strong_nat
% 5.02/5.29 thf(fact_3591_zdvd__imp__le,axiom,
% 5.02/5.29 ! [Z: int,N2: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ Z @ N2 )
% 5.02/5.29 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.02/5.29 => ( ord_less_eq_int @ Z @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zdvd_imp_le
% 5.02/5.29 thf(fact_3592_mod__int__pos__iff,axiom,
% 5.02/5.29 ! [K: int,L: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.02/5.29 = ( ( dvd_dvd_int @ L @ K )
% 5.02/5.29 | ( ( L = zero_zero_int )
% 5.02/5.29 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.02/5.29 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_int_pos_iff
% 5.02/5.29 thf(fact_3593_mod__greater__zero__iff__not__dvd,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.02/5.29 = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_greater_zero_iff_not_dvd
% 5.02/5.29 thf(fact_3594_mod__pos__geq,axiom,
% 5.02/5.29 ! [L: int,K: int] :
% 5.02/5.29 ( ( ord_less_int @ zero_zero_int @ L )
% 5.02/5.29 => ( ( ord_less_eq_int @ L @ K )
% 5.02/5.29 => ( ( modulo_modulo_int @ K @ L )
% 5.02/5.29 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod_pos_geq
% 5.02/5.29 thf(fact_3595_minusinfinity,axiom,
% 5.02/5.29 ! [D: int,P1: int > $o,P: int > $o] :
% 5.02/5.29 ( ( ord_less_int @ zero_zero_int @ D )
% 5.02/5.29 => ( ! [X5: int,K2: int] :
% 5.02/5.29 ( ( P1 @ X5 )
% 5.02/5.29 = ( P1 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.02/5.29 => ( ? [Z4: int] :
% 5.02/5.29 ! [X5: int] :
% 5.02/5.29 ( ( ord_less_int @ X5 @ Z4 )
% 5.02/5.29 => ( ( P @ X5 )
% 5.02/5.29 = ( P1 @ X5 ) ) )
% 5.02/5.29 => ( ? [X_1: int] : ( P1 @ X_1 )
% 5.02/5.29 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % minusinfinity
% 5.02/5.29 thf(fact_3596_plusinfinity,axiom,
% 5.02/5.29 ! [D: int,P5: int > $o,P: int > $o] :
% 5.02/5.29 ( ( ord_less_int @ zero_zero_int @ D )
% 5.02/5.29 => ( ! [X5: int,K2: int] :
% 5.02/5.29 ( ( P5 @ X5 )
% 5.02/5.29 = ( P5 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.02/5.29 => ( ? [Z4: int] :
% 5.02/5.29 ! [X5: int] :
% 5.02/5.29 ( ( ord_less_int @ Z4 @ X5 )
% 5.02/5.29 => ( ( P @ X5 )
% 5.02/5.29 = ( P5 @ X5 ) ) )
% 5.02/5.29 => ( ? [X_1: int] : ( P5 @ X_1 )
% 5.02/5.29 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % plusinfinity
% 5.02/5.29 thf(fact_3597_int__induct,axiom,
% 5.02/5.29 ! [P: int > $o,K: int,I3: int] :
% 5.02/5.29 ( ( P @ K )
% 5.02/5.29 => ( ! [I2: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ K @ I2 )
% 5.02/5.29 => ( ( P @ I2 )
% 5.02/5.29 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 5.02/5.29 => ( ! [I2: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ I2 @ K )
% 5.02/5.29 => ( ( P @ I2 )
% 5.02/5.29 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 5.02/5.29 => ( P @ I3 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % int_induct
% 5.02/5.29 thf(fact_3598_even__mask__div__iff_H,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.29 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_mask_div_iff'
% 5.02/5.29 thf(fact_3599_even__mask__div__iff_H,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.29 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_mask_div_iff'
% 5.02/5.29 thf(fact_3600_even__mask__div__iff_H,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.29 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_mask_div_iff'
% 5.02/5.29 thf(fact_3601_even__mask__div__iff,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.29 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 = zero_z3403309356797280102nteger )
% 5.02/5.29 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_mask_div_iff
% 5.02/5.29 thf(fact_3602_even__mask__div__iff,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.29 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 = zero_zero_nat )
% 5.02/5.29 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_mask_div_iff
% 5.02/5.29 thf(fact_3603_even__mask__div__iff,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.29 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 = zero_zero_int )
% 5.02/5.29 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_mask_div_iff
% 5.02/5.29 thf(fact_3604_even__zero,axiom,
% 5.02/5.29 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.02/5.29
% 5.02/5.29 % even_zero
% 5.02/5.29 thf(fact_3605_even__zero,axiom,
% 5.02/5.29 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.02/5.29
% 5.02/5.29 % even_zero
% 5.02/5.29 thf(fact_3606_even__zero,axiom,
% 5.02/5.29 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.02/5.29
% 5.02/5.29 % even_zero
% 5.02/5.29 thf(fact_3607_is__unit__div__mult__cancel__right,axiom,
% 5.02/5.29 ! [A: code_integer,B: code_integer] :
% 5.02/5.29 ( ( A != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.02/5.29 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.02/5.29 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult_cancel_right
% 5.02/5.29 thf(fact_3608_is__unit__div__mult__cancel__right,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( A != zero_zero_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.02/5.29 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.02/5.29 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult_cancel_right
% 5.02/5.29 thf(fact_3609_is__unit__div__mult__cancel__right,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( A != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.02/5.29 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.02/5.29 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult_cancel_right
% 5.02/5.29 thf(fact_3610_is__unit__div__mult__cancel__left,axiom,
% 5.02/5.29 ! [A: code_integer,B: code_integer] :
% 5.02/5.29 ( ( A != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.02/5.29 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.02/5.29 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult_cancel_left
% 5.02/5.29 thf(fact_3611_is__unit__div__mult__cancel__left,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( A != zero_zero_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.02/5.29 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.02/5.29 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult_cancel_left
% 5.02/5.29 thf(fact_3612_is__unit__div__mult__cancel__left,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( A != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.02/5.29 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.02/5.29 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unit_div_mult_cancel_left
% 5.02/5.29 thf(fact_3613_is__unitE,axiom,
% 5.02/5.29 ! [A: code_integer,C: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.02/5.29 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.02/5.29 => ! [B3: code_integer] :
% 5.02/5.29 ( ( B3 != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 5.02/5.29 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.02/5.29 = B3 )
% 5.02/5.29 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 5.02/5.29 = A )
% 5.02/5.29 => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 5.02/5.29 = one_one_Code_integer )
% 5.02/5.29 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.02/5.29 != ( times_3573771949741848930nteger @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unitE
% 5.02/5.29 thf(fact_3614_is__unitE,axiom,
% 5.02/5.29 ! [A: nat,C: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.02/5.29 => ~ ( ( A != zero_zero_nat )
% 5.02/5.29 => ! [B3: nat] :
% 5.02/5.29 ( ( B3 != zero_zero_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 5.02/5.29 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.02/5.29 = B3 )
% 5.02/5.29 => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 5.02/5.29 = A )
% 5.02/5.29 => ( ( ( times_times_nat @ A @ B3 )
% 5.02/5.29 = one_one_nat )
% 5.02/5.29 => ( ( divide_divide_nat @ C @ A )
% 5.02/5.29 != ( times_times_nat @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unitE
% 5.02/5.29 thf(fact_3615_is__unitE,axiom,
% 5.02/5.29 ! [A: int,C: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.02/5.29 => ~ ( ( A != zero_zero_int )
% 5.02/5.29 => ! [B3: int] :
% 5.02/5.29 ( ( B3 != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 5.02/5.29 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.02/5.29 = B3 )
% 5.02/5.29 => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 5.02/5.29 = A )
% 5.02/5.29 => ( ( ( times_times_int @ A @ B3 )
% 5.02/5.29 = one_one_int )
% 5.02/5.29 => ( ( divide_divide_int @ C @ A )
% 5.02/5.29 != ( times_times_int @ C @ B3 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % is_unitE
% 5.02/5.29 thf(fact_3616_evenE,axiom,
% 5.02/5.29 ! [A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ~ ! [B3: code_integer] :
% 5.02/5.29 ( A
% 5.02/5.29 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % evenE
% 5.02/5.29 thf(fact_3617_evenE,axiom,
% 5.02/5.29 ! [A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ~ ! [B3: nat] :
% 5.02/5.29 ( A
% 5.02/5.29 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % evenE
% 5.02/5.29 thf(fact_3618_evenE,axiom,
% 5.02/5.29 ! [A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ~ ! [B3: int] :
% 5.02/5.29 ( A
% 5.02/5.29 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % evenE
% 5.02/5.29 thf(fact_3619_odd__one,axiom,
% 5.02/5.29 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.02/5.29
% 5.02/5.29 % odd_one
% 5.02/5.29 thf(fact_3620_odd__one,axiom,
% 5.02/5.29 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.02/5.29
% 5.02/5.29 % odd_one
% 5.02/5.29 thf(fact_3621_odd__one,axiom,
% 5.02/5.29 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.02/5.29
% 5.02/5.29 % odd_one
% 5.02/5.29 thf(fact_3622_odd__even__add,axiom,
% 5.02/5.29 ! [A: code_integer,B: code_integer] :
% 5.02/5.29 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.02/5.29 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % odd_even_add
% 5.02/5.29 thf(fact_3623_odd__even__add,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.02/5.29 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % odd_even_add
% 5.02/5.29 thf(fact_3624_odd__even__add,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.02/5.29 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % odd_even_add
% 5.02/5.29 thf(fact_3625_frac__le__eq,axiom,
% 5.02/5.29 ! [Y: real,Z: real,X2: real,W: real] :
% 5.02/5.29 ( ( Y != zero_zero_real )
% 5.02/5.29 => ( ( Z != zero_zero_real )
% 5.02/5.29 => ( ( ord_less_eq_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.02/5.29 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % frac_le_eq
% 5.02/5.29 thf(fact_3626_frac__le__eq,axiom,
% 5.02/5.29 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 5.02/5.29 ( ( Y != zero_zero_rat )
% 5.02/5.29 => ( ( Z != zero_zero_rat )
% 5.02/5.29 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.02/5.29 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % frac_le_eq
% 5.02/5.29 thf(fact_3627_bit__eq__rec,axiom,
% 5.02/5.29 ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 5.02/5.29 = ( ^ [A5: code_integer,B5: code_integer] :
% 5.02/5.29 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 )
% 5.02/5.29 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) )
% 5.02/5.29 & ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( divide6298287555418463151nteger @ B5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % bit_eq_rec
% 5.02/5.29 thf(fact_3628_bit__eq__rec,axiom,
% 5.02/5.29 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.02/5.29 = ( ^ [A5: nat,B5: nat] :
% 5.02/5.29 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 )
% 5.02/5.29 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) )
% 5.02/5.29 & ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( divide_divide_nat @ B5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % bit_eq_rec
% 5.02/5.29 thf(fact_3629_bit__eq__rec,axiom,
% 5.02/5.29 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.02/5.29 = ( ^ [A5: int,B5: int] :
% 5.02/5.29 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 )
% 5.02/5.29 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) )
% 5.02/5.29 & ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( divide_divide_int @ B5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % bit_eq_rec
% 5.02/5.29 thf(fact_3630_frac__less__eq,axiom,
% 5.02/5.29 ! [Y: real,Z: real,X2: real,W: real] :
% 5.02/5.29 ( ( Y != zero_zero_real )
% 5.02/5.29 => ( ( Z != zero_zero_real )
% 5.02/5.29 => ( ( ord_less_real @ ( divide_divide_real @ X2 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.02/5.29 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X2 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % frac_less_eq
% 5.02/5.29 thf(fact_3631_frac__less__eq,axiom,
% 5.02/5.29 ! [Y: rat,Z: rat,X2: rat,W: rat] :
% 5.02/5.29 ( ( Y != zero_zero_rat )
% 5.02/5.29 => ( ( Z != zero_zero_rat )
% 5.02/5.29 => ( ( ord_less_rat @ ( divide_divide_rat @ X2 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.02/5.29 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X2 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % frac_less_eq
% 5.02/5.29 thf(fact_3632_dvd__power__iff,axiom,
% 5.02/5.29 ! [X2: code_integer,M: nat,N2: nat] :
% 5.02/5.29 ( ( X2 != zero_z3403309356797280102nteger )
% 5.02/5.29 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X2 @ M ) @ ( power_8256067586552552935nteger @ X2 @ N2 ) )
% 5.02/5.29 = ( ( dvd_dvd_Code_integer @ X2 @ one_one_Code_integer )
% 5.02/5.29 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_iff
% 5.02/5.29 thf(fact_3633_dvd__power__iff,axiom,
% 5.02/5.29 ! [X2: nat,M: nat,N2: nat] :
% 5.02/5.29 ( ( X2 != zero_zero_nat )
% 5.02/5.29 => ( ( dvd_dvd_nat @ ( power_power_nat @ X2 @ M ) @ ( power_power_nat @ X2 @ N2 ) )
% 5.02/5.29 = ( ( dvd_dvd_nat @ X2 @ one_one_nat )
% 5.02/5.29 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_iff
% 5.02/5.29 thf(fact_3634_dvd__power__iff,axiom,
% 5.02/5.29 ! [X2: int,M: nat,N2: nat] :
% 5.02/5.29 ( ( X2 != zero_zero_int )
% 5.02/5.29 => ( ( dvd_dvd_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ N2 ) )
% 5.02/5.29 = ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.02/5.29 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_iff
% 5.02/5.29 thf(fact_3635_dvd__power,axiom,
% 5.02/5.29 ! [N2: nat,X2: code_integer] :
% 5.02/5.29 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 | ( X2 = one_one_Code_integer ) )
% 5.02/5.29 => ( dvd_dvd_Code_integer @ X2 @ ( power_8256067586552552935nteger @ X2 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power
% 5.02/5.29 thf(fact_3636_dvd__power,axiom,
% 5.02/5.29 ! [N2: nat,X2: rat] :
% 5.02/5.29 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 | ( X2 = one_one_rat ) )
% 5.02/5.29 => ( dvd_dvd_rat @ X2 @ ( power_power_rat @ X2 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power
% 5.02/5.29 thf(fact_3637_dvd__power,axiom,
% 5.02/5.29 ! [N2: nat,X2: nat] :
% 5.02/5.29 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 | ( X2 = one_one_nat ) )
% 5.02/5.29 => ( dvd_dvd_nat @ X2 @ ( power_power_nat @ X2 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power
% 5.02/5.29 thf(fact_3638_dvd__power,axiom,
% 5.02/5.29 ! [N2: nat,X2: int] :
% 5.02/5.29 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 | ( X2 = one_one_int ) )
% 5.02/5.29 => ( dvd_dvd_int @ X2 @ ( power_power_int @ X2 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power
% 5.02/5.29 thf(fact_3639_dvd__power,axiom,
% 5.02/5.29 ! [N2: nat,X2: real] :
% 5.02/5.29 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 | ( X2 = one_one_real ) )
% 5.02/5.29 => ( dvd_dvd_real @ X2 @ ( power_power_real @ X2 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power
% 5.02/5.29 thf(fact_3640_dvd__power,axiom,
% 5.02/5.29 ! [N2: nat,X2: complex] :
% 5.02/5.29 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 | ( X2 = one_one_complex ) )
% 5.02/5.29 => ( dvd_dvd_complex @ X2 @ ( power_power_complex @ X2 @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power
% 5.02/5.29 thf(fact_3641_power2__commute,axiom,
% 5.02/5.29 ! [X2: complex,Y: complex] :
% 5.02/5.29 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( power_power_complex @ ( minus_minus_complex @ Y @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power2_commute
% 5.02/5.29 thf(fact_3642_power2__commute,axiom,
% 5.02/5.29 ! [X2: real,Y: real] :
% 5.02/5.29 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( power_power_real @ ( minus_minus_real @ Y @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power2_commute
% 5.02/5.29 thf(fact_3643_power2__commute,axiom,
% 5.02/5.29 ! [X2: rat,Y: rat] :
% 5.02/5.29 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( power_power_rat @ ( minus_minus_rat @ Y @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power2_commute
% 5.02/5.29 thf(fact_3644_power2__commute,axiom,
% 5.02/5.29 ! [X2: int,Y: int] :
% 5.02/5.29 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( power_power_int @ ( minus_minus_int @ Y @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power2_commute
% 5.02/5.29 thf(fact_3645_even__even__mod__4__iff,axiom,
% 5.02/5.29 ! [N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_even_mod_4_iff
% 5.02/5.29 thf(fact_3646_dvd__mult__cancel1,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.29 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 5.02/5.29 = ( N2 = one_one_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_mult_cancel1
% 5.02/5.29 thf(fact_3647_dvd__mult__cancel2,axiom,
% 5.02/5.29 ! [M: nat,N2: nat] :
% 5.02/5.29 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.29 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 5.02/5.29 = ( N2 = one_one_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_mult_cancel2
% 5.02/5.29 thf(fact_3648_power__dvd__imp__le,axiom,
% 5.02/5.29 ! [I3: nat,M: nat,N2: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( power_power_nat @ I3 @ M ) @ ( power_power_nat @ I3 @ N2 ) )
% 5.02/5.29 => ( ( ord_less_nat @ one_one_nat @ I3 )
% 5.02/5.29 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_dvd_imp_le
% 5.02/5.29 thf(fact_3649_decr__mult__lemma,axiom,
% 5.02/5.29 ! [D: int,P: int > $o,K: int] :
% 5.02/5.29 ( ( ord_less_int @ zero_zero_int @ D )
% 5.02/5.29 => ( ! [X5: int] :
% 5.02/5.29 ( ( P @ X5 )
% 5.02/5.29 => ( P @ ( minus_minus_int @ X5 @ D ) ) )
% 5.02/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.29 => ! [X3: int] :
% 5.02/5.29 ( ( P @ X3 )
% 5.02/5.29 => ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % decr_mult_lemma
% 5.02/5.29 thf(fact_3650_even__two__times__div__two,axiom,
% 5.02/5.29 ! [A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.02/5.29 = A ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_two_times_div_two
% 5.02/5.29 thf(fact_3651_even__two__times__div__two,axiom,
% 5.02/5.29 ! [A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.29 = A ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_two_times_div_two
% 5.02/5.29 thf(fact_3652_even__two__times__div__two,axiom,
% 5.02/5.29 ! [A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.02/5.29 = A ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_two_times_div_two
% 5.02/5.29 thf(fact_3653_scaling__mono,axiom,
% 5.02/5.29 ! [U: real,V: real,R2: real,S2: real] :
% 5.02/5.29 ( ( ord_less_eq_real @ U @ V )
% 5.02/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.02/5.29 => ( ( ord_less_eq_real @ R2 @ S2 )
% 5.02/5.29 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R2 @ ( minus_minus_real @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % scaling_mono
% 5.02/5.29 thf(fact_3654_scaling__mono,axiom,
% 5.02/5.29 ! [U: rat,V: rat,R2: rat,S2: rat] :
% 5.02/5.29 ( ( ord_less_eq_rat @ U @ V )
% 5.02/5.29 => ( ( ord_less_eq_rat @ zero_zero_rat @ R2 )
% 5.02/5.29 => ( ( ord_less_eq_rat @ R2 @ S2 )
% 5.02/5.29 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R2 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % scaling_mono
% 5.02/5.29 thf(fact_3655_even__iff__mod__2__eq__zero,axiom,
% 5.02/5.29 ! [A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.29 = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_iff_mod_2_eq_zero
% 5.02/5.29 thf(fact_3656_even__iff__mod__2__eq__zero,axiom,
% 5.02/5.29 ! [A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = zero_zero_nat ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_iff_mod_2_eq_zero
% 5.02/5.29 thf(fact_3657_even__iff__mod__2__eq__zero,axiom,
% 5.02/5.29 ! [A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.29 = zero_zero_int ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_iff_mod_2_eq_zero
% 5.02/5.29 thf(fact_3658_odd__iff__mod__2__eq__one,axiom,
% 5.02/5.29 ! [A: code_integer] :
% 5.02/5.29 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.29 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.29 = one_one_Code_integer ) ) ).
% 5.02/5.29
% 5.02/5.29 % odd_iff_mod_2_eq_one
% 5.02/5.29 thf(fact_3659_odd__iff__mod__2__eq__one,axiom,
% 5.02/5.29 ! [A: nat] :
% 5.02/5.29 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.29 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = one_one_nat ) ) ).
% 5.02/5.29
% 5.02/5.29 % odd_iff_mod_2_eq_one
% 5.02/5.29 thf(fact_3660_odd__iff__mod__2__eq__one,axiom,
% 5.02/5.29 ! [A: int] :
% 5.02/5.29 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.29 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.29 = one_one_int ) ) ).
% 5.02/5.29
% 5.02/5.29 % odd_iff_mod_2_eq_one
% 5.02/5.29 thf(fact_3661_power__mono__odd,axiom,
% 5.02/5.29 ! [N2: nat,A: real,B: real] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ( ord_less_eq_real @ A @ B )
% 5.02/5.29 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_mono_odd
% 5.02/5.29 thf(fact_3662_power__mono__odd,axiom,
% 5.02/5.29 ! [N2: nat,A: rat,B: rat] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.29 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_mono_odd
% 5.02/5.29 thf(fact_3663_power__mono__odd,axiom,
% 5.02/5.29 ! [N2: nat,A: int,B: int] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ( ord_less_eq_int @ A @ B )
% 5.02/5.29 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_mono_odd
% 5.02/5.29 thf(fact_3664_odd__pos,axiom,
% 5.02/5.29 ! [N2: nat] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.02/5.29
% 5.02/5.29 % odd_pos
% 5.02/5.29 thf(fact_3665_dvd__power__iff__le,axiom,
% 5.02/5.29 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.29 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.02/5.29 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 5.02/5.29 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % dvd_power_iff_le
% 5.02/5.29 thf(fact_3666_signed__take__bit__int__less__exp,axiom,
% 5.02/5.29 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.29
% 5.02/5.29 % signed_take_bit_int_less_exp
% 5.02/5.29 thf(fact_3667_even__unset__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 | ( M = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_unset_bit_iff
% 5.02/5.29 thf(fact_3668_even__unset__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 | ( M = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_unset_bit_iff
% 5.02/5.29 thf(fact_3669_even__unset__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 | ( M = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_unset_bit_iff
% 5.02/5.29 thf(fact_3670_even__set__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 & ( M != zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_set_bit_iff
% 5.02/5.29 thf(fact_3671_even__set__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 & ( M != zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_set_bit_iff
% 5.02/5.29 thf(fact_3672_even__set__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 & ( M != zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_set_bit_iff
% 5.02/5.29 thf(fact_3673_even__flip__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: code_integer] :
% 5.02/5.29 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 != ( M = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_flip_bit_iff
% 5.02/5.29 thf(fact_3674_even__flip__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: int] :
% 5.02/5.29 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 != ( M = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_flip_bit_iff
% 5.02/5.29 thf(fact_3675_even__flip__bit__iff,axiom,
% 5.02/5.29 ! [M: nat,A: nat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.02/5.29 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 != ( M = zero_zero_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % even_flip_bit_iff
% 5.02/5.29 thf(fact_3676_num_Osize__gen_I1_J,axiom,
% 5.02/5.29 ( ( size_num @ one )
% 5.02/5.29 = zero_zero_nat ) ).
% 5.02/5.29
% 5.02/5.29 % num.size_gen(1)
% 5.02/5.29 thf(fact_3677_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.02/5.29 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S2: vEBT_VEBT,X2: nat] :
% 5.02/5.29 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S2 ) @ X2 )
% 5.02/5.29 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.02/5.29 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.naive_member.simps(3)
% 5.02/5.29 thf(fact_3678_oddE,axiom,
% 5.02/5.29 ! [A: code_integer] :
% 5.02/5.29 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ~ ! [B3: code_integer] :
% 5.02/5.29 ( A
% 5.02/5.29 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % oddE
% 5.02/5.29 thf(fact_3679_oddE,axiom,
% 5.02/5.29 ! [A: nat] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ~ ! [B3: nat] :
% 5.02/5.29 ( A
% 5.02/5.29 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % oddE
% 5.02/5.29 thf(fact_3680_oddE,axiom,
% 5.02/5.29 ! [A: int] :
% 5.02/5.29 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ~ ! [B3: int] :
% 5.02/5.29 ( A
% 5.02/5.29 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % oddE
% 5.02/5.29 thf(fact_3681_mod2__eq__if,axiom,
% 5.02/5.29 ! [A: code_integer] :
% 5.02/5.29 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.29 = zero_z3403309356797280102nteger ) )
% 5.02/5.29 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.29 = one_one_Code_integer ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod2_eq_if
% 5.02/5.29 thf(fact_3682_mod2__eq__if,axiom,
% 5.02/5.29 ! [A: nat] :
% 5.02/5.29 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = zero_zero_nat ) )
% 5.02/5.29 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = one_one_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod2_eq_if
% 5.02/5.29 thf(fact_3683_mod2__eq__if,axiom,
% 5.02/5.29 ! [A: int] :
% 5.02/5.29 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.29 = zero_zero_int ) )
% 5.02/5.29 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.29 = one_one_int ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % mod2_eq_if
% 5.02/5.29 thf(fact_3684_parity__cases,axiom,
% 5.02/5.29 ! [A: code_integer] :
% 5.02/5.29 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.29 != zero_z3403309356797280102nteger ) )
% 5.02/5.29 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.29 != one_one_Code_integer ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % parity_cases
% 5.02/5.29 thf(fact_3685_parity__cases,axiom,
% 5.02/5.29 ! [A: nat] :
% 5.02/5.29 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 != zero_zero_nat ) )
% 5.02/5.29 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 != one_one_nat ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % parity_cases
% 5.02/5.29 thf(fact_3686_parity__cases,axiom,
% 5.02/5.29 ! [A: int] :
% 5.02/5.29 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.29 != zero_zero_int ) )
% 5.02/5.29 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.29 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.29 != one_one_int ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % parity_cases
% 5.02/5.29 thf(fact_3687_zero__le__power__eq,axiom,
% 5.02/5.29 ! [A: real,N2: nat] :
% 5.02/5.29 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.02/5.29 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_power_eq
% 5.02/5.29 thf(fact_3688_zero__le__power__eq,axiom,
% 5.02/5.29 ! [A: rat,N2: nat] :
% 5.02/5.29 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.02/5.29 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_power_eq
% 5.02/5.29 thf(fact_3689_zero__le__power__eq,axiom,
% 5.02/5.29 ! [A: int,N2: nat] :
% 5.02/5.29 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.02/5.29 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_power_eq
% 5.02/5.29 thf(fact_3690_zero__le__odd__power,axiom,
% 5.02/5.29 ! [N2: nat,A: real] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.02/5.29 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_odd_power
% 5.02/5.29 thf(fact_3691_zero__le__odd__power,axiom,
% 5.02/5.29 ! [N2: nat,A: rat] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.02/5.29 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_odd_power
% 5.02/5.29 thf(fact_3692_zero__le__odd__power,axiom,
% 5.02/5.29 ! [N2: nat,A: int] :
% 5.02/5.29 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.02/5.29 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_odd_power
% 5.02/5.29 thf(fact_3693_zero__le__even__power,axiom,
% 5.02/5.29 ! [N2: nat,A: real] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_even_power
% 5.02/5.29 thf(fact_3694_zero__le__even__power,axiom,
% 5.02/5.29 ! [N2: nat,A: rat] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_even_power
% 5.02/5.29 thf(fact_3695_zero__le__even__power,axiom,
% 5.02/5.29 ! [N2: nat,A: int] :
% 5.02/5.29 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_le_even_power
% 5.02/5.29 thf(fact_3696_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.02/5.29 ! [K: int,N2: nat] :
% 5.02/5.29 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.02/5.29 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % signed_take_bit_int_greater_eq_self_iff
% 5.02/5.29 thf(fact_3697_signed__take__bit__int__less__self__iff,axiom,
% 5.02/5.29 ! [N2: nat,K: int] :
% 5.02/5.29 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.02/5.29 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.02/5.29
% 5.02/5.29 % signed_take_bit_int_less_self_iff
% 5.02/5.29 thf(fact_3698_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.02/5.29 ! [V: nat,TreeList: list_VEBT_VEBT,Vd2: vEBT_VEBT,X2: nat] :
% 5.02/5.29 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd2 ) @ X2 )
% 5.02/5.29 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.02/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.membermima.simps(5)
% 5.02/5.29 thf(fact_3699_div__pos__geq,axiom,
% 5.02/5.29 ! [L: int,K: int] :
% 5.02/5.29 ( ( ord_less_int @ zero_zero_int @ L )
% 5.02/5.29 => ( ( ord_less_eq_int @ L @ K )
% 5.02/5.29 => ( ( divide_divide_int @ K @ L )
% 5.02/5.29 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % div_pos_geq
% 5.02/5.29 thf(fact_3700_vebt__member_Osimps_I5_J,axiom,
% 5.02/5.29 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.02/5.29 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X2 )
% 5.02/5.29 = ( ( X2 != Mi )
% 5.02/5.29 => ( ( X2 != Ma )
% 5.02/5.29 => ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.02/5.29 & ( ~ ( ord_less_nat @ X2 @ Mi )
% 5.02/5.29 => ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.02/5.29 & ( ~ ( ord_less_nat @ Ma @ X2 )
% 5.02/5.29 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.02/5.29 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % vebt_member.simps(5)
% 5.02/5.29 thf(fact_3701_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.02/5.29 ! [Mi: nat,Ma: nat,V: nat,TreeList: list_VEBT_VEBT,Vc: vEBT_VEBT,X2: nat] :
% 5.02/5.29 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList @ Vc ) @ X2 )
% 5.02/5.29 = ( ( X2 = Mi )
% 5.02/5.29 | ( X2 = Ma )
% 5.02/5.29 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.02/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ X2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.membermima.simps(4)
% 5.02/5.29 thf(fact_3702_add__0__iff,axiom,
% 5.02/5.29 ! [B: complex,A: complex] :
% 5.02/5.29 ( ( B
% 5.02/5.29 = ( plus_plus_complex @ B @ A ) )
% 5.02/5.29 = ( A = zero_zero_complex ) ) ).
% 5.02/5.29
% 5.02/5.29 % add_0_iff
% 5.02/5.29 thf(fact_3703_add__0__iff,axiom,
% 5.02/5.29 ! [B: real,A: real] :
% 5.02/5.29 ( ( B
% 5.02/5.29 = ( plus_plus_real @ B @ A ) )
% 5.02/5.29 = ( A = zero_zero_real ) ) ).
% 5.02/5.29
% 5.02/5.29 % add_0_iff
% 5.02/5.29 thf(fact_3704_add__0__iff,axiom,
% 5.02/5.29 ! [B: rat,A: rat] :
% 5.02/5.29 ( ( B
% 5.02/5.29 = ( plus_plus_rat @ B @ A ) )
% 5.02/5.29 = ( A = zero_zero_rat ) ) ).
% 5.02/5.29
% 5.02/5.29 % add_0_iff
% 5.02/5.29 thf(fact_3705_add__0__iff,axiom,
% 5.02/5.29 ! [B: nat,A: nat] :
% 5.02/5.29 ( ( B
% 5.02/5.29 = ( plus_plus_nat @ B @ A ) )
% 5.02/5.29 = ( A = zero_zero_nat ) ) ).
% 5.02/5.29
% 5.02/5.29 % add_0_iff
% 5.02/5.29 thf(fact_3706_add__0__iff,axiom,
% 5.02/5.29 ! [B: int,A: int] :
% 5.02/5.29 ( ( B
% 5.02/5.29 = ( plus_plus_int @ B @ A ) )
% 5.02/5.29 = ( A = zero_zero_int ) ) ).
% 5.02/5.29
% 5.02/5.29 % add_0_iff
% 5.02/5.29 thf(fact_3707_crossproduct__eq,axiom,
% 5.02/5.29 ! [W: real,Y: real,X2: real,Z: real] :
% 5.02/5.29 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X2 @ Z ) )
% 5.02/5.29 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X2 @ Y ) ) )
% 5.02/5.29 = ( ( W = X2 )
% 5.02/5.29 | ( Y = Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % crossproduct_eq
% 5.02/5.29 thf(fact_3708_crossproduct__eq,axiom,
% 5.02/5.29 ! [W: rat,Y: rat,X2: rat,Z: rat] :
% 5.02/5.29 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X2 @ Z ) )
% 5.02/5.29 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X2 @ Y ) ) )
% 5.02/5.29 = ( ( W = X2 )
% 5.02/5.29 | ( Y = Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % crossproduct_eq
% 5.02/5.29 thf(fact_3709_crossproduct__eq,axiom,
% 5.02/5.29 ! [W: nat,Y: nat,X2: nat,Z: nat] :
% 5.02/5.29 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X2 @ Z ) )
% 5.02/5.29 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X2 @ Y ) ) )
% 5.02/5.29 = ( ( W = X2 )
% 5.02/5.29 | ( Y = Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % crossproduct_eq
% 5.02/5.29 thf(fact_3710_crossproduct__eq,axiom,
% 5.02/5.29 ! [W: int,Y: int,X2: int,Z: int] :
% 5.02/5.29 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X2 @ Z ) )
% 5.02/5.29 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X2 @ Y ) ) )
% 5.02/5.29 = ( ( W = X2 )
% 5.02/5.29 | ( Y = Z ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % crossproduct_eq
% 5.02/5.29 thf(fact_3711_crossproduct__noteq,axiom,
% 5.02/5.29 ! [A: real,B: real,C: real,D: real] :
% 5.02/5.29 ( ( ( A != B )
% 5.02/5.29 & ( C != D ) )
% 5.02/5.29 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.02/5.29 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % crossproduct_noteq
% 5.02/5.29 thf(fact_3712_crossproduct__noteq,axiom,
% 5.02/5.29 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.02/5.29 ( ( ( A != B )
% 5.02/5.29 & ( C != D ) )
% 5.02/5.29 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.02/5.29 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % crossproduct_noteq
% 5.02/5.29 thf(fact_3713_crossproduct__noteq,axiom,
% 5.02/5.29 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.02/5.29 ( ( ( A != B )
% 5.02/5.29 & ( C != D ) )
% 5.02/5.29 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.02/5.29 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % crossproduct_noteq
% 5.02/5.29 thf(fact_3714_crossproduct__noteq,axiom,
% 5.02/5.29 ! [A: int,B: int,C: int,D: int] :
% 5.02/5.29 ( ( ( A != B )
% 5.02/5.29 & ( C != D ) )
% 5.02/5.29 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.02/5.29 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % crossproduct_noteq
% 5.02/5.29 thf(fact_3715_power2__diff,axiom,
% 5.02/5.29 ! [X2: complex,Y: complex] :
% 5.02/5.29 ( ( power_power_complex @ ( minus_minus_complex @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) @ Y ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power2_diff
% 5.02/5.29 thf(fact_3716_power2__diff,axiom,
% 5.02/5.29 ! [X2: real,Y: real] :
% 5.02/5.29 ( ( power_power_real @ ( minus_minus_real @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( 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 ) ) @ X2 ) @ Y ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power2_diff
% 5.02/5.29 thf(fact_3717_power2__diff,axiom,
% 5.02/5.29 ! [X2: rat,Y: rat] :
% 5.02/5.29 ( ( power_power_rat @ ( minus_minus_rat @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X2 @ ( 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 ) ) @ X2 ) @ Y ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power2_diff
% 5.02/5.29 thf(fact_3718_power2__diff,axiom,
% 5.02/5.29 ! [X2: int,Y: int] :
% 5.02/5.29 ( ( power_power_int @ ( minus_minus_int @ X2 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.29 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X2 @ ( 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 ) ) @ X2 ) @ Y ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power2_diff
% 5.02/5.29 thf(fact_3719_zero__less__power__eq,axiom,
% 5.02/5.29 ! [A: real,N2: nat] :
% 5.02/5.29 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.02/5.29 = ( ( N2 = zero_zero_nat )
% 5.02/5.29 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( A != zero_zero_real ) )
% 5.02/5.29 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_less_power_eq
% 5.02/5.29 thf(fact_3720_zero__less__power__eq,axiom,
% 5.02/5.29 ! [A: rat,N2: nat] :
% 5.02/5.29 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.02/5.29 = ( ( N2 = zero_zero_nat )
% 5.02/5.29 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( A != zero_zero_rat ) )
% 5.02/5.29 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_less_power_eq
% 5.02/5.29 thf(fact_3721_zero__less__power__eq,axiom,
% 5.02/5.29 ! [A: int,N2: nat] :
% 5.02/5.29 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.02/5.29 = ( ( N2 = zero_zero_nat )
% 5.02/5.29 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( A != zero_zero_int ) )
% 5.02/5.29 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % zero_less_power_eq
% 5.02/5.29 thf(fact_3722_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.02/5.29 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.29 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.02/5.29 => ( ! [A4: $o,B3: $o] :
% 5.02/5.29 ( ( X2
% 5.02/5.29 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.29 => ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.29 => A4 )
% 5.02/5.29 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.29 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.29 => B3 )
% 5.02/5.29 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.02/5.29 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.02/5.29 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [S: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.02/5.29 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.naive_member.elims(3)
% 5.02/5.29 thf(fact_3723_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.02/5.29 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.29 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.02/5.29 => ( ! [A4: $o,B3: $o] :
% 5.02/5.29 ( ( X2
% 5.02/5.29 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.29 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.29 => A4 )
% 5.02/5.29 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.29 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.29 => B3 )
% 5.02/5.29 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.02/5.29 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [S: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.02/5.29 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.naive_member.elims(2)
% 5.02/5.29 thf(fact_3724_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.02/5.29 ! [X2: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.02/5.29 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.02/5.29 = Y )
% 5.02/5.29 => ( ! [A4: $o,B3: $o] :
% 5.02/5.29 ( ( X2
% 5.02/5.29 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.29 => ( Y
% 5.02/5.29 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.29 => A4 )
% 5.02/5.29 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.29 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.29 => B3 )
% 5.02/5.29 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.02/5.29 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.02/5.29 => Y )
% 5.02/5.29 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [S: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.02/5.29 => ( Y
% 5.02/5.29 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.naive_member.elims(1)
% 5.02/5.29 thf(fact_3725_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.02/5.29 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.29 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.02/5.29 => ( ! [Mi2: nat,Ma2: nat] :
% 5.02/5.29 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.02/5.29 => ~ ( ( Xa2 = Mi2 )
% 5.02/5.29 | ( Xa2 = Ma2 ) ) )
% 5.02/5.29 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [Vc2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.02/5.29 => ~ ( ( Xa2 = Mi2 )
% 5.02/5.29 | ( Xa2 = Ma2 )
% 5.02/5.29 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.02/5.29 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [Vd: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) )
% 5.02/5.29 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.membermima.elims(2)
% 5.02/5.29 thf(fact_3726_divmod__digit__1_I2_J,axiom,
% 5.02/5.29 ! [A: nat,B: nat] :
% 5.02/5.29 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.02/5.29 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.02/5.29 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.02/5.29 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.02/5.29 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % divmod_digit_1(2)
% 5.02/5.29 thf(fact_3727_divmod__digit__1_I2_J,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.02/5.29 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.29 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.02/5.29 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.02/5.29 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % divmod_digit_1(2)
% 5.02/5.29 thf(fact_3728_power__le__zero__eq,axiom,
% 5.02/5.29 ! [A: real,N2: nat] :
% 5.02/5.29 ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.02/5.29 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.02/5.29 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_le_zero_eq
% 5.02/5.29 thf(fact_3729_power__le__zero__eq,axiom,
% 5.02/5.29 ! [A: rat,N2: nat] :
% 5.02/5.29 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.02/5.29 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.02/5.29 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_le_zero_eq
% 5.02/5.29 thf(fact_3730_power__le__zero__eq,axiom,
% 5.02/5.29 ! [A: int,N2: nat] :
% 5.02/5.29 ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.02/5.29 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.29 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.02/5.29 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.29 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % power_le_zero_eq
% 5.02/5.29 thf(fact_3731_vebt__member_Oelims_I2_J,axiom,
% 5.02/5.29 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.29 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.02/5.29 => ( ! [A4: $o,B3: $o] :
% 5.02/5.29 ( ( X2
% 5.02/5.29 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.29 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.29 => A4 )
% 5.02/5.29 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.29 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.29 => B3 )
% 5.02/5.29 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.02/5.29 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [Summary2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.29 => ~ ( ( Xa2 != Mi2 )
% 5.02/5.29 => ( ( Xa2 != Ma2 )
% 5.02/5.29 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.29 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.29 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.29 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.29 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % vebt_member.elims(2)
% 5.02/5.29 thf(fact_3732_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.02/5.29 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.29 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.02/5.29 => ( ! [Uu2: $o,Uv2: $o] :
% 5.02/5.29 ( X2
% 5.02/5.29 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.29 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.02/5.29 => ( ! [Mi2: nat,Ma2: nat] :
% 5.02/5.29 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.02/5.29 => ( ( Xa2 = Mi2 )
% 5.02/5.29 | ( Xa2 = Ma2 ) ) )
% 5.02/5.29 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [Vc2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.02/5.29 => ( ( Xa2 = Mi2 )
% 5.02/5.29 | ( Xa2 = Ma2 )
% 5.02/5.29 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.02/5.29 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [Vd: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) )
% 5.02/5.29 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.membermima.elims(3)
% 5.02/5.29 thf(fact_3733_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.02/5.29 ! [X2: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.02/5.29 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.02/5.29 = Y )
% 5.02/5.29 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.29 => Y )
% 5.02/5.29 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.02/5.29 => Y )
% 5.02/5.29 => ( ! [Mi2: nat,Ma2: nat] :
% 5.02/5.29 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.02/5.29 => ( Y
% 5.02/5.29 = ( ~ ( ( Xa2 = Mi2 )
% 5.02/5.29 | ( Xa2 = Ma2 ) ) ) ) )
% 5.02/5.29 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [Vc2: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.02/5.29 => ( Y
% 5.02/5.29 = ( ~ ( ( Xa2 = Mi2 )
% 5.02/5.29 | ( Xa2 = Ma2 )
% 5.02/5.29 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) )
% 5.02/5.29 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.29 ( ? [Vd: vEBT_VEBT] :
% 5.02/5.29 ( X2
% 5.02/5.29 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) )
% 5.02/5.29 => ( Y
% 5.02/5.29 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.29 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.29 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % VEBT_internal.membermima.elims(1)
% 5.02/5.29 thf(fact_3734_neg__zmod__mult__2,axiom,
% 5.02/5.29 ! [A: int,B: int] :
% 5.02/5.29 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.02/5.29 => ( ( 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 ) )
% 5.02/5.29 = ( 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 ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % neg_zmod_mult_2
% 5.02/5.29 thf(fact_3735_vebt__insert_Osimps_I5_J,axiom,
% 5.02/5.29 ! [Mi: nat,Ma: nat,Va2: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,X2: nat] :
% 5.02/5.29 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) @ X2 )
% 5.02/5.29 = ( if_VEBT_VEBT
% 5.02/5.29 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 5.02/5.29 & ~ ( ( X2 = Mi )
% 5.02/5.29 | ( X2 = Ma ) ) )
% 5.02/5.29 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ X2 @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ Ma ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X2 @ Mi ) @ Mi @ X2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.02/5.29 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList @ Summary ) ) ) ).
% 5.02/5.29
% 5.02/5.29 % vebt_insert.simps(5)
% 5.02/5.29 thf(fact_3736_vebt__member_Oelims_I3_J,axiom,
% 5.02/5.29 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.29 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.02/5.29 => ( ! [A4: $o,B3: $o] :
% 5.02/5.29 ( ( X2
% 5.02/5.29 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.29 => ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.29 => A4 )
% 5.02/5.29 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.29 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.30 => B3 )
% 5.02/5.30 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.02/5.30 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.02/5.30 ( X2
% 5.02/5.30 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.02/5.30 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.02/5.30 ( X2
% 5.02/5.30 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.02/5.30 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.02/5.30 ( X2
% 5.02/5.30 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.02/5.30 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.30 ( ? [Summary2: vEBT_VEBT] :
% 5.02/5.30 ( X2
% 5.02/5.30 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.30 => ( ( Xa2 != Mi2 )
% 5.02/5.30 => ( ( Xa2 != Ma2 )
% 5.02/5.30 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.30 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.30 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.30 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.30 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.30 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.30 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % vebt_member.elims(3)
% 5.02/5.30 thf(fact_3737_vebt__member_Oelims_I1_J,axiom,
% 5.02/5.30 ! [X2: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.02/5.30 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.02/5.30 = Y )
% 5.02/5.30 => ( ! [A4: $o,B3: $o] :
% 5.02/5.30 ( ( X2
% 5.02/5.30 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.30 => ( Y
% 5.02/5.30 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.30 => A4 )
% 5.02/5.30 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.30 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.30 => B3 )
% 5.02/5.30 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.02/5.30 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.02/5.30 ( X2
% 5.02/5.30 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.02/5.30 => Y )
% 5.02/5.30 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.02/5.30 ( X2
% 5.02/5.30 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.02/5.30 => Y )
% 5.02/5.30 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.02/5.30 ( X2
% 5.02/5.30 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.02/5.30 => Y )
% 5.02/5.30 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT] :
% 5.02/5.30 ( ? [Summary2: vEBT_VEBT] :
% 5.02/5.30 ( X2
% 5.02/5.30 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.30 => ( Y
% 5.02/5.30 = ( ~ ( ( Xa2 != Mi2 )
% 5.02/5.30 => ( ( Xa2 != Ma2 )
% 5.02/5.30 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.30 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.30 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.30 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.30 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.30 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.30 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % vebt_member.elims(1)
% 5.02/5.30 thf(fact_3738_divmod__step__eq,axiom,
% 5.02/5.30 ! [L: num,R2: nat,Q2: nat] :
% 5.02/5.30 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.02/5.30 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.02/5.30 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R2 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.02/5.30 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R2 )
% 5.02/5.30 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R2 ) )
% 5.02/5.30 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % divmod_step_eq
% 5.02/5.30 thf(fact_3739_divmod__step__eq,axiom,
% 5.02/5.30 ! [L: num,R2: int,Q2: int] :
% 5.02/5.30 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.02/5.30 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.02/5.30 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R2 @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.02/5.30 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R2 )
% 5.02/5.30 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.02/5.30 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % divmod_step_eq
% 5.02/5.30 thf(fact_3740_divmod__step__eq,axiom,
% 5.02/5.30 ! [L: num,R2: code_integer,Q2: code_integer] :
% 5.02/5.30 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.02/5.30 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.02/5.30 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R2 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.02/5.30 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R2 )
% 5.02/5.30 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R2 ) )
% 5.02/5.30 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % divmod_step_eq
% 5.02/5.30 thf(fact_3741_max__bot,axiom,
% 5.02/5.30 ! [X2: set_nat] :
% 5.02/5.30 ( ( ord_max_set_nat @ bot_bot_set_nat @ X2 )
% 5.02/5.30 = X2 ) ).
% 5.02/5.30
% 5.02/5.30 % max_bot
% 5.02/5.30 thf(fact_3742_max__bot,axiom,
% 5.02/5.30 ! [X2: set_int] :
% 5.02/5.30 ( ( ord_max_set_int @ bot_bot_set_int @ X2 )
% 5.02/5.30 = X2 ) ).
% 5.02/5.30
% 5.02/5.30 % max_bot
% 5.02/5.30 thf(fact_3743_max__bot,axiom,
% 5.02/5.30 ! [X2: set_real] :
% 5.02/5.30 ( ( ord_max_set_real @ bot_bot_set_real @ X2 )
% 5.02/5.30 = X2 ) ).
% 5.02/5.30
% 5.02/5.30 % max_bot
% 5.02/5.30 thf(fact_3744_max__bot,axiom,
% 5.02/5.30 ! [X2: nat] :
% 5.02/5.30 ( ( ord_max_nat @ bot_bot_nat @ X2 )
% 5.02/5.30 = X2 ) ).
% 5.02/5.30
% 5.02/5.30 % max_bot
% 5.02/5.30 thf(fact_3745_max__bot2,axiom,
% 5.02/5.30 ! [X2: set_nat] :
% 5.02/5.30 ( ( ord_max_set_nat @ X2 @ bot_bot_set_nat )
% 5.02/5.30 = X2 ) ).
% 5.02/5.30
% 5.02/5.30 % max_bot2
% 5.02/5.30 thf(fact_3746_max__bot2,axiom,
% 5.02/5.30 ! [X2: set_int] :
% 5.02/5.30 ( ( ord_max_set_int @ X2 @ bot_bot_set_int )
% 5.02/5.30 = X2 ) ).
% 5.02/5.30
% 5.02/5.30 % max_bot2
% 5.02/5.30 thf(fact_3747_max__bot2,axiom,
% 5.02/5.30 ! [X2: set_real] :
% 5.02/5.30 ( ( ord_max_set_real @ X2 @ bot_bot_set_real )
% 5.02/5.30 = X2 ) ).
% 5.02/5.30
% 5.02/5.30 % max_bot2
% 5.02/5.30 thf(fact_3748_max__bot2,axiom,
% 5.02/5.30 ! [X2: nat] :
% 5.02/5.30 ( ( ord_max_nat @ X2 @ bot_bot_nat )
% 5.02/5.30 = X2 ) ).
% 5.02/5.30
% 5.02/5.30 % max_bot2
% 5.02/5.30 thf(fact_3749_empty__subsetI,axiom,
% 5.02/5.30 ! [A3: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % empty_subsetI
% 5.02/5.30 thf(fact_3750_empty__subsetI,axiom,
% 5.02/5.30 ! [A3: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % empty_subsetI
% 5.02/5.30 thf(fact_3751_empty__subsetI,axiom,
% 5.02/5.30 ! [A3: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % empty_subsetI
% 5.02/5.30 thf(fact_3752_subset__empty,axiom,
% 5.02/5.30 ! [A3: set_int] :
% 5.02/5.30 ( ( ord_less_eq_set_int @ A3 @ bot_bot_set_int )
% 5.02/5.30 = ( A3 = bot_bot_set_int ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_empty
% 5.02/5.30 thf(fact_3753_subset__empty,axiom,
% 5.02/5.30 ! [A3: set_real] :
% 5.02/5.30 ( ( ord_less_eq_set_real @ A3 @ bot_bot_set_real )
% 5.02/5.30 = ( A3 = bot_bot_set_real ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_empty
% 5.02/5.30 thf(fact_3754_subset__empty,axiom,
% 5.02/5.30 ! [A3: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ bot_bot_set_nat )
% 5.02/5.30 = ( A3 = bot_bot_set_nat ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_empty
% 5.02/5.30 thf(fact_3755_vebt__insert_Opelims,axiom,
% 5.02/5.30 ! [X2: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.02/5.30 ( ( ( vEBT_vebt_insert @ X2 @ Xa2 )
% 5.02/5.30 = Y )
% 5.02/5.30 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.30 => ( ! [A4: $o,B3: $o] :
% 5.02/5.30 ( ( X2
% 5.02/5.30 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.30 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.30 => ( Y
% 5.02/5.30 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 5.02/5.30 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.30 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.30 => ( Y
% 5.02/5.30 = ( vEBT_Leaf @ A4 @ $true ) ) )
% 5.02/5.30 & ( ( Xa2 != one_one_nat )
% 5.02/5.30 => ( Y
% 5.02/5.30 = ( vEBT_Leaf @ A4 @ B3 ) ) ) ) ) )
% 5.02/5.30 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 5.02/5.30 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.02/5.30 ( ( X2
% 5.02/5.30 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 5.02/5.30 => ( ( Y
% 5.02/5.30 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) )
% 5.02/5.30 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S ) @ Xa2 ) ) ) )
% 5.02/5.30 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.02/5.30 ( ( X2
% 5.02/5.30 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 5.02/5.30 => ( ( Y
% 5.02/5.30 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) )
% 5.02/5.30 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S ) @ Xa2 ) ) ) )
% 5.02/5.30 => ( ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.30 ( ( X2
% 5.02/5.30 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.30 => ( ( Y
% 5.02/5.30 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.30 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) )
% 5.02/5.30 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.30 ( ( X2
% 5.02/5.30 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.30 => ( ( Y
% 5.02/5.30 = ( if_VEBT_VEBT
% 5.02/5.30 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.30 & ~ ( ( Xa2 = Mi2 )
% 5.02/5.30 | ( Xa2 = Ma2 ) ) )
% 5.02/5.30 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.02/5.30 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) ) )
% 5.02/5.30 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % vebt_insert.pelims
% 5.02/5.30 thf(fact_3756_div2__even__ext__nat,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.30 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.30 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 )
% 5.02/5.30 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.02/5.30 => ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % div2_even_ext_nat
% 5.02/5.30 thf(fact_3757_dual__order_Orefl,axiom,
% 5.02/5.30 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.refl
% 5.02/5.30 thf(fact_3758_dual__order_Orefl,axiom,
% 5.02/5.30 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.refl
% 5.02/5.30 thf(fact_3759_dual__order_Orefl,axiom,
% 5.02/5.30 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.refl
% 5.02/5.30 thf(fact_3760_dual__order_Orefl,axiom,
% 5.02/5.30 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.refl
% 5.02/5.30 thf(fact_3761_dual__order_Orefl,axiom,
% 5.02/5.30 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.refl
% 5.02/5.30 thf(fact_3762_order__refl,axiom,
% 5.02/5.30 ! [X2: set_nat] : ( ord_less_eq_set_nat @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_refl
% 5.02/5.30 thf(fact_3763_order__refl,axiom,
% 5.02/5.30 ! [X2: rat] : ( ord_less_eq_rat @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_refl
% 5.02/5.30 thf(fact_3764_order__refl,axiom,
% 5.02/5.30 ! [X2: num] : ( ord_less_eq_num @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_refl
% 5.02/5.30 thf(fact_3765_order__refl,axiom,
% 5.02/5.30 ! [X2: nat] : ( ord_less_eq_nat @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_refl
% 5.02/5.30 thf(fact_3766_order__refl,axiom,
% 5.02/5.30 ! [X2: int] : ( ord_less_eq_int @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_refl
% 5.02/5.30 thf(fact_3767_Suc__diff__diff,axiom,
% 5.02/5.30 ! [M: nat,N2: nat,K: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 5.02/5.30 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 5.02/5.30
% 5.02/5.30 % Suc_diff_diff
% 5.02/5.30 thf(fact_3768_diff__Suc__Suc,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.02/5.30 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_Suc_Suc
% 5.02/5.30 thf(fact_3769_diff__self__eq__0,axiom,
% 5.02/5.30 ! [M: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ M @ M )
% 5.02/5.30 = zero_zero_nat ) ).
% 5.02/5.30
% 5.02/5.30 % diff_self_eq_0
% 5.02/5.30 thf(fact_3770_diff__0__eq__0,axiom,
% 5.02/5.30 ! [N2: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 = zero_zero_nat ) ).
% 5.02/5.30
% 5.02/5.30 % diff_0_eq_0
% 5.02/5.30 thf(fact_3771_subsetI,axiom,
% 5.02/5.30 ! [A3: set_complex,B4: set_complex] :
% 5.02/5.30 ( ! [X5: complex] :
% 5.02/5.30 ( ( member_complex @ X5 @ A3 )
% 5.02/5.30 => ( member_complex @ X5 @ B4 ) )
% 5.02/5.30 => ( ord_le211207098394363844omplex @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetI
% 5.02/5.30 thf(fact_3772_subsetI,axiom,
% 5.02/5.30 ! [A3: set_real,B4: set_real] :
% 5.02/5.30 ( ! [X5: real] :
% 5.02/5.30 ( ( member_real @ X5 @ A3 )
% 5.02/5.30 => ( member_real @ X5 @ B4 ) )
% 5.02/5.30 => ( ord_less_eq_set_real @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetI
% 5.02/5.30 thf(fact_3773_subsetI,axiom,
% 5.02/5.30 ! [A3: set_set_nat,B4: set_set_nat] :
% 5.02/5.30 ( ! [X5: set_nat] :
% 5.02/5.30 ( ( member_set_nat @ X5 @ A3 )
% 5.02/5.30 => ( member_set_nat @ X5 @ B4 ) )
% 5.02/5.30 => ( ord_le6893508408891458716et_nat @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetI
% 5.02/5.30 thf(fact_3774_subsetI,axiom,
% 5.02/5.30 ! [A3: set_int,B4: set_int] :
% 5.02/5.30 ( ! [X5: int] :
% 5.02/5.30 ( ( member_int @ X5 @ A3 )
% 5.02/5.30 => ( member_int @ X5 @ B4 ) )
% 5.02/5.30 => ( ord_less_eq_set_int @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetI
% 5.02/5.30 thf(fact_3775_subsetI,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ! [X5: nat] :
% 5.02/5.30 ( ( member_nat @ X5 @ A3 )
% 5.02/5.30 => ( member_nat @ X5 @ B4 ) )
% 5.02/5.30 => ( ord_less_eq_set_nat @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetI
% 5.02/5.30 thf(fact_3776_subset__antisym,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ B4 @ A3 )
% 5.02/5.30 => ( A3 = B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_antisym
% 5.02/5.30 thf(fact_3777_diff__diff__cancel,axiom,
% 5.02/5.30 ! [I3: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.02/5.30 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I3 ) )
% 5.02/5.30 = I3 ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_diff_cancel
% 5.02/5.30 thf(fact_3778_diff__diff__left,axiom,
% 5.02/5.30 ! [I3: nat,J: nat,K: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J ) @ K )
% 5.02/5.30 = ( minus_minus_nat @ I3 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_diff_left
% 5.02/5.30 thf(fact_3779_Diff__eq__empty__iff,axiom,
% 5.02/5.30 ! [A3: set_int,B4: set_int] :
% 5.02/5.30 ( ( ( minus_minus_set_int @ A3 @ B4 )
% 5.02/5.30 = bot_bot_set_int )
% 5.02/5.30 = ( ord_less_eq_set_int @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % Diff_eq_empty_iff
% 5.02/5.30 thf(fact_3780_Diff__eq__empty__iff,axiom,
% 5.02/5.30 ! [A3: set_real,B4: set_real] :
% 5.02/5.30 ( ( ( minus_minus_set_real @ A3 @ B4 )
% 5.02/5.30 = bot_bot_set_real )
% 5.02/5.30 = ( ord_less_eq_set_real @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % Diff_eq_empty_iff
% 5.02/5.30 thf(fact_3781_Diff__eq__empty__iff,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( ( minus_minus_set_nat @ A3 @ B4 )
% 5.02/5.30 = bot_bot_set_nat )
% 5.02/5.30 = ( ord_less_eq_set_nat @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % Diff_eq_empty_iff
% 5.02/5.30 thf(fact_3782_zero__less__diff,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 5.02/5.30 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % zero_less_diff
% 5.02/5.30 thf(fact_3783_diff__is__0__eq_H,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.30 => ( ( minus_minus_nat @ M @ N2 )
% 5.02/5.30 = zero_zero_nat ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_is_0_eq'
% 5.02/5.30 thf(fact_3784_diff__is__0__eq,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( ( minus_minus_nat @ M @ N2 )
% 5.02/5.30 = zero_zero_nat )
% 5.02/5.30 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_is_0_eq
% 5.02/5.30 thf(fact_3785_Nat_Odiff__diff__right,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( minus_minus_nat @ I3 @ ( minus_minus_nat @ J @ K ) )
% 5.02/5.30 = ( minus_minus_nat @ ( plus_plus_nat @ I3 @ K ) @ J ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.diff_diff_right
% 5.02/5.30 thf(fact_3786_Nat_Oadd__diff__assoc2,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I3 )
% 5.02/5.30 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I3 ) @ K ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.add_diff_assoc2
% 5.02/5.30 thf(fact_3787_Nat_Oadd__diff__assoc,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( plus_plus_nat @ I3 @ ( minus_minus_nat @ J @ K ) )
% 5.02/5.30 = ( minus_minus_nat @ ( plus_plus_nat @ I3 @ J ) @ K ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.add_diff_assoc
% 5.02/5.30 thf(fact_3788_diff__Suc__1,axiom,
% 5.02/5.30 ! [N2: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.02/5.30 = N2 ) ).
% 5.02/5.30
% 5.02/5.30 % diff_Suc_1
% 5.02/5.30 thf(fact_3789_psubsetI,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( A3 != B4 )
% 5.02/5.30 => ( ord_less_set_nat @ A3 @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % psubsetI
% 5.02/5.30 thf(fact_3790_Suc__pred,axiom,
% 5.02/5.30 ! [N2: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.02/5.30 = N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % Suc_pred
% 5.02/5.30 thf(fact_3791_diff__Suc__diff__eq2,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I3 )
% 5.02/5.30 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I3 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_Suc_diff_eq2
% 5.02/5.30 thf(fact_3792_diff__Suc__diff__eq1,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( minus_minus_nat @ I3 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.02/5.30 = ( minus_minus_nat @ ( plus_plus_nat @ I3 @ K ) @ ( suc @ J ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_Suc_diff_eq1
% 5.02/5.30 thf(fact_3793_Suc__diff__1,axiom,
% 5.02/5.30 ! [N2: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.02/5.30 = N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % Suc_diff_1
% 5.02/5.30 thf(fact_3794_odd__Suc__minus__one,axiom,
% 5.02/5.30 ! [N2: nat] :
% 5.02/5.30 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.30 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.02/5.30 = N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % odd_Suc_minus_one
% 5.02/5.30 thf(fact_3795_even__diff__nat,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 = ( ( ord_less_nat @ M @ N2 )
% 5.02/5.30 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % even_diff_nat
% 5.02/5.30 thf(fact_3796_odd__two__times__div__two__nat,axiom,
% 5.02/5.30 ! [N2: nat] :
% 5.02/5.30 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.30 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.30 = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % odd_two_times_div_two_nat
% 5.02/5.30 thf(fact_3797_dvd__diff__nat,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( dvd_dvd_nat @ K @ M )
% 5.02/5.30 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.02/5.30 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dvd_diff_nat
% 5.02/5.30 thf(fact_3798_dvd__antisym,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( dvd_dvd_nat @ M @ N2 )
% 5.02/5.30 => ( ( dvd_dvd_nat @ N2 @ M )
% 5.02/5.30 => ( M = N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dvd_antisym
% 5.02/5.30 thf(fact_3799_Diff__mono,axiom,
% 5.02/5.30 ! [A3: set_nat,C5: set_nat,D4: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ C5 )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ D4 @ B4 )
% 5.02/5.30 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B4 ) @ ( minus_minus_set_nat @ C5 @ D4 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Diff_mono
% 5.02/5.30 thf(fact_3800_Diff__subset,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B4 ) @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % Diff_subset
% 5.02/5.30 thf(fact_3801_double__diff,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat,C5: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 5.02/5.30 => ( ( minus_minus_set_nat @ B4 @ ( minus_minus_set_nat @ C5 @ A3 ) )
% 5.02/5.30 = A3 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % double_diff
% 5.02/5.30 thf(fact_3802_bot__nat__def,axiom,
% 5.02/5.30 bot_bot_nat = zero_zero_nat ).
% 5.02/5.30
% 5.02/5.30 % bot_nat_def
% 5.02/5.30 thf(fact_3803_zero__induct__lemma,axiom,
% 5.02/5.30 ! [P: nat > $o,K: nat,I3: nat] :
% 5.02/5.30 ( ( P @ K )
% 5.02/5.30 => ( ! [N: nat] :
% 5.02/5.30 ( ( P @ ( suc @ N ) )
% 5.02/5.30 => ( P @ N ) )
% 5.02/5.30 => ( P @ ( minus_minus_nat @ K @ I3 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % zero_induct_lemma
% 5.02/5.30 thf(fact_3804_diffs0__imp__equal,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( ( minus_minus_nat @ M @ N2 )
% 5.02/5.30 = zero_zero_nat )
% 5.02/5.30 => ( ( ( minus_minus_nat @ N2 @ M )
% 5.02/5.30 = zero_zero_nat )
% 5.02/5.30 => ( M = N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diffs0_imp_equal
% 5.02/5.30 thf(fact_3805_minus__nat_Odiff__0,axiom,
% 5.02/5.30 ! [M: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.02/5.30 = M ) ).
% 5.02/5.30
% 5.02/5.30 % minus_nat.diff_0
% 5.02/5.30 thf(fact_3806_less__imp__diff__less,axiom,
% 5.02/5.30 ! [J: nat,K: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_nat @ J @ K )
% 5.02/5.30 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_imp_diff_less
% 5.02/5.30 thf(fact_3807_diff__less__mono2,axiom,
% 5.02/5.30 ! [M: nat,N2: nat,L: nat] :
% 5.02/5.30 ( ( ord_less_nat @ M @ N2 )
% 5.02/5.30 => ( ( ord_less_nat @ M @ L )
% 5.02/5.30 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_less_mono2
% 5.02/5.30 thf(fact_3808_dvd__minus__self,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 5.02/5.30 = ( ( ord_less_nat @ N2 @ M )
% 5.02/5.30 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dvd_minus_self
% 5.02/5.30 thf(fact_3809_diff__le__mono2,axiom,
% 5.02/5.30 ! [M: nat,N2: nat,L: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_le_mono2
% 5.02/5.30 thf(fact_3810_le__diff__iff_H,axiom,
% 5.02/5.30 ! [A: nat,C: nat,B: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ C )
% 5.02/5.30 => ( ( ord_less_eq_nat @ B @ C )
% 5.02/5.30 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.02/5.30 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_diff_iff'
% 5.02/5.30 thf(fact_3811_diff__le__self,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 5.02/5.30
% 5.02/5.30 % diff_le_self
% 5.02/5.30 thf(fact_3812_diff__le__mono,axiom,
% 5.02/5.30 ! [M: nat,N2: nat,L: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_le_mono
% 5.02/5.30 thf(fact_3813_Nat_Odiff__diff__eq,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ M )
% 5.02/5.30 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.30 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.02/5.30 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.diff_diff_eq
% 5.02/5.30 thf(fact_3814_le__diff__iff,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ M )
% 5.02/5.30 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.30 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.02/5.30 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_diff_iff
% 5.02/5.30 thf(fact_3815_eq__diff__iff,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ M )
% 5.02/5.30 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.30 => ( ( ( minus_minus_nat @ M @ K )
% 5.02/5.30 = ( minus_minus_nat @ N2 @ K ) )
% 5.02/5.30 = ( M = N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % eq_diff_iff
% 5.02/5.30 thf(fact_3816_dvd__diffD,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.02/5.30 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dvd_diffD
% 5.02/5.30 thf(fact_3817_dvd__diffD1,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 => ( ( dvd_dvd_nat @ K @ M )
% 5.02/5.30 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dvd_diffD1
% 5.02/5.30 thf(fact_3818_less__eq__dvd__minus,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.30 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.02/5.30 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_eq_dvd_minus
% 5.02/5.30 thf(fact_3819_diff__add__inverse2,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 5.02/5.30 = M ) ).
% 5.02/5.30
% 5.02/5.30 % diff_add_inverse2
% 5.02/5.30 thf(fact_3820_diff__add__inverse,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 5.02/5.30 = M ) ).
% 5.02/5.30
% 5.02/5.30 % diff_add_inverse
% 5.02/5.30 thf(fact_3821_diff__cancel2,axiom,
% 5.02/5.30 ! [M: nat,K: nat,N2: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.02/5.30 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_cancel2
% 5.02/5.30 thf(fact_3822_Nat_Odiff__cancel,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.02/5.30 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.diff_cancel
% 5.02/5.30 thf(fact_3823_diff__mult__distrib,axiom,
% 5.02/5.30 ! [M: nat,N2: nat,K: nat] :
% 5.02/5.30 ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 5.02/5.30 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_mult_distrib
% 5.02/5.30 thf(fact_3824_diff__mult__distrib2,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_mult_distrib2
% 5.02/5.30 thf(fact_3825_bezout1__nat,axiom,
% 5.02/5.30 ! [A: nat,B: nat] :
% 5.02/5.30 ? [D3: nat,X5: nat,Y3: nat] :
% 5.02/5.30 ( ( dvd_dvd_nat @ D3 @ A )
% 5.02/5.30 & ( dvd_dvd_nat @ D3 @ B )
% 5.02/5.30 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.02/5.30 = D3 )
% 5.02/5.30 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.02/5.30 = D3 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % bezout1_nat
% 5.02/5.30 thf(fact_3826_diff__less__Suc,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_less_Suc
% 5.02/5.30 thf(fact_3827_Suc__diff__Suc,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_nat @ N2 @ M )
% 5.02/5.30 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.30 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Suc_diff_Suc
% 5.02/5.30 thf(fact_3828_diff__less,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.30 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_less
% 5.02/5.30 thf(fact_3829_Suc__diff__le,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.02/5.30 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Suc_diff_le
% 5.02/5.30 thf(fact_3830_diff__less__mono,axiom,
% 5.02/5.30 ! [A: nat,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_nat @ C @ A )
% 5.02/5.30 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_less_mono
% 5.02/5.30 thf(fact_3831_less__diff__iff,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ M )
% 5.02/5.30 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.30 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.02/5.30 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_diff_iff
% 5.02/5.30 thf(fact_3832_diff__add__0,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 5.02/5.30 = zero_zero_nat ) ).
% 5.02/5.30
% 5.02/5.30 % diff_add_0
% 5.02/5.30 thf(fact_3833_add__diff__inverse__nat,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ~ ( ord_less_nat @ M @ N2 )
% 5.02/5.30 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 = M ) ) ).
% 5.02/5.30
% 5.02/5.30 % add_diff_inverse_nat
% 5.02/5.30 thf(fact_3834_less__diff__conv,axiom,
% 5.02/5.30 ! [I3: nat,J: nat,K: nat] :
% 5.02/5.30 ( ( ord_less_nat @ I3 @ ( minus_minus_nat @ J @ K ) )
% 5.02/5.30 = ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ J ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_diff_conv
% 5.02/5.30 thf(fact_3835_Nat_Ole__imp__diff__is__add,axiom,
% 5.02/5.30 ! [I3: nat,J: nat,K: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.30 => ( ( ( minus_minus_nat @ J @ I3 )
% 5.02/5.30 = K )
% 5.02/5.30 = ( J
% 5.02/5.30 = ( plus_plus_nat @ K @ I3 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.le_imp_diff_is_add
% 5.02/5.30 thf(fact_3836_Nat_Odiff__add__assoc2,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I3 ) @ K )
% 5.02/5.30 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I3 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.diff_add_assoc2
% 5.02/5.30 thf(fact_3837_Nat_Odiff__add__assoc,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( minus_minus_nat @ ( plus_plus_nat @ I3 @ J ) @ K )
% 5.02/5.30 = ( plus_plus_nat @ I3 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.diff_add_assoc
% 5.02/5.30 thf(fact_3838_Nat_Ole__diff__conv2,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( ord_less_eq_nat @ I3 @ ( minus_minus_nat @ J @ K ) )
% 5.02/5.30 = ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ K ) @ J ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Nat.le_diff_conv2
% 5.02/5.30 thf(fact_3839_le__diff__conv,axiom,
% 5.02/5.30 ! [J: nat,K: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I3 )
% 5.02/5.30 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I3 @ K ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_diff_conv
% 5.02/5.30 thf(fact_3840_diff__Suc__eq__diff__pred,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.02/5.30 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_Suc_eq_diff_pred
% 5.02/5.30 thf(fact_3841_mod__if,axiom,
% 5.02/5.30 ( modulo_modulo_nat
% 5.02/5.30 = ( ^ [M6: nat,N3: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N3 ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N3 ) @ N3 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % mod_if
% 5.02/5.30 thf(fact_3842_mod__geq,axiom,
% 5.02/5.30 ! [M: nat,N2: nat] :
% 5.02/5.30 ( ~ ( ord_less_nat @ M @ N2 )
% 5.02/5.30 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.02/5.30 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % mod_geq
% 5.02/5.30 thf(fact_3843_le__mod__geq,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.02/5.30 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_mod_geq
% 5.02/5.30 thf(fact_3844_mod__eq__dvd__iff__nat,axiom,
% 5.02/5.30 ! [N2: nat,M: nat,Q2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.02/5.30 = ( modulo_modulo_nat @ N2 @ Q2 ) )
% 5.02/5.30 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % mod_eq_dvd_iff_nat
% 5.02/5.30 thf(fact_3845_nat__minus__add__max,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 5.02/5.30 = ( ord_max_nat @ N2 @ M ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_minus_add_max
% 5.02/5.30 thf(fact_3846_add__diff__assoc__enat,axiom,
% 5.02/5.30 ! [Z: extended_enat,Y: extended_enat,X2: extended_enat] :
% 5.02/5.30 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 5.02/5.30 => ( ( plus_p3455044024723400733d_enat @ X2 @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 5.02/5.30 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X2 @ Y ) @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % add_diff_assoc_enat
% 5.02/5.30 thf(fact_3847_diff__Suc__less,axiom,
% 5.02/5.30 ! [N2: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) @ N2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_Suc_less
% 5.02/5.30 thf(fact_3848_nat__diff__split__asm,axiom,
% 5.02/5.30 ! [P: nat > $o,A: nat,B: nat] :
% 5.02/5.30 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.02/5.30 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.02/5.30 & ~ ( P @ zero_zero_nat ) )
% 5.02/5.30 | ? [D2: nat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( plus_plus_nat @ B @ D2 ) )
% 5.02/5.30 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_diff_split_asm
% 5.02/5.30 thf(fact_3849_nat__diff__split,axiom,
% 5.02/5.30 ! [P: nat > $o,A: nat,B: nat] :
% 5.02/5.30 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.02/5.30 = ( ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ( P @ zero_zero_nat ) )
% 5.02/5.30 & ! [D2: nat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( plus_plus_nat @ B @ D2 ) )
% 5.02/5.30 => ( P @ D2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_diff_split
% 5.02/5.30 thf(fact_3850_less__diff__conv2,axiom,
% 5.02/5.30 ! [K: nat,J: nat,I3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ K @ J )
% 5.02/5.30 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I3 )
% 5.02/5.30 = ( ord_less_nat @ J @ ( plus_plus_nat @ I3 @ K ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_diff_conv2
% 5.02/5.30 thf(fact_3851_order__antisym__conv,axiom,
% 5.02/5.30 ! [Y: set_nat,X2: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ Y @ X2 )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym_conv
% 5.02/5.30 thf(fact_3852_order__antisym__conv,axiom,
% 5.02/5.30 ! [Y: rat,X2: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ Y @ X2 )
% 5.02/5.30 => ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym_conv
% 5.02/5.30 thf(fact_3853_order__antisym__conv,axiom,
% 5.02/5.30 ! [Y: num,X2: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ Y @ X2 )
% 5.02/5.30 => ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym_conv
% 5.02/5.30 thf(fact_3854_order__antisym__conv,axiom,
% 5.02/5.30 ! [Y: nat,X2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ Y @ X2 )
% 5.02/5.30 => ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym_conv
% 5.02/5.30 thf(fact_3855_order__antisym__conv,axiom,
% 5.02/5.30 ! [Y: int,X2: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ Y @ X2 )
% 5.02/5.30 => ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym_conv
% 5.02/5.30 thf(fact_3856_linorder__le__cases,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ~ ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_cases
% 5.02/5.30 thf(fact_3857_linorder__le__cases,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ~ ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_cases
% 5.02/5.30 thf(fact_3858_linorder__le__cases,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ~ ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_cases
% 5.02/5.30 thf(fact_3859_linorder__le__cases,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ~ ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_cases
% 5.02/5.30 thf(fact_3860_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3861_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3862_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3863_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3864_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3865_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3866_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3867_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3868_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3869_ord__le__eq__subst,axiom,
% 5.02/5.30 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_subst
% 5.02/5.30 thf(fact_3870_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3871_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3872_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3873_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3874_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3875_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: num,F: num > num,B: num,C: num] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3876_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3877_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: int,F: num > int,B: num,C: num] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3878_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_nat @ B @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3879_ord__eq__le__subst,axiom,
% 5.02/5.30 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_nat @ B @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_subst
% 5.02/5.30 thf(fact_3880_linorder__linear,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 | ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_linear
% 5.02/5.30 thf(fact_3881_linorder__linear,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 | ( ord_less_eq_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_linear
% 5.02/5.30 thf(fact_3882_linorder__linear,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 | ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_linear
% 5.02/5.30 thf(fact_3883_linorder__linear,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 | ( ord_less_eq_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_linear
% 5.02/5.30 thf(fact_3884_order__eq__refl,axiom,
% 5.02/5.30 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.30 ( ( X2 = Y )
% 5.02/5.30 => ( ord_less_eq_set_nat @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_eq_refl
% 5.02/5.30 thf(fact_3885_order__eq__refl,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( X2 = Y )
% 5.02/5.30 => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_eq_refl
% 5.02/5.30 thf(fact_3886_order__eq__refl,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( X2 = Y )
% 5.02/5.30 => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_eq_refl
% 5.02/5.30 thf(fact_3887_order__eq__refl,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( X2 = Y )
% 5.02/5.30 => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_eq_refl
% 5.02/5.30 thf(fact_3888_order__eq__refl,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( X2 = Y )
% 5.02/5.30 => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_eq_refl
% 5.02/5.30 thf(fact_3889_order__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3890_order__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3891_order__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3892_order__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3893_order__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3894_order__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3895_order__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3896_order__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3897_order__subst2,axiom,
% 5.02/5.30 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3898_order__subst2,axiom,
% 5.02/5.30 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst2
% 5.02/5.30 thf(fact_3899_order__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3900_order__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3901_order__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_nat @ B @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3902_order__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_int @ B @ C )
% 5.02/5.30 => ( ! [X5: int,Y3: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3903_order__subst1,axiom,
% 5.02/5.30 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3904_order__subst1,axiom,
% 5.02/5.30 ! [A: num,F: num > num,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3905_order__subst1,axiom,
% 5.02/5.30 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_nat @ B @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3906_order__subst1,axiom,
% 5.02/5.30 ! [A: num,F: int > num,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_int @ B @ C )
% 5.02/5.30 => ( ! [X5: int,Y3: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3907_order__subst1,axiom,
% 5.02/5.30 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3908_order__subst1,axiom,
% 5.02/5.30 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_subst1
% 5.02/5.30 thf(fact_3909_Orderings_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 5.02/5.30 & ( ord_less_eq_set_nat @ B5 @ A5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Orderings.order_eq_iff
% 5.02/5.30 thf(fact_3910_Orderings_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: rat,B5: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.02/5.30 & ( ord_less_eq_rat @ B5 @ A5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Orderings.order_eq_iff
% 5.02/5.30 thf(fact_3911_Orderings_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: num,B5: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.02/5.30 & ( ord_less_eq_num @ B5 @ A5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Orderings.order_eq_iff
% 5.02/5.30 thf(fact_3912_Orderings_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: nat,B5: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.02/5.30 & ( ord_less_eq_nat @ B5 @ A5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Orderings.order_eq_iff
% 5.02/5.30 thf(fact_3913_Orderings_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: int,B5: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.02/5.30 & ( ord_less_eq_int @ B5 @ A5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Orderings.order_eq_iff
% 5.02/5.30 thf(fact_3914_antisym,axiom,
% 5.02/5.30 ! [A: set_nat,B: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ B @ A )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym
% 5.02/5.30 thf(fact_3915_antisym,axiom,
% 5.02/5.30 ! [A: rat,B: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ A )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym
% 5.02/5.30 thf(fact_3916_antisym,axiom,
% 5.02/5.30 ! [A: num,B: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ A )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym
% 5.02/5.30 thf(fact_3917_antisym,axiom,
% 5.02/5.30 ! [A: nat,B: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_nat @ B @ A )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym
% 5.02/5.30 thf(fact_3918_antisym,axiom,
% 5.02/5.30 ! [A: int,B: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_int @ B @ A )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym
% 5.02/5.30 thf(fact_3919_dual__order_Otrans,axiom,
% 5.02/5.30 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.02/5.30 => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.trans
% 5.02/5.30 thf(fact_3920_dual__order_Otrans,axiom,
% 5.02/5.30 ! [B: rat,A: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_rat @ C @ B )
% 5.02/5.30 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.trans
% 5.02/5.30 thf(fact_3921_dual__order_Otrans,axiom,
% 5.02/5.30 ! [B: num,A: num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_num @ C @ B )
% 5.02/5.30 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.trans
% 5.02/5.30 thf(fact_3922_dual__order_Otrans,axiom,
% 5.02/5.30 ! [B: nat,A: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_nat @ C @ B )
% 5.02/5.30 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.trans
% 5.02/5.30 thf(fact_3923_dual__order_Otrans,axiom,
% 5.02/5.30 ! [B: int,A: int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_int @ C @ B )
% 5.02/5.30 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.trans
% 5.02/5.30 thf(fact_3924_dual__order_Oantisym,axiom,
% 5.02/5.30 ! [B: set_nat,A: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.antisym
% 5.02/5.30 thf(fact_3925_dual__order_Oantisym,axiom,
% 5.02/5.30 ! [B: rat,A: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.antisym
% 5.02/5.30 thf(fact_3926_dual__order_Oantisym,axiom,
% 5.02/5.30 ! [B: num,A: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.antisym
% 5.02/5.30 thf(fact_3927_dual__order_Oantisym,axiom,
% 5.02/5.30 ! [B: nat,A: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.antisym
% 5.02/5.30 thf(fact_3928_dual__order_Oantisym,axiom,
% 5.02/5.30 ! [B: int,A: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ B @ A )
% 5.02/5.30 => ( ( ord_less_eq_int @ A @ B )
% 5.02/5.30 => ( A = B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.antisym
% 5.02/5.30 thf(fact_3929_dual__order_Oeq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ B5 @ A5 )
% 5.02/5.30 & ( ord_less_eq_set_nat @ A5 @ B5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.eq_iff
% 5.02/5.30 thf(fact_3930_dual__order_Oeq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: rat,B5: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ B5 @ A5 )
% 5.02/5.30 & ( ord_less_eq_rat @ A5 @ B5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.eq_iff
% 5.02/5.30 thf(fact_3931_dual__order_Oeq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: num,B5: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ B5 @ A5 )
% 5.02/5.30 & ( ord_less_eq_num @ A5 @ B5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.eq_iff
% 5.02/5.30 thf(fact_3932_dual__order_Oeq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: nat,B5: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ B5 @ A5 )
% 5.02/5.30 & ( ord_less_eq_nat @ A5 @ B5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.eq_iff
% 5.02/5.30 thf(fact_3933_dual__order_Oeq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A5: int,B5: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ B5 @ A5 )
% 5.02/5.30 & ( ord_less_eq_int @ A5 @ B5 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.eq_iff
% 5.02/5.30 thf(fact_3934_linorder__wlog,axiom,
% 5.02/5.30 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.02/5.30 ( ! [A4: rat,B3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: rat,B3: rat] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_wlog
% 5.02/5.30 thf(fact_3935_linorder__wlog,axiom,
% 5.02/5.30 ! [P: num > num > $o,A: num,B: num] :
% 5.02/5.30 ( ! [A4: num,B3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: num,B3: num] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_wlog
% 5.02/5.30 thf(fact_3936_linorder__wlog,axiom,
% 5.02/5.30 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.02/5.30 ( ! [A4: nat,B3: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: nat,B3: nat] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_wlog
% 5.02/5.30 thf(fact_3937_linorder__wlog,axiom,
% 5.02/5.30 ! [P: int > int > $o,A: int,B: int] :
% 5.02/5.30 ( ! [A4: int,B3: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: int,B3: int] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_wlog
% 5.02/5.30 thf(fact_3938_order__trans,axiom,
% 5.02/5.30 ! [X2: set_nat,Y: set_nat,Z: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ Y @ Z )
% 5.02/5.30 => ( ord_less_eq_set_nat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_trans
% 5.02/5.30 thf(fact_3939_order__trans,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat,Z: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.02/5.30 => ( ord_less_eq_rat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_trans
% 5.02/5.30 thf(fact_3940_order__trans,axiom,
% 5.02/5.30 ! [X2: num,Y: num,Z: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_num @ Y @ Z )
% 5.02/5.30 => ( ord_less_eq_num @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_trans
% 5.02/5.30 thf(fact_3941_order__trans,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat,Z: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.02/5.30 => ( ord_less_eq_nat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_trans
% 5.02/5.30 thf(fact_3942_order__trans,axiom,
% 5.02/5.30 ! [X2: int,Y: int,Z: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_int @ Y @ Z )
% 5.02/5.30 => ( ord_less_eq_int @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_trans
% 5.02/5.30 thf(fact_3943_order_Otrans,axiom,
% 5.02/5.30 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.02/5.30 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.trans
% 5.02/5.30 thf(fact_3944_order_Otrans,axiom,
% 5.02/5.30 ! [A: rat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.trans
% 5.02/5.30 thf(fact_3945_order_Otrans,axiom,
% 5.02/5.30 ! [A: num,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.trans
% 5.02/5.30 thf(fact_3946_order_Otrans,axiom,
% 5.02/5.30 ! [A: nat,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_nat @ B @ C )
% 5.02/5.30 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.trans
% 5.02/5.30 thf(fact_3947_order_Otrans,axiom,
% 5.02/5.30 ! [A: int,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_int @ B @ C )
% 5.02/5.30 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.trans
% 5.02/5.30 thf(fact_3948_order__antisym,axiom,
% 5.02/5.30 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ Y @ X2 )
% 5.02/5.30 => ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym
% 5.02/5.30 thf(fact_3949_order__antisym,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_rat @ Y @ X2 )
% 5.02/5.30 => ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym
% 5.02/5.30 thf(fact_3950_order__antisym,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_num @ Y @ X2 )
% 5.02/5.30 => ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym
% 5.02/5.30 thf(fact_3951_order__antisym,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_nat @ Y @ X2 )
% 5.02/5.30 => ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym
% 5.02/5.30 thf(fact_3952_order__antisym,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_int @ Y @ X2 )
% 5.02/5.30 => ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_antisym
% 5.02/5.30 thf(fact_3953_ord__le__eq__trans,axiom,
% 5.02/5.30 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_trans
% 5.02/5.30 thf(fact_3954_ord__le__eq__trans,axiom,
% 5.02/5.30 ! [A: rat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_trans
% 5.02/5.30 thf(fact_3955_ord__le__eq__trans,axiom,
% 5.02/5.30 ! [A: num,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_trans
% 5.02/5.30 thf(fact_3956_ord__le__eq__trans,axiom,
% 5.02/5.30 ! [A: nat,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_trans
% 5.02/5.30 thf(fact_3957_ord__le__eq__trans,axiom,
% 5.02/5.30 ! [A: int,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_le_eq_trans
% 5.02/5.30 thf(fact_3958_ord__eq__le__trans,axiom,
% 5.02/5.30 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.02/5.30 => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_trans
% 5.02/5.30 thf(fact_3959_ord__eq__le__trans,axiom,
% 5.02/5.30 ! [A: rat,B: rat,C: rat] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_trans
% 5.02/5.30 thf(fact_3960_ord__eq__le__trans,axiom,
% 5.02/5.30 ! [A: num,B: num,C: num] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_trans
% 5.02/5.30 thf(fact_3961_ord__eq__le__trans,axiom,
% 5.02/5.30 ! [A: nat,B: nat,C: nat] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_eq_nat @ B @ C )
% 5.02/5.30 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_trans
% 5.02/5.30 thf(fact_3962_ord__eq__le__trans,axiom,
% 5.02/5.30 ! [A: int,B: int,C: int] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_eq_int @ B @ C )
% 5.02/5.30 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_le_trans
% 5.02/5.30 thf(fact_3963_order__class_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [X: set_nat,Y6: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ X @ Y6 )
% 5.02/5.30 & ( ord_less_eq_set_nat @ Y6 @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_class.order_eq_iff
% 5.02/5.30 thf(fact_3964_order__class_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [X: rat,Y6: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X @ Y6 )
% 5.02/5.30 & ( ord_less_eq_rat @ Y6 @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_class.order_eq_iff
% 5.02/5.30 thf(fact_3965_order__class_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [X: num,Y6: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X @ Y6 )
% 5.02/5.30 & ( ord_less_eq_num @ Y6 @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_class.order_eq_iff
% 5.02/5.30 thf(fact_3966_order__class_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [X: nat,Y6: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X @ Y6 )
% 5.02/5.30 & ( ord_less_eq_nat @ Y6 @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_class.order_eq_iff
% 5.02/5.30 thf(fact_3967_order__class_Oorder__eq__iff,axiom,
% 5.02/5.30 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [X: int,Y6: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X @ Y6 )
% 5.02/5.30 & ( ord_less_eq_int @ Y6 @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_class.order_eq_iff
% 5.02/5.30 thf(fact_3968_le__cases3,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat,Z: rat] :
% 5.02/5.30 ( ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 5.02/5.30 => ( ( ( ord_less_eq_rat @ Y @ X2 )
% 5.02/5.30 => ~ ( ord_less_eq_rat @ X2 @ Z ) )
% 5.02/5.30 => ( ( ( ord_less_eq_rat @ X2 @ Z )
% 5.02/5.30 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 5.02/5.30 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 5.02/5.30 => ~ ( ord_less_eq_rat @ Y @ X2 ) )
% 5.02/5.30 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 5.02/5.30 => ~ ( ord_less_eq_rat @ Z @ X2 ) )
% 5.02/5.30 => ~ ( ( ord_less_eq_rat @ Z @ X2 )
% 5.02/5.30 => ~ ( ord_less_eq_rat @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_cases3
% 5.02/5.30 thf(fact_3969_le__cases3,axiom,
% 5.02/5.30 ! [X2: num,Y: num,Z: num] :
% 5.02/5.30 ( ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 5.02/5.30 => ( ( ( ord_less_eq_num @ Y @ X2 )
% 5.02/5.30 => ~ ( ord_less_eq_num @ X2 @ Z ) )
% 5.02/5.30 => ( ( ( ord_less_eq_num @ X2 @ Z )
% 5.02/5.30 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 5.02/5.30 => ( ( ( ord_less_eq_num @ Z @ Y )
% 5.02/5.30 => ~ ( ord_less_eq_num @ Y @ X2 ) )
% 5.02/5.30 => ( ( ( ord_less_eq_num @ Y @ Z )
% 5.02/5.30 => ~ ( ord_less_eq_num @ Z @ X2 ) )
% 5.02/5.30 => ~ ( ( ord_less_eq_num @ Z @ X2 )
% 5.02/5.30 => ~ ( ord_less_eq_num @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_cases3
% 5.02/5.30 thf(fact_3970_le__cases3,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat,Z: nat] :
% 5.02/5.30 ( ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 5.02/5.30 => ( ( ( ord_less_eq_nat @ Y @ X2 )
% 5.02/5.30 => ~ ( ord_less_eq_nat @ X2 @ Z ) )
% 5.02/5.30 => ( ( ( ord_less_eq_nat @ X2 @ Z )
% 5.02/5.30 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 5.02/5.30 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 5.02/5.30 => ~ ( ord_less_eq_nat @ Y @ X2 ) )
% 5.02/5.30 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 5.02/5.30 => ~ ( ord_less_eq_nat @ Z @ X2 ) )
% 5.02/5.30 => ~ ( ( ord_less_eq_nat @ Z @ X2 )
% 5.02/5.30 => ~ ( ord_less_eq_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_cases3
% 5.02/5.30 thf(fact_3971_le__cases3,axiom,
% 5.02/5.30 ! [X2: int,Y: int,Z: int] :
% 5.02/5.30 ( ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 5.02/5.30 => ( ( ( ord_less_eq_int @ Y @ X2 )
% 5.02/5.30 => ~ ( ord_less_eq_int @ X2 @ Z ) )
% 5.02/5.30 => ( ( ( ord_less_eq_int @ X2 @ Z )
% 5.02/5.30 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 5.02/5.30 => ( ( ( ord_less_eq_int @ Z @ Y )
% 5.02/5.30 => ~ ( ord_less_eq_int @ Y @ X2 ) )
% 5.02/5.30 => ( ( ( ord_less_eq_int @ Y @ Z )
% 5.02/5.30 => ~ ( ord_less_eq_int @ Z @ X2 ) )
% 5.02/5.30 => ~ ( ( ord_less_eq_int @ Z @ X2 )
% 5.02/5.30 => ~ ( ord_less_eq_int @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_cases3
% 5.02/5.30 thf(fact_3972_nle__le,axiom,
% 5.02/5.30 ! [A: rat,B: rat] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.02/5.30 = ( ( ord_less_eq_rat @ B @ A )
% 5.02/5.30 & ( B != A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nle_le
% 5.02/5.30 thf(fact_3973_nle__le,axiom,
% 5.02/5.30 ! [A: num,B: num] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.02/5.30 = ( ( ord_less_eq_num @ B @ A )
% 5.02/5.30 & ( B != A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nle_le
% 5.02/5.30 thf(fact_3974_nle__le,axiom,
% 5.02/5.30 ! [A: nat,B: nat] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.02/5.30 = ( ( ord_less_eq_nat @ B @ A )
% 5.02/5.30 & ( B != A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nle_le
% 5.02/5.30 thf(fact_3975_nle__le,axiom,
% 5.02/5.30 ! [A: int,B: int] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.02/5.30 = ( ( ord_less_eq_int @ B @ A )
% 5.02/5.30 & ( B != A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nle_le
% 5.02/5.30 thf(fact_3976_order__less__imp__not__less,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_less
% 5.02/5.30 thf(fact_3977_order__less__imp__not__less,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_less
% 5.02/5.30 thf(fact_3978_order__less__imp__not__less,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_less
% 5.02/5.30 thf(fact_3979_order__less__imp__not__less,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_less
% 5.02/5.30 thf(fact_3980_order__less__imp__not__less,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_less
% 5.02/5.30 thf(fact_3981_order__less__imp__not__eq2,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( Y != X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq2
% 5.02/5.30 thf(fact_3982_order__less__imp__not__eq2,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( Y != X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq2
% 5.02/5.30 thf(fact_3983_order__less__imp__not__eq2,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( Y != X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq2
% 5.02/5.30 thf(fact_3984_order__less__imp__not__eq2,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( Y != X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq2
% 5.02/5.30 thf(fact_3985_order__less__imp__not__eq2,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( Y != X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq2
% 5.02/5.30 thf(fact_3986_order__less__imp__not__eq,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq
% 5.02/5.30 thf(fact_3987_order__less__imp__not__eq,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq
% 5.02/5.30 thf(fact_3988_order__less__imp__not__eq,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq
% 5.02/5.30 thf(fact_3989_order__less__imp__not__eq,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq
% 5.02/5.30 thf(fact_3990_order__less__imp__not__eq,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_not_eq
% 5.02/5.30 thf(fact_3991_linorder__less__linear,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y )
% 5.02/5.30 | ( ord_less_real @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_linear
% 5.02/5.30 thf(fact_3992_linorder__less__linear,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y )
% 5.02/5.30 | ( ord_less_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_linear
% 5.02/5.30 thf(fact_3993_linorder__less__linear,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y )
% 5.02/5.30 | ( ord_less_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_linear
% 5.02/5.30 thf(fact_3994_linorder__less__linear,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y )
% 5.02/5.30 | ( ord_less_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_linear
% 5.02/5.30 thf(fact_3995_linorder__less__linear,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y )
% 5.02/5.30 | ( ord_less_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_linear
% 5.02/5.30 thf(fact_3996_order__less__imp__triv,axiom,
% 5.02/5.30 ! [X2: real,Y: real,P: $o] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_real @ Y @ X2 )
% 5.02/5.30 => P ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_triv
% 5.02/5.30 thf(fact_3997_order__less__imp__triv,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat,P: $o] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_rat @ Y @ X2 )
% 5.02/5.30 => P ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_triv
% 5.02/5.30 thf(fact_3998_order__less__imp__triv,axiom,
% 5.02/5.30 ! [X2: num,Y: num,P: $o] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_num @ Y @ X2 )
% 5.02/5.30 => P ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_triv
% 5.02/5.30 thf(fact_3999_order__less__imp__triv,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat,P: $o] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_nat @ Y @ X2 )
% 5.02/5.30 => P ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_triv
% 5.02/5.30 thf(fact_4000_order__less__imp__triv,axiom,
% 5.02/5.30 ! [X2: int,Y: int,P: $o] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_int @ Y @ X2 )
% 5.02/5.30 => P ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_triv
% 5.02/5.30 thf(fact_4001_order__less__not__sym,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_not_sym
% 5.02/5.30 thf(fact_4002_order__less__not__sym,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_not_sym
% 5.02/5.30 thf(fact_4003_order__less__not__sym,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_not_sym
% 5.02/5.30 thf(fact_4004_order__less__not__sym,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_not_sym
% 5.02/5.30 thf(fact_4005_order__less__not__sym,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_not_sym
% 5.02/5.30 thf(fact_4006_order__less__subst2,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > real,C: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4007_order__less__subst2,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4008_order__less__subst2,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > num,C: num] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4009_order__less__subst2,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4010_order__less__subst2,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > int,C: int] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4011_order__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4012_order__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4013_order__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4014_order__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4015_order__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst2
% 5.02/5.30 thf(fact_4016_order__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: real > real,B: real,C: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4017_order__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4018_order__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: num > real,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4019_order__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_nat @ B @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4020_order__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: int > real,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_int @ B @ C )
% 5.02/5.30 => ( ! [X5: int,Y3: int] :
% 5.02/5.30 ( ( ord_less_int @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4021_order__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.02/5.30 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4022_order__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4023_order__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4024_order__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_nat @ B @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4025_order__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_int @ B @ C )
% 5.02/5.30 => ( ! [X5: int,Y3: int] :
% 5.02/5.30 ( ( ord_less_int @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_subst1
% 5.02/5.30 thf(fact_4026_order__less__irrefl,axiom,
% 5.02/5.30 ! [X2: real] :
% 5.02/5.30 ~ ( ord_less_real @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_irrefl
% 5.02/5.30 thf(fact_4027_order__less__irrefl,axiom,
% 5.02/5.30 ! [X2: rat] :
% 5.02/5.30 ~ ( ord_less_rat @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_irrefl
% 5.02/5.30 thf(fact_4028_order__less__irrefl,axiom,
% 5.02/5.30 ! [X2: num] :
% 5.02/5.30 ~ ( ord_less_num @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_irrefl
% 5.02/5.30 thf(fact_4029_order__less__irrefl,axiom,
% 5.02/5.30 ! [X2: nat] :
% 5.02/5.30 ~ ( ord_less_nat @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_irrefl
% 5.02/5.30 thf(fact_4030_order__less__irrefl,axiom,
% 5.02/5.30 ! [X2: int] :
% 5.02/5.30 ~ ( ord_less_int @ X2 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_irrefl
% 5.02/5.30 thf(fact_4031_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > real,C: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4032_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4033_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > num,C: num] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4034_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4035_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > int,C: int] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4036_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4037_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4038_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4039_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4040_ord__less__eq__subst,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ( F @ B )
% 5.02/5.30 = C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_subst
% 5.02/5.30 thf(fact_4041_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: real,F: real > real,B: real,C: real] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4042_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4043_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: num,F: real > num,B: real,C: real] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4044_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4045_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: int,F: real > int,B: real,C: real] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4046_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4047_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4048_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4049_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4050_ord__eq__less__subst,axiom,
% 5.02/5.30 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.02/5.30 ( ( A
% 5.02/5.30 = ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_subst
% 5.02/5.30 thf(fact_4051_order__less__trans,axiom,
% 5.02/5.30 ! [X2: real,Y: real,Z: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_real @ Y @ Z )
% 5.02/5.30 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_trans
% 5.02/5.30 thf(fact_4052_order__less__trans,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat,Z: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_rat @ Y @ Z )
% 5.02/5.30 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_trans
% 5.02/5.30 thf(fact_4053_order__less__trans,axiom,
% 5.02/5.30 ! [X2: num,Y: num,Z: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_num @ Y @ Z )
% 5.02/5.30 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_trans
% 5.02/5.30 thf(fact_4054_order__less__trans,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat,Z: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_nat @ Y @ Z )
% 5.02/5.30 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_trans
% 5.02/5.30 thf(fact_4055_order__less__trans,axiom,
% 5.02/5.30 ! [X2: int,Y: int,Z: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_int @ Y @ Z )
% 5.02/5.30 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_trans
% 5.02/5.30 thf(fact_4056_order__less__asym_H,axiom,
% 5.02/5.30 ! [A: real,B: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym'
% 5.02/5.30 thf(fact_4057_order__less__asym_H,axiom,
% 5.02/5.30 ! [A: rat,B: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym'
% 5.02/5.30 thf(fact_4058_order__less__asym_H,axiom,
% 5.02/5.30 ! [A: num,B: num] :
% 5.02/5.30 ( ( ord_less_num @ A @ B )
% 5.02/5.30 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym'
% 5.02/5.30 thf(fact_4059_order__less__asym_H,axiom,
% 5.02/5.30 ! [A: nat,B: nat] :
% 5.02/5.30 ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym'
% 5.02/5.30 thf(fact_4060_order__less__asym_H,axiom,
% 5.02/5.30 ! [A: int,B: int] :
% 5.02/5.30 ( ( ord_less_int @ A @ B )
% 5.02/5.30 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym'
% 5.02/5.30 thf(fact_4061_linorder__neq__iff,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 = ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 | ( ord_less_real @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neq_iff
% 5.02/5.30 thf(fact_4062_linorder__neq__iff,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 = ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 | ( ord_less_rat @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neq_iff
% 5.02/5.30 thf(fact_4063_linorder__neq__iff,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 = ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 | ( ord_less_num @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neq_iff
% 5.02/5.30 thf(fact_4064_linorder__neq__iff,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 = ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 | ( ord_less_nat @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neq_iff
% 5.02/5.30 thf(fact_4065_linorder__neq__iff,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 = ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 | ( ord_less_int @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neq_iff
% 5.02/5.30 thf(fact_4066_order__less__asym,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_real @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym
% 5.02/5.30 thf(fact_4067_order__less__asym,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym
% 5.02/5.30 thf(fact_4068_order__less__asym,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym
% 5.02/5.30 thf(fact_4069_order__less__asym,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym
% 5.02/5.30 thf(fact_4070_order__less__asym,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_asym
% 5.02/5.30 thf(fact_4071_linorder__neqE,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 => ( ~ ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neqE
% 5.02/5.30 thf(fact_4072_linorder__neqE,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 => ( ~ ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neqE
% 5.02/5.30 thf(fact_4073_linorder__neqE,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 => ( ~ ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( ord_less_num @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neqE
% 5.02/5.30 thf(fact_4074_linorder__neqE,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 => ( ~ ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neqE
% 5.02/5.30 thf(fact_4075_linorder__neqE,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( X2 != Y )
% 5.02/5.30 => ( ~ ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_neqE
% 5.02/5.30 thf(fact_4076_dual__order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [B: real,A: real] :
% 5.02/5.30 ( ( ord_less_real @ B @ A )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4077_dual__order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [B: rat,A: rat] :
% 5.02/5.30 ( ( ord_less_rat @ B @ A )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4078_dual__order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [B: num,A: num] :
% 5.02/5.30 ( ( ord_less_num @ B @ A )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4079_dual__order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [B: nat,A: nat] :
% 5.02/5.30 ( ( ord_less_nat @ B @ A )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4080_dual__order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [B: int,A: int] :
% 5.02/5.30 ( ( ord_less_int @ B @ A )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4081_order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [A: real,B: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4082_order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [A: rat,B: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4083_order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [A: num,B: num] :
% 5.02/5.30 ( ( ord_less_num @ A @ B )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4084_order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [A: nat,B: nat] :
% 5.02/5.30 ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4085_order_Ostrict__implies__not__eq,axiom,
% 5.02/5.30 ! [A: int,B: int] :
% 5.02/5.30 ( ( ord_less_int @ A @ B )
% 5.02/5.30 => ( A != B ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_implies_not_eq
% 5.02/5.30 thf(fact_4086_dual__order_Ostrict__trans,axiom,
% 5.02/5.30 ! [B: real,A: real,C: real] :
% 5.02/5.30 ( ( ord_less_real @ B @ A )
% 5.02/5.30 => ( ( ord_less_real @ C @ B )
% 5.02/5.30 => ( ord_less_real @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_trans
% 5.02/5.30 thf(fact_4087_dual__order_Ostrict__trans,axiom,
% 5.02/5.30 ! [B: rat,A: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_rat @ B @ A )
% 5.02/5.30 => ( ( ord_less_rat @ C @ B )
% 5.02/5.30 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_trans
% 5.02/5.30 thf(fact_4088_dual__order_Ostrict__trans,axiom,
% 5.02/5.30 ! [B: num,A: num,C: num] :
% 5.02/5.30 ( ( ord_less_num @ B @ A )
% 5.02/5.30 => ( ( ord_less_num @ C @ B )
% 5.02/5.30 => ( ord_less_num @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_trans
% 5.02/5.30 thf(fact_4089_dual__order_Ostrict__trans,axiom,
% 5.02/5.30 ! [B: nat,A: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_nat @ B @ A )
% 5.02/5.30 => ( ( ord_less_nat @ C @ B )
% 5.02/5.30 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_trans
% 5.02/5.30 thf(fact_4090_dual__order_Ostrict__trans,axiom,
% 5.02/5.30 ! [B: int,A: int,C: int] :
% 5.02/5.30 ( ( ord_less_int @ B @ A )
% 5.02/5.30 => ( ( ord_less_int @ C @ B )
% 5.02/5.30 => ( ord_less_int @ C @ A ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_trans
% 5.02/5.30 thf(fact_4091_not__less__iff__gr__or__eq,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 5.02/5.30 = ( ( ord_less_real @ Y @ X2 )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % not_less_iff_gr_or_eq
% 5.02/5.30 thf(fact_4092_not__less__iff__gr__or__eq,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 5.02/5.30 = ( ( ord_less_rat @ Y @ X2 )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % not_less_iff_gr_or_eq
% 5.02/5.30 thf(fact_4093_not__less__iff__gr__or__eq,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 5.02/5.30 = ( ( ord_less_num @ Y @ X2 )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % not_less_iff_gr_or_eq
% 5.02/5.30 thf(fact_4094_not__less__iff__gr__or__eq,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 5.02/5.30 = ( ( ord_less_nat @ Y @ X2 )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % not_less_iff_gr_or_eq
% 5.02/5.30 thf(fact_4095_not__less__iff__gr__or__eq,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 5.02/5.30 = ( ( ord_less_int @ Y @ X2 )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % not_less_iff_gr_or_eq
% 5.02/5.30 thf(fact_4096_order_Ostrict__trans,axiom,
% 5.02/5.30 ! [A: real,B: real,C: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ord_less_real @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_trans
% 5.02/5.30 thf(fact_4097_order_Ostrict__trans,axiom,
% 5.02/5.30 ! [A: rat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_trans
% 5.02/5.30 thf(fact_4098_order_Ostrict__trans,axiom,
% 5.02/5.30 ! [A: num,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_num @ B @ C )
% 5.02/5.30 => ( ord_less_num @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_trans
% 5.02/5.30 thf(fact_4099_order_Ostrict__trans,axiom,
% 5.02/5.30 ! [A: nat,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_nat @ B @ C )
% 5.02/5.30 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_trans
% 5.02/5.30 thf(fact_4100_order_Ostrict__trans,axiom,
% 5.02/5.30 ! [A: int,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_int @ A @ B )
% 5.02/5.30 => ( ( ord_less_int @ B @ C )
% 5.02/5.30 => ( ord_less_int @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.strict_trans
% 5.02/5.30 thf(fact_4101_linorder__less__wlog,axiom,
% 5.02/5.30 ! [P: real > real > $o,A: real,B: real] :
% 5.02/5.30 ( ! [A4: real,B3: real] :
% 5.02/5.30 ( ( ord_less_real @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: real] : ( P @ A4 @ A4 )
% 5.02/5.30 => ( ! [A4: real,B3: real] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_wlog
% 5.02/5.30 thf(fact_4102_linorder__less__wlog,axiom,
% 5.02/5.30 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.02/5.30 ( ! [A4: rat,B3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: rat] : ( P @ A4 @ A4 )
% 5.02/5.30 => ( ! [A4: rat,B3: rat] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_wlog
% 5.02/5.30 thf(fact_4103_linorder__less__wlog,axiom,
% 5.02/5.30 ! [P: num > num > $o,A: num,B: num] :
% 5.02/5.30 ( ! [A4: num,B3: num] :
% 5.02/5.30 ( ( ord_less_num @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: num] : ( P @ A4 @ A4 )
% 5.02/5.30 => ( ! [A4: num,B3: num] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_wlog
% 5.02/5.30 thf(fact_4104_linorder__less__wlog,axiom,
% 5.02/5.30 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.02/5.30 ( ! [A4: nat,B3: nat] :
% 5.02/5.30 ( ( ord_less_nat @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 5.02/5.30 => ( ! [A4: nat,B3: nat] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_wlog
% 5.02/5.30 thf(fact_4105_linorder__less__wlog,axiom,
% 5.02/5.30 ! [P: int > int > $o,A: int,B: int] :
% 5.02/5.30 ( ! [A4: int,B3: int] :
% 5.02/5.30 ( ( ord_less_int @ A4 @ B3 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 5.02/5.30 => ( ! [A4: int,B3: int] :
% 5.02/5.30 ( ( P @ B3 @ A4 )
% 5.02/5.30 => ( P @ A4 @ B3 ) )
% 5.02/5.30 => ( P @ A @ B ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_less_wlog
% 5.02/5.30 thf(fact_4106_exists__least__iff,axiom,
% 5.02/5.30 ( ( ^ [P3: nat > $o] :
% 5.02/5.30 ? [X7: nat] : ( P3 @ X7 ) )
% 5.02/5.30 = ( ^ [P4: nat > $o] :
% 5.02/5.30 ? [N3: nat] :
% 5.02/5.30 ( ( P4 @ N3 )
% 5.02/5.30 & ! [M6: nat] :
% 5.02/5.30 ( ( ord_less_nat @ M6 @ N3 )
% 5.02/5.30 => ~ ( P4 @ M6 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % exists_least_iff
% 5.02/5.30 thf(fact_4107_dual__order_Oirrefl,axiom,
% 5.02/5.30 ! [A: real] :
% 5.02/5.30 ~ ( ord_less_real @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.irrefl
% 5.02/5.30 thf(fact_4108_dual__order_Oirrefl,axiom,
% 5.02/5.30 ! [A: rat] :
% 5.02/5.30 ~ ( ord_less_rat @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.irrefl
% 5.02/5.30 thf(fact_4109_dual__order_Oirrefl,axiom,
% 5.02/5.30 ! [A: num] :
% 5.02/5.30 ~ ( ord_less_num @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.irrefl
% 5.02/5.30 thf(fact_4110_dual__order_Oirrefl,axiom,
% 5.02/5.30 ! [A: nat] :
% 5.02/5.30 ~ ( ord_less_nat @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.irrefl
% 5.02/5.30 thf(fact_4111_dual__order_Oirrefl,axiom,
% 5.02/5.30 ! [A: int] :
% 5.02/5.30 ~ ( ord_less_int @ A @ A ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.irrefl
% 5.02/5.30 thf(fact_4112_dual__order_Oasym,axiom,
% 5.02/5.30 ! [B: real,A: real] :
% 5.02/5.30 ( ( ord_less_real @ B @ A )
% 5.02/5.30 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.asym
% 5.02/5.30 thf(fact_4113_dual__order_Oasym,axiom,
% 5.02/5.30 ! [B: rat,A: rat] :
% 5.02/5.30 ( ( ord_less_rat @ B @ A )
% 5.02/5.30 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.asym
% 5.02/5.30 thf(fact_4114_dual__order_Oasym,axiom,
% 5.02/5.30 ! [B: num,A: num] :
% 5.02/5.30 ( ( ord_less_num @ B @ A )
% 5.02/5.30 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.asym
% 5.02/5.30 thf(fact_4115_dual__order_Oasym,axiom,
% 5.02/5.30 ! [B: nat,A: nat] :
% 5.02/5.30 ( ( ord_less_nat @ B @ A )
% 5.02/5.30 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.asym
% 5.02/5.30 thf(fact_4116_dual__order_Oasym,axiom,
% 5.02/5.30 ! [B: int,A: int] :
% 5.02/5.30 ( ( ord_less_int @ B @ A )
% 5.02/5.30 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.asym
% 5.02/5.30 thf(fact_4117_linorder__cases,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ~ ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( ( X2 != Y )
% 5.02/5.30 => ( ord_less_real @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_cases
% 5.02/5.30 thf(fact_4118_linorder__cases,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ~ ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( ( X2 != Y )
% 5.02/5.30 => ( ord_less_rat @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_cases
% 5.02/5.30 thf(fact_4119_linorder__cases,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ~ ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( ( X2 != Y )
% 5.02/5.30 => ( ord_less_num @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_cases
% 5.02/5.30 thf(fact_4120_linorder__cases,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ~ ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( ( X2 != Y )
% 5.02/5.30 => ( ord_less_nat @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_cases
% 5.02/5.30 thf(fact_4121_linorder__cases,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ~ ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( ( X2 != Y )
% 5.02/5.30 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_cases
% 5.02/5.30 thf(fact_4122_antisym__conv3,axiom,
% 5.02/5.30 ! [Y: real,X2: real] :
% 5.02/5.30 ( ~ ( ord_less_real @ Y @ X2 )
% 5.02/5.30 => ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym_conv3
% 5.02/5.30 thf(fact_4123_antisym__conv3,axiom,
% 5.02/5.30 ! [Y: rat,X2: rat] :
% 5.02/5.30 ( ~ ( ord_less_rat @ Y @ X2 )
% 5.02/5.30 => ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym_conv3
% 5.02/5.30 thf(fact_4124_antisym__conv3,axiom,
% 5.02/5.30 ! [Y: num,X2: num] :
% 5.02/5.30 ( ~ ( ord_less_num @ Y @ X2 )
% 5.02/5.30 => ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym_conv3
% 5.02/5.30 thf(fact_4125_antisym__conv3,axiom,
% 5.02/5.30 ! [Y: nat,X2: nat] :
% 5.02/5.30 ( ~ ( ord_less_nat @ Y @ X2 )
% 5.02/5.30 => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym_conv3
% 5.02/5.30 thf(fact_4126_antisym__conv3,axiom,
% 5.02/5.30 ! [Y: int,X2: int] :
% 5.02/5.30 ( ~ ( ord_less_int @ Y @ X2 )
% 5.02/5.30 => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 5.02/5.30 = ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % antisym_conv3
% 5.02/5.30 thf(fact_4127_less__induct,axiom,
% 5.02/5.30 ! [P: nat > $o,A: nat] :
% 5.02/5.30 ( ! [X5: nat] :
% 5.02/5.30 ( ! [Y5: nat] :
% 5.02/5.30 ( ( ord_less_nat @ Y5 @ X5 )
% 5.02/5.30 => ( P @ Y5 ) )
% 5.02/5.30 => ( P @ X5 ) )
% 5.02/5.30 => ( P @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_induct
% 5.02/5.30 thf(fact_4128_ord__less__eq__trans,axiom,
% 5.02/5.30 ! [A: real,B: real,C: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_real @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_trans
% 5.02/5.30 thf(fact_4129_ord__less__eq__trans,axiom,
% 5.02/5.30 ! [A: rat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_trans
% 5.02/5.30 thf(fact_4130_ord__less__eq__trans,axiom,
% 5.02/5.30 ! [A: num,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_num @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_num @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_trans
% 5.02/5.30 thf(fact_4131_ord__less__eq__trans,axiom,
% 5.02/5.30 ! [A: nat,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_trans
% 5.02/5.30 thf(fact_4132_ord__less__eq__trans,axiom,
% 5.02/5.30 ! [A: int,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_int @ A @ B )
% 5.02/5.30 => ( ( B = C )
% 5.02/5.30 => ( ord_less_int @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_less_eq_trans
% 5.02/5.30 thf(fact_4133_ord__eq__less__trans,axiom,
% 5.02/5.30 ! [A: real,B: real,C: real] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ord_less_real @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_trans
% 5.02/5.30 thf(fact_4134_ord__eq__less__trans,axiom,
% 5.02/5.30 ! [A: rat,B: rat,C: rat] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_trans
% 5.02/5.30 thf(fact_4135_ord__eq__less__trans,axiom,
% 5.02/5.30 ! [A: num,B: num,C: num] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_num @ B @ C )
% 5.02/5.30 => ( ord_less_num @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_trans
% 5.02/5.30 thf(fact_4136_ord__eq__less__trans,axiom,
% 5.02/5.30 ! [A: nat,B: nat,C: nat] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_nat @ B @ C )
% 5.02/5.30 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_trans
% 5.02/5.30 thf(fact_4137_ord__eq__less__trans,axiom,
% 5.02/5.30 ! [A: int,B: int,C: int] :
% 5.02/5.30 ( ( A = B )
% 5.02/5.30 => ( ( ord_less_int @ B @ C )
% 5.02/5.30 => ( ord_less_int @ A @ C ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % ord_eq_less_trans
% 5.02/5.30 thf(fact_4138_order_Oasym,axiom,
% 5.02/5.30 ! [A: real,B: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.asym
% 5.02/5.30 thf(fact_4139_order_Oasym,axiom,
% 5.02/5.30 ! [A: rat,B: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.asym
% 5.02/5.30 thf(fact_4140_order_Oasym,axiom,
% 5.02/5.30 ! [A: num,B: num] :
% 5.02/5.30 ( ( ord_less_num @ A @ B )
% 5.02/5.30 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.asym
% 5.02/5.30 thf(fact_4141_order_Oasym,axiom,
% 5.02/5.30 ! [A: nat,B: nat] :
% 5.02/5.30 ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.asym
% 5.02/5.30 thf(fact_4142_order_Oasym,axiom,
% 5.02/5.30 ! [A: int,B: int] :
% 5.02/5.30 ( ( ord_less_int @ A @ B )
% 5.02/5.30 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % order.asym
% 5.02/5.30 thf(fact_4143_less__imp__neq,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_imp_neq
% 5.02/5.30 thf(fact_4144_less__imp__neq,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_imp_neq
% 5.02/5.30 thf(fact_4145_less__imp__neq,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_imp_neq
% 5.02/5.30 thf(fact_4146_less__imp__neq,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_imp_neq
% 5.02/5.30 thf(fact_4147_less__imp__neq,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( X2 != Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_imp_neq
% 5.02/5.30 thf(fact_4148_dense,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ? [Z3: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Z3 )
% 5.02/5.30 & ( ord_less_real @ Z3 @ Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dense
% 5.02/5.30 thf(fact_4149_dense,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ? [Z3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Z3 )
% 5.02/5.30 & ( ord_less_rat @ Z3 @ Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dense
% 5.02/5.30 thf(fact_4150_gt__ex,axiom,
% 5.02/5.30 ! [X2: real] :
% 5.02/5.30 ? [X_12: real] : ( ord_less_real @ X2 @ X_12 ) ).
% 5.02/5.30
% 5.02/5.30 % gt_ex
% 5.02/5.30 thf(fact_4151_gt__ex,axiom,
% 5.02/5.30 ! [X2: rat] :
% 5.02/5.30 ? [X_12: rat] : ( ord_less_rat @ X2 @ X_12 ) ).
% 5.02/5.30
% 5.02/5.30 % gt_ex
% 5.02/5.30 thf(fact_4152_gt__ex,axiom,
% 5.02/5.30 ! [X2: nat] :
% 5.02/5.30 ? [X_12: nat] : ( ord_less_nat @ X2 @ X_12 ) ).
% 5.02/5.30
% 5.02/5.30 % gt_ex
% 5.02/5.30 thf(fact_4153_gt__ex,axiom,
% 5.02/5.30 ! [X2: int] :
% 5.02/5.30 ? [X_12: int] : ( ord_less_int @ X2 @ X_12 ) ).
% 5.02/5.30
% 5.02/5.30 % gt_ex
% 5.02/5.30 thf(fact_4154_lt__ex,axiom,
% 5.02/5.30 ! [X2: real] :
% 5.02/5.30 ? [Y3: real] : ( ord_less_real @ Y3 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % lt_ex
% 5.02/5.30 thf(fact_4155_lt__ex,axiom,
% 5.02/5.30 ! [X2: rat] :
% 5.02/5.30 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % lt_ex
% 5.02/5.30 thf(fact_4156_lt__ex,axiom,
% 5.02/5.30 ! [X2: int] :
% 5.02/5.30 ? [Y3: int] : ( ord_less_int @ Y3 @ X2 ) ).
% 5.02/5.30
% 5.02/5.30 % lt_ex
% 5.02/5.30 thf(fact_4157_nat__diff__add__eq2,axiom,
% 5.02/5.30 ! [I3: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.30 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.02/5.30 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I3 ) @ U ) @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_diff_add_eq2
% 5.02/5.30 thf(fact_4158_nat__diff__add__eq1,axiom,
% 5.02/5.30 ! [J: nat,I3: nat,U: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ J @ I3 )
% 5.02/5.30 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.02/5.30 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I3 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_diff_add_eq1
% 5.02/5.30 thf(fact_4159_nat__le__add__iff2,axiom,
% 5.02/5.30 ! [I3: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.30 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.02/5.30 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I3 ) @ U ) @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_le_add_iff2
% 5.02/5.30 thf(fact_4160_nat__le__add__iff1,axiom,
% 5.02/5.30 ! [J: nat,I3: nat,U: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ J @ I3 )
% 5.02/5.30 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.02/5.30 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I3 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_le_add_iff1
% 5.02/5.30 thf(fact_4161_nat__eq__add__iff2,axiom,
% 5.02/5.30 ! [I3: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.30 => ( ( ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ M )
% 5.02/5.30 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.02/5.30 = ( M
% 5.02/5.30 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I3 ) @ U ) @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_eq_add_iff2
% 5.02/5.30 thf(fact_4162_nat__eq__add__iff1,axiom,
% 5.02/5.30 ! [J: nat,I3: nat,U: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ J @ I3 )
% 5.02/5.30 => ( ( ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ M )
% 5.02/5.30 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.02/5.30 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I3 @ J ) @ U ) @ M )
% 5.02/5.30 = N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_eq_add_iff1
% 5.02/5.30 thf(fact_4163_dvd__minus__add,axiom,
% 5.02/5.30 ! [Q2: nat,N2: nat,R2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ Q2 @ N2 )
% 5.02/5.30 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R2 @ M ) )
% 5.02/5.30 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q2 ) )
% 5.02/5.30 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R2 @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % dvd_minus_add
% 5.02/5.30 thf(fact_4164_mod__nat__eqI,axiom,
% 5.02/5.30 ! [R2: nat,N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_nat @ R2 @ N2 )
% 5.02/5.30 => ( ( ord_less_eq_nat @ R2 @ M )
% 5.02/5.30 => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R2 ) )
% 5.02/5.30 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.02/5.30 = R2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % mod_nat_eqI
% 5.02/5.30 thf(fact_4165_modulo__nat__def,axiom,
% 5.02/5.30 ( modulo_modulo_nat
% 5.02/5.30 = ( ^ [M6: nat,N3: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N3 ) @ N3 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % modulo_nat_def
% 5.02/5.30 thf(fact_4166_in__mono,axiom,
% 5.02/5.30 ! [A3: set_complex,B4: set_complex,X2: complex] :
% 5.02/5.30 ( ( ord_le211207098394363844omplex @ A3 @ B4 )
% 5.02/5.30 => ( ( member_complex @ X2 @ A3 )
% 5.02/5.30 => ( member_complex @ X2 @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % in_mono
% 5.02/5.30 thf(fact_4167_in__mono,axiom,
% 5.02/5.30 ! [A3: set_real,B4: set_real,X2: real] :
% 5.02/5.30 ( ( ord_less_eq_set_real @ A3 @ B4 )
% 5.02/5.30 => ( ( member_real @ X2 @ A3 )
% 5.02/5.30 => ( member_real @ X2 @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % in_mono
% 5.02/5.30 thf(fact_4168_in__mono,axiom,
% 5.02/5.30 ! [A3: set_set_nat,B4: set_set_nat,X2: set_nat] :
% 5.02/5.30 ( ( ord_le6893508408891458716et_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( member_set_nat @ X2 @ A3 )
% 5.02/5.30 => ( member_set_nat @ X2 @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % in_mono
% 5.02/5.30 thf(fact_4169_in__mono,axiom,
% 5.02/5.30 ! [A3: set_int,B4: set_int,X2: int] :
% 5.02/5.30 ( ( ord_less_eq_set_int @ A3 @ B4 )
% 5.02/5.30 => ( ( member_int @ X2 @ A3 )
% 5.02/5.30 => ( member_int @ X2 @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % in_mono
% 5.02/5.30 thf(fact_4170_in__mono,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat,X2: nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( member_nat @ X2 @ A3 )
% 5.02/5.30 => ( member_nat @ X2 @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % in_mono
% 5.02/5.30 thf(fact_4171_subsetD,axiom,
% 5.02/5.30 ! [A3: set_complex,B4: set_complex,C: complex] :
% 5.02/5.30 ( ( ord_le211207098394363844omplex @ A3 @ B4 )
% 5.02/5.30 => ( ( member_complex @ C @ A3 )
% 5.02/5.30 => ( member_complex @ C @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetD
% 5.02/5.30 thf(fact_4172_subsetD,axiom,
% 5.02/5.30 ! [A3: set_real,B4: set_real,C: real] :
% 5.02/5.30 ( ( ord_less_eq_set_real @ A3 @ B4 )
% 5.02/5.30 => ( ( member_real @ C @ A3 )
% 5.02/5.30 => ( member_real @ C @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetD
% 5.02/5.30 thf(fact_4173_subsetD,axiom,
% 5.02/5.30 ! [A3: set_set_nat,B4: set_set_nat,C: set_nat] :
% 5.02/5.30 ( ( ord_le6893508408891458716et_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( member_set_nat @ C @ A3 )
% 5.02/5.30 => ( member_set_nat @ C @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetD
% 5.02/5.30 thf(fact_4174_subsetD,axiom,
% 5.02/5.30 ! [A3: set_int,B4: set_int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_set_int @ A3 @ B4 )
% 5.02/5.30 => ( ( member_int @ C @ A3 )
% 5.02/5.30 => ( member_int @ C @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetD
% 5.02/5.30 thf(fact_4175_subsetD,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( member_nat @ C @ A3 )
% 5.02/5.30 => ( member_nat @ C @ B4 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subsetD
% 5.02/5.30 thf(fact_4176_psubsetE,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( ord_less_set_nat @ A3 @ B4 )
% 5.02/5.30 => ~ ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ord_less_eq_set_nat @ B4 @ A3 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % psubsetE
% 5.02/5.30 thf(fact_4177_equalityE,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( A3 = B4 )
% 5.02/5.30 => ~ ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ~ ( ord_less_eq_set_nat @ B4 @ A3 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % equalityE
% 5.02/5.30 thf(fact_4178_subset__eq,axiom,
% 5.02/5.30 ( ord_le211207098394363844omplex
% 5.02/5.30 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.02/5.30 ! [X: complex] :
% 5.02/5.30 ( ( member_complex @ X @ A6 )
% 5.02/5.30 => ( member_complex @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_eq
% 5.02/5.30 thf(fact_4179_subset__eq,axiom,
% 5.02/5.30 ( ord_less_eq_set_real
% 5.02/5.30 = ( ^ [A6: set_real,B7: set_real] :
% 5.02/5.30 ! [X: real] :
% 5.02/5.30 ( ( member_real @ X @ A6 )
% 5.02/5.30 => ( member_real @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_eq
% 5.02/5.30 thf(fact_4180_subset__eq,axiom,
% 5.02/5.30 ( ord_le6893508408891458716et_nat
% 5.02/5.30 = ( ^ [A6: set_set_nat,B7: set_set_nat] :
% 5.02/5.30 ! [X: set_nat] :
% 5.02/5.30 ( ( member_set_nat @ X @ A6 )
% 5.02/5.30 => ( member_set_nat @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_eq
% 5.02/5.30 thf(fact_4181_subset__eq,axiom,
% 5.02/5.30 ( ord_less_eq_set_int
% 5.02/5.30 = ( ^ [A6: set_int,B7: set_int] :
% 5.02/5.30 ! [X: int] :
% 5.02/5.30 ( ( member_int @ X @ A6 )
% 5.02/5.30 => ( member_int @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_eq
% 5.02/5.30 thf(fact_4182_subset__eq,axiom,
% 5.02/5.30 ( ord_less_eq_set_nat
% 5.02/5.30 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.02/5.30 ! [X: nat] :
% 5.02/5.30 ( ( member_nat @ X @ A6 )
% 5.02/5.30 => ( member_nat @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_eq
% 5.02/5.30 thf(fact_4183_equalityD1,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( A3 = B4 )
% 5.02/5.30 => ( ord_less_eq_set_nat @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % equalityD1
% 5.02/5.30 thf(fact_4184_equalityD2,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( A3 = B4 )
% 5.02/5.30 => ( ord_less_eq_set_nat @ B4 @ A3 ) ) ).
% 5.02/5.30
% 5.02/5.30 % equalityD2
% 5.02/5.30 thf(fact_4185_psubset__eq,axiom,
% 5.02/5.30 ( ord_less_set_nat
% 5.02/5.30 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A6 @ B7 )
% 5.02/5.30 & ( A6 != B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % psubset_eq
% 5.02/5.30 thf(fact_4186_subset__iff,axiom,
% 5.02/5.30 ( ord_le211207098394363844omplex
% 5.02/5.30 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.02/5.30 ! [T: complex] :
% 5.02/5.30 ( ( member_complex @ T @ A6 )
% 5.02/5.30 => ( member_complex @ T @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_iff
% 5.02/5.30 thf(fact_4187_subset__iff,axiom,
% 5.02/5.30 ( ord_less_eq_set_real
% 5.02/5.30 = ( ^ [A6: set_real,B7: set_real] :
% 5.02/5.30 ! [T: real] :
% 5.02/5.30 ( ( member_real @ T @ A6 )
% 5.02/5.30 => ( member_real @ T @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_iff
% 5.02/5.30 thf(fact_4188_subset__iff,axiom,
% 5.02/5.30 ( ord_le6893508408891458716et_nat
% 5.02/5.30 = ( ^ [A6: set_set_nat,B7: set_set_nat] :
% 5.02/5.30 ! [T: set_nat] :
% 5.02/5.30 ( ( member_set_nat @ T @ A6 )
% 5.02/5.30 => ( member_set_nat @ T @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_iff
% 5.02/5.30 thf(fact_4189_subset__iff,axiom,
% 5.02/5.30 ( ord_less_eq_set_int
% 5.02/5.30 = ( ^ [A6: set_int,B7: set_int] :
% 5.02/5.30 ! [T: int] :
% 5.02/5.30 ( ( member_int @ T @ A6 )
% 5.02/5.30 => ( member_int @ T @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_iff
% 5.02/5.30 thf(fact_4190_subset__iff,axiom,
% 5.02/5.30 ( ord_less_eq_set_nat
% 5.02/5.30 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.02/5.30 ! [T: nat] :
% 5.02/5.30 ( ( member_nat @ T @ A6 )
% 5.02/5.30 => ( member_nat @ T @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_iff
% 5.02/5.30 thf(fact_4191_subset__refl,axiom,
% 5.02/5.30 ! [A3: set_nat] : ( ord_less_eq_set_nat @ A3 @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % subset_refl
% 5.02/5.30 thf(fact_4192_Collect__mono,axiom,
% 5.02/5.30 ! [P: real > $o,Q: real > $o] :
% 5.02/5.30 ( ! [X5: real] :
% 5.02/5.30 ( ( P @ X5 )
% 5.02/5.30 => ( Q @ X5 ) )
% 5.02/5.30 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono
% 5.02/5.30 thf(fact_4193_Collect__mono,axiom,
% 5.02/5.30 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.02/5.30 ( ! [X5: list_nat] :
% 5.02/5.30 ( ( P @ X5 )
% 5.02/5.30 => ( Q @ X5 ) )
% 5.02/5.30 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono
% 5.02/5.30 thf(fact_4194_Collect__mono,axiom,
% 5.02/5.30 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.02/5.30 ( ! [X5: set_nat] :
% 5.02/5.30 ( ( P @ X5 )
% 5.02/5.30 => ( Q @ X5 ) )
% 5.02/5.30 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono
% 5.02/5.30 thf(fact_4195_Collect__mono,axiom,
% 5.02/5.30 ! [P: int > $o,Q: int > $o] :
% 5.02/5.30 ( ! [X5: int] :
% 5.02/5.30 ( ( P @ X5 )
% 5.02/5.30 => ( Q @ X5 ) )
% 5.02/5.30 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono
% 5.02/5.30 thf(fact_4196_Collect__mono,axiom,
% 5.02/5.30 ! [P: nat > $o,Q: nat > $o] :
% 5.02/5.30 ( ! [X5: nat] :
% 5.02/5.30 ( ( P @ X5 )
% 5.02/5.30 => ( Q @ X5 ) )
% 5.02/5.30 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono
% 5.02/5.30 thf(fact_4197_subset__trans,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat,C5: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 5.02/5.30 => ( ord_less_eq_set_nat @ A3 @ C5 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_trans
% 5.02/5.30 thf(fact_4198_set__eq__subset,axiom,
% 5.02/5.30 ( ( ^ [Y4: set_nat,Z2: set_nat] : ( Y4 = Z2 ) )
% 5.02/5.30 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A6 @ B7 )
% 5.02/5.30 & ( ord_less_eq_set_nat @ B7 @ A6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % set_eq_subset
% 5.02/5.30 thf(fact_4199_Collect__mono__iff,axiom,
% 5.02/5.30 ! [P: real > $o,Q: real > $o] :
% 5.02/5.30 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 5.02/5.30 = ( ! [X: real] :
% 5.02/5.30 ( ( P @ X )
% 5.02/5.30 => ( Q @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono_iff
% 5.02/5.30 thf(fact_4200_Collect__mono__iff,axiom,
% 5.02/5.30 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.02/5.30 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.02/5.30 = ( ! [X: list_nat] :
% 5.02/5.30 ( ( P @ X )
% 5.02/5.30 => ( Q @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono_iff
% 5.02/5.30 thf(fact_4201_Collect__mono__iff,axiom,
% 5.02/5.30 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.02/5.30 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 5.02/5.30 = ( ! [X: set_nat] :
% 5.02/5.30 ( ( P @ X )
% 5.02/5.30 => ( Q @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono_iff
% 5.02/5.30 thf(fact_4202_Collect__mono__iff,axiom,
% 5.02/5.30 ! [P: int > $o,Q: int > $o] :
% 5.02/5.30 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.02/5.30 = ( ! [X: int] :
% 5.02/5.30 ( ( P @ X )
% 5.02/5.30 => ( Q @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono_iff
% 5.02/5.30 thf(fact_4203_Collect__mono__iff,axiom,
% 5.02/5.30 ! [P: nat > $o,Q: nat > $o] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.02/5.30 = ( ! [X: nat] :
% 5.02/5.30 ( ( P @ X )
% 5.02/5.30 => ( Q @ X ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_mono_iff
% 5.02/5.30 thf(fact_4204_psubset__imp__subset,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.30 ( ( ord_less_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ord_less_eq_set_nat @ A3 @ B4 ) ) ).
% 5.02/5.30
% 5.02/5.30 % psubset_imp_subset
% 5.02/5.30 thf(fact_4205_psubset__subset__trans,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat,C5: set_nat] :
% 5.02/5.30 ( ( ord_less_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ B4 @ C5 )
% 5.02/5.30 => ( ord_less_set_nat @ A3 @ C5 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % psubset_subset_trans
% 5.02/5.30 thf(fact_4206_subset__not__subset__eq,axiom,
% 5.02/5.30 ( ord_less_set_nat
% 5.02/5.30 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A6 @ B7 )
% 5.02/5.30 & ~ ( ord_less_eq_set_nat @ B7 @ A6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_not_subset_eq
% 5.02/5.30 thf(fact_4207_subset__psubset__trans,axiom,
% 5.02/5.30 ! [A3: set_nat,B4: set_nat,C5: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.30 => ( ( ord_less_set_nat @ B4 @ C5 )
% 5.02/5.30 => ( ord_less_set_nat @ A3 @ C5 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_psubset_trans
% 5.02/5.30 thf(fact_4208_subset__iff__psubset__eq,axiom,
% 5.02/5.30 ( ord_less_eq_set_nat
% 5.02/5.30 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.02/5.30 ( ( ord_less_set_nat @ A6 @ B7 )
% 5.02/5.30 | ( A6 = B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % subset_iff_psubset_eq
% 5.02/5.30 thf(fact_4209_prod__decode__aux_Ocases,axiom,
% 5.02/5.30 ! [X2: product_prod_nat_nat] :
% 5.02/5.30 ~ ! [K2: nat,M3: nat] :
% 5.02/5.30 ( X2
% 5.02/5.30 != ( product_Pair_nat_nat @ K2 @ M3 ) ) ).
% 5.02/5.30
% 5.02/5.30 % prod_decode_aux.cases
% 5.02/5.30 thf(fact_4210_power__diff,axiom,
% 5.02/5.30 ! [A: complex,N2: nat,M: nat] :
% 5.02/5.30 ( ( A != zero_zero_complex )
% 5.02/5.30 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_diff
% 5.02/5.30 thf(fact_4211_power__diff,axiom,
% 5.02/5.30 ! [A: real,N2: nat,M: nat] :
% 5.02/5.30 ( ( A != zero_zero_real )
% 5.02/5.30 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_diff
% 5.02/5.30 thf(fact_4212_power__diff,axiom,
% 5.02/5.30 ! [A: rat,N2: nat,M: nat] :
% 5.02/5.30 ( ( A != zero_zero_rat )
% 5.02/5.30 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_diff
% 5.02/5.30 thf(fact_4213_power__diff,axiom,
% 5.02/5.30 ! [A: nat,N2: nat,M: nat] :
% 5.02/5.30 ( ( A != zero_zero_nat )
% 5.02/5.30 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_diff
% 5.02/5.30 thf(fact_4214_power__diff,axiom,
% 5.02/5.30 ! [A: int,N2: nat,M: nat] :
% 5.02/5.30 ( ( A != zero_zero_int )
% 5.02/5.30 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.30 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_diff
% 5.02/5.30 thf(fact_4215_Suc__diff__eq__diff__pred,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.02/5.30 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Suc_diff_eq_diff_pred
% 5.02/5.30 thf(fact_4216_Suc__pred_H,axiom,
% 5.02/5.30 ! [N2: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( N2
% 5.02/5.30 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % Suc_pred'
% 5.02/5.30 thf(fact_4217_div__if,axiom,
% 5.02/5.30 ( divide_divide_nat
% 5.02/5.30 = ( ^ [M6: nat,N3: nat] :
% 5.02/5.30 ( if_nat
% 5.02/5.30 @ ( ( ord_less_nat @ M6 @ N3 )
% 5.02/5.30 | ( N3 = zero_zero_nat ) )
% 5.02/5.30 @ zero_zero_nat
% 5.02/5.30 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N3 ) @ N3 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % div_if
% 5.02/5.30 thf(fact_4218_div__geq,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.02/5.30 => ( ( divide_divide_nat @ M @ N2 )
% 5.02/5.30 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % div_geq
% 5.02/5.30 thf(fact_4219_add__eq__if,axiom,
% 5.02/5.30 ( plus_plus_nat
% 5.02/5.30 = ( ^ [M6: nat,N3: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N3 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % add_eq_if
% 5.02/5.30 thf(fact_4220_nat__less__add__iff2,axiom,
% 5.02/5.30 ! [I3: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.30 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.02/5.30 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I3 ) @ U ) @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_less_add_iff2
% 5.02/5.30 thf(fact_4221_nat__less__add__iff1,axiom,
% 5.02/5.30 ! [J: nat,I3: nat,U: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ J @ I3 )
% 5.02/5.30 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I3 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.02/5.30 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I3 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % nat_less_add_iff1
% 5.02/5.30 thf(fact_4222_mult__eq__if,axiom,
% 5.02/5.30 ( times_times_nat
% 5.02/5.30 = ( ^ [M6: nat,N3: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N3 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N3 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % mult_eq_if
% 5.02/5.30 thf(fact_4223_Collect__subset,axiom,
% 5.02/5.30 ! [A3: set_complex,P: complex > $o] :
% 5.02/5.30 ( ord_le211207098394363844omplex
% 5.02/5.30 @ ( collect_complex
% 5.02/5.30 @ ^ [X: complex] :
% 5.02/5.30 ( ( member_complex @ X @ A3 )
% 5.02/5.30 & ( P @ X ) ) )
% 5.02/5.30 @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_subset
% 5.02/5.30 thf(fact_4224_Collect__subset,axiom,
% 5.02/5.30 ! [A3: set_real,P: real > $o] :
% 5.02/5.30 ( ord_less_eq_set_real
% 5.02/5.30 @ ( collect_real
% 5.02/5.30 @ ^ [X: real] :
% 5.02/5.30 ( ( member_real @ X @ A3 )
% 5.02/5.30 & ( P @ X ) ) )
% 5.02/5.30 @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_subset
% 5.02/5.30 thf(fact_4225_Collect__subset,axiom,
% 5.02/5.30 ! [A3: set_list_nat,P: list_nat > $o] :
% 5.02/5.30 ( ord_le6045566169113846134st_nat
% 5.02/5.30 @ ( collect_list_nat
% 5.02/5.30 @ ^ [X: list_nat] :
% 5.02/5.30 ( ( member_list_nat @ X @ A3 )
% 5.02/5.30 & ( P @ X ) ) )
% 5.02/5.30 @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_subset
% 5.02/5.30 thf(fact_4226_Collect__subset,axiom,
% 5.02/5.30 ! [A3: set_set_nat,P: set_nat > $o] :
% 5.02/5.30 ( ord_le6893508408891458716et_nat
% 5.02/5.30 @ ( collect_set_nat
% 5.02/5.30 @ ^ [X: set_nat] :
% 5.02/5.30 ( ( member_set_nat @ X @ A3 )
% 5.02/5.30 & ( P @ X ) ) )
% 5.02/5.30 @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_subset
% 5.02/5.30 thf(fact_4227_Collect__subset,axiom,
% 5.02/5.30 ! [A3: set_int,P: int > $o] :
% 5.02/5.30 ( ord_less_eq_set_int
% 5.02/5.30 @ ( collect_int
% 5.02/5.30 @ ^ [X: int] :
% 5.02/5.30 ( ( member_int @ X @ A3 )
% 5.02/5.30 & ( P @ X ) ) )
% 5.02/5.30 @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_subset
% 5.02/5.30 thf(fact_4228_Collect__subset,axiom,
% 5.02/5.30 ! [A3: set_nat,P: nat > $o] :
% 5.02/5.30 ( ord_less_eq_set_nat
% 5.02/5.30 @ ( collect_nat
% 5.02/5.30 @ ^ [X: nat] :
% 5.02/5.30 ( ( member_nat @ X @ A3 )
% 5.02/5.30 & ( P @ X ) ) )
% 5.02/5.30 @ A3 ) ).
% 5.02/5.30
% 5.02/5.30 % Collect_subset
% 5.02/5.30 thf(fact_4229_less__eq__set__def,axiom,
% 5.02/5.30 ( ord_le211207098394363844omplex
% 5.02/5.30 = ( ^ [A6: set_complex,B7: set_complex] :
% 5.02/5.30 ( ord_le4573692005234683329plex_o
% 5.02/5.30 @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 5.02/5.30 @ ^ [X: complex] : ( member_complex @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_eq_set_def
% 5.02/5.30 thf(fact_4230_less__eq__set__def,axiom,
% 5.02/5.30 ( ord_less_eq_set_real
% 5.02/5.30 = ( ^ [A6: set_real,B7: set_real] :
% 5.02/5.30 ( ord_less_eq_real_o
% 5.02/5.30 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.02/5.30 @ ^ [X: real] : ( member_real @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_eq_set_def
% 5.02/5.30 thf(fact_4231_less__eq__set__def,axiom,
% 5.02/5.30 ( ord_le6893508408891458716et_nat
% 5.02/5.30 = ( ^ [A6: set_set_nat,B7: set_set_nat] :
% 5.02/5.30 ( ord_le3964352015994296041_nat_o
% 5.02/5.30 @ ^ [X: set_nat] : ( member_set_nat @ X @ A6 )
% 5.02/5.30 @ ^ [X: set_nat] : ( member_set_nat @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_eq_set_def
% 5.02/5.30 thf(fact_4232_less__eq__set__def,axiom,
% 5.02/5.30 ( ord_less_eq_set_int
% 5.02/5.30 = ( ^ [A6: set_int,B7: set_int] :
% 5.02/5.30 ( ord_less_eq_int_o
% 5.02/5.30 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.02/5.30 @ ^ [X: int] : ( member_int @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_eq_set_def
% 5.02/5.30 thf(fact_4233_less__eq__set__def,axiom,
% 5.02/5.30 ( ord_less_eq_set_nat
% 5.02/5.30 = ( ^ [A6: set_nat,B7: set_nat] :
% 5.02/5.30 ( ord_less_eq_nat_o
% 5.02/5.30 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.02/5.30 @ ^ [X: nat] : ( member_nat @ X @ B7 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % less_eq_set_def
% 5.02/5.30 thf(fact_4234_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.30 != zero_zero_nat )
% 5.02/5.30 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.02/5.30 != zero_zero_nat ) ) ).
% 5.02/5.30
% 5.02/5.30 % exp_not_zero_imp_exp_diff_not_zero
% 5.02/5.30 thf(fact_4235_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.30 != zero_zero_int )
% 5.02/5.30 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.02/5.30 != zero_zero_int ) ) ).
% 5.02/5.30
% 5.02/5.30 % exp_not_zero_imp_exp_diff_not_zero
% 5.02/5.30 thf(fact_4236_power__diff__power__eq,axiom,
% 5.02/5.30 ! [A: nat,N2: nat,M: nat] :
% 5.02/5.30 ( ( A != zero_zero_nat )
% 5.02/5.30 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.02/5.30 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.02/5.30 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.02/5.30 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_diff_power_eq
% 5.02/5.30 thf(fact_4237_power__diff__power__eq,axiom,
% 5.02/5.30 ! [A: int,N2: nat,M: nat] :
% 5.02/5.30 ( ( A != zero_zero_int )
% 5.02/5.30 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.02/5.30 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.02/5.30 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.02/5.30 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_diff_power_eq
% 5.02/5.30 thf(fact_4238_power__eq__if,axiom,
% 5.02/5.30 ( power_power_complex
% 5.02/5.30 = ( ^ [P6: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P6 @ ( power_power_complex @ P6 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_eq_if
% 5.02/5.30 thf(fact_4239_power__eq__if,axiom,
% 5.02/5.30 ( power_power_real
% 5.02/5.30 = ( ^ [P6: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P6 @ ( power_power_real @ P6 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_eq_if
% 5.02/5.30 thf(fact_4240_power__eq__if,axiom,
% 5.02/5.30 ( power_power_rat
% 5.02/5.30 = ( ^ [P6: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P6 @ ( power_power_rat @ P6 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_eq_if
% 5.02/5.30 thf(fact_4241_power__eq__if,axiom,
% 5.02/5.30 ( power_power_nat
% 5.02/5.30 = ( ^ [P6: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P6 @ ( power_power_nat @ P6 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_eq_if
% 5.02/5.30 thf(fact_4242_power__eq__if,axiom,
% 5.02/5.30 ( power_power_int
% 5.02/5.30 = ( ^ [P6: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P6 @ ( power_power_int @ P6 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_eq_if
% 5.02/5.30 thf(fact_4243_power__minus__mult,axiom,
% 5.02/5.30 ! [N2: nat,A: complex] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.02/5.30 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_minus_mult
% 5.02/5.30 thf(fact_4244_power__minus__mult,axiom,
% 5.02/5.30 ! [N2: nat,A: real] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.02/5.30 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_minus_mult
% 5.02/5.30 thf(fact_4245_power__minus__mult,axiom,
% 5.02/5.30 ! [N2: nat,A: rat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.02/5.30 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_minus_mult
% 5.02/5.30 thf(fact_4246_power__minus__mult,axiom,
% 5.02/5.30 ! [N2: nat,A: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.02/5.30 = ( power_power_nat @ A @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_minus_mult
% 5.02/5.30 thf(fact_4247_power__minus__mult,axiom,
% 5.02/5.30 ! [N2: nat,A: int] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.02/5.30 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % power_minus_mult
% 5.02/5.30 thf(fact_4248_diff__le__diff__pow,axiom,
% 5.02/5.30 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.02/5.30 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % diff_le_diff_pow
% 5.02/5.30 thf(fact_4249_le__div__geq,axiom,
% 5.02/5.30 ! [N2: nat,M: nat] :
% 5.02/5.30 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.30 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.30 => ( ( divide_divide_nat @ M @ N2 )
% 5.02/5.30 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % le_div_geq
% 5.02/5.30 thf(fact_4250_order__le__imp__less__or__eq,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_imp_less_or_eq
% 5.02/5.30 thf(fact_4251_order__le__imp__less__or__eq,axiom,
% 5.02/5.30 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_set_nat @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_imp_less_or_eq
% 5.02/5.30 thf(fact_4252_order__le__imp__less__or__eq,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_imp_less_or_eq
% 5.02/5.30 thf(fact_4253_order__le__imp__less__or__eq,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_imp_less_or_eq
% 5.02/5.30 thf(fact_4254_order__le__imp__less__or__eq,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_imp_less_or_eq
% 5.02/5.30 thf(fact_4255_order__le__imp__less__or__eq,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 | ( X2 = Y ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_imp_less_or_eq
% 5.02/5.30 thf(fact_4256_linorder__le__less__linear,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.30 | ( ord_less_real @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_less_linear
% 5.02/5.30 thf(fact_4257_linorder__le__less__linear,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 | ( ord_less_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_less_linear
% 5.02/5.30 thf(fact_4258_linorder__le__less__linear,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 | ( ord_less_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_less_linear
% 5.02/5.30 thf(fact_4259_linorder__le__less__linear,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 | ( ord_less_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_less_linear
% 5.02/5.30 thf(fact_4260_linorder__le__less__linear,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 | ( ord_less_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_le_less_linear
% 5.02/5.30 thf(fact_4261_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > real,C: real] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4262_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4263_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > real,C: real] :
% 5.02/5.30 ( ( ord_less_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4264_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.02/5.30 ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4265_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: int,B: int,F: int > real,C: real] :
% 5.02/5.30 ( ( ord_less_int @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: int,Y3: int] :
% 5.02/5.30 ( ( ord_less_int @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4266_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_real @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4267_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4268_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4269_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_nat @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4270_order__less__le__subst2,axiom,
% 5.02/5.30 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_int @ A @ B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: int,Y3: int] :
% 5.02/5.30 ( ( ord_less_int @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst2
% 5.02/5.30 thf(fact_4271_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4272_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4273_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4274_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4275_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4276_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: real,F: num > real,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4277_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4278_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: num,F: num > num,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4279_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4280_order__less__le__subst1,axiom,
% 5.02/5.30 ! [A: int,F: num > int,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_subst1
% 5.02/5.30 thf(fact_4281_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4282_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4283_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4284_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4285_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4286_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > real,C: real] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4287_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4288_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4289_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4290_order__le__less__subst2,axiom,
% 5.02/5.30 ! [A: num,B: num,F: num > int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst2
% 5.02/5.30 thf(fact_4291_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: real > real,B: real,C: real] :
% 5.02/5.30 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4292_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4293_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: num > real,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4294_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_nat @ B @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4295_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: real,F: int > real,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_int @ B @ C )
% 5.02/5.30 => ( ! [X5: int,Y3: int] :
% 5.02/5.30 ( ( ord_less_int @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4296_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_real @ B @ C )
% 5.02/5.30 => ( ! [X5: real,Y3: real] :
% 5.02/5.30 ( ( ord_less_real @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4297_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_rat @ B @ C )
% 5.02/5.30 => ( ! [X5: rat,Y3: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4298_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_num @ B @ C )
% 5.02/5.30 => ( ! [X5: num,Y3: num] :
% 5.02/5.30 ( ( ord_less_num @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4299_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_nat @ B @ C )
% 5.02/5.30 => ( ! [X5: nat,Y3: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4300_order__le__less__subst1,axiom,
% 5.02/5.30 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.02/5.30 => ( ( ord_less_int @ B @ C )
% 5.02/5.30 => ( ! [X5: int,Y3: int] :
% 5.02/5.30 ( ( ord_less_int @ X5 @ Y3 )
% 5.02/5.30 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.02/5.30 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_subst1
% 5.02/5.30 thf(fact_4301_order__less__le__trans,axiom,
% 5.02/5.30 ! [X2: real,Y: real,Z: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_real @ Y @ Z )
% 5.02/5.30 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_trans
% 5.02/5.30 thf(fact_4302_order__less__le__trans,axiom,
% 5.02/5.30 ! [X2: set_nat,Y: set_nat,Z: set_nat] :
% 5.02/5.30 ( ( ord_less_set_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ Y @ Z )
% 5.02/5.30 => ( ord_less_set_nat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_trans
% 5.02/5.30 thf(fact_4303_order__less__le__trans,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat,Z: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.02/5.30 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_trans
% 5.02/5.30 thf(fact_4304_order__less__le__trans,axiom,
% 5.02/5.30 ! [X2: num,Y: num,Z: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_num @ Y @ Z )
% 5.02/5.30 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_trans
% 5.02/5.30 thf(fact_4305_order__less__le__trans,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat,Z: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.02/5.30 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_trans
% 5.02/5.30 thf(fact_4306_order__less__le__trans,axiom,
% 5.02/5.30 ! [X2: int,Y: int,Z: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_eq_int @ Y @ Z )
% 5.02/5.30 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le_trans
% 5.02/5.30 thf(fact_4307_order__le__less__trans,axiom,
% 5.02/5.30 ! [X2: real,Y: real,Z: real] :
% 5.02/5.30 ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_real @ Y @ Z )
% 5.02/5.30 => ( ord_less_real @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_trans
% 5.02/5.30 thf(fact_4308_order__le__less__trans,axiom,
% 5.02/5.30 ! [X2: set_nat,Y: set_nat,Z: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_set_nat @ Y @ Z )
% 5.02/5.30 => ( ord_less_set_nat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_trans
% 5.02/5.30 thf(fact_4309_order__le__less__trans,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat,Z: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_rat @ Y @ Z )
% 5.02/5.30 => ( ord_less_rat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_trans
% 5.02/5.30 thf(fact_4310_order__le__less__trans,axiom,
% 5.02/5.30 ! [X2: num,Y: num,Z: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_num @ Y @ Z )
% 5.02/5.30 => ( ord_less_num @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_trans
% 5.02/5.30 thf(fact_4311_order__le__less__trans,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat,Z: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_nat @ Y @ Z )
% 5.02/5.30 => ( ord_less_nat @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_trans
% 5.02/5.30 thf(fact_4312_order__le__less__trans,axiom,
% 5.02/5.30 ! [X2: int,Y: int,Z: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.30 => ( ( ord_less_int @ Y @ Z )
% 5.02/5.30 => ( ord_less_int @ X2 @ Z ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less_trans
% 5.02/5.30 thf(fact_4313_order__neq__le__trans,axiom,
% 5.02/5.30 ! [A: real,B: real] :
% 5.02/5.30 ( ( A != B )
% 5.02/5.30 => ( ( ord_less_eq_real @ A @ B )
% 5.02/5.30 => ( ord_less_real @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_neq_le_trans
% 5.02/5.30 thf(fact_4314_order__neq__le__trans,axiom,
% 5.02/5.30 ! [A: set_nat,B: set_nat] :
% 5.02/5.30 ( ( A != B )
% 5.02/5.30 => ( ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.30 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_neq_le_trans
% 5.02/5.30 thf(fact_4315_order__neq__le__trans,axiom,
% 5.02/5.30 ! [A: rat,B: rat] :
% 5.02/5.30 ( ( A != B )
% 5.02/5.30 => ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_neq_le_trans
% 5.02/5.30 thf(fact_4316_order__neq__le__trans,axiom,
% 5.02/5.30 ! [A: num,B: num] :
% 5.02/5.30 ( ( A != B )
% 5.02/5.30 => ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ord_less_num @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_neq_le_trans
% 5.02/5.30 thf(fact_4317_order__neq__le__trans,axiom,
% 5.02/5.30 ! [A: nat,B: nat] :
% 5.02/5.30 ( ( A != B )
% 5.02/5.30 => ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_neq_le_trans
% 5.02/5.30 thf(fact_4318_order__neq__le__trans,axiom,
% 5.02/5.30 ! [A: int,B: int] :
% 5.02/5.30 ( ( A != B )
% 5.02/5.30 => ( ( ord_less_eq_int @ A @ B )
% 5.02/5.30 => ( ord_less_int @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_neq_le_trans
% 5.02/5.30 thf(fact_4319_order__le__neq__trans,axiom,
% 5.02/5.30 ! [A: real,B: real] :
% 5.02/5.30 ( ( ord_less_eq_real @ A @ B )
% 5.02/5.30 => ( ( A != B )
% 5.02/5.30 => ( ord_less_real @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_neq_trans
% 5.02/5.30 thf(fact_4320_order__le__neq__trans,axiom,
% 5.02/5.30 ! [A: set_nat,B: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.30 => ( ( A != B )
% 5.02/5.30 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_neq_trans
% 5.02/5.30 thf(fact_4321_order__le__neq__trans,axiom,
% 5.02/5.30 ! [A: rat,B: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.30 => ( ( A != B )
% 5.02/5.30 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_neq_trans
% 5.02/5.30 thf(fact_4322_order__le__neq__trans,axiom,
% 5.02/5.30 ! [A: num,B: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.30 => ( ( A != B )
% 5.02/5.30 => ( ord_less_num @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_neq_trans
% 5.02/5.30 thf(fact_4323_order__le__neq__trans,axiom,
% 5.02/5.30 ! [A: nat,B: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.30 => ( ( A != B )
% 5.02/5.30 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_neq_trans
% 5.02/5.30 thf(fact_4324_order__le__neq__trans,axiom,
% 5.02/5.30 ! [A: int,B: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ A @ B )
% 5.02/5.30 => ( ( A != B )
% 5.02/5.30 => ( ord_less_int @ A @ B ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_neq_trans
% 5.02/5.30 thf(fact_4325_order__less__imp__le,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_le
% 5.02/5.30 thf(fact_4326_order__less__imp__le,axiom,
% 5.02/5.30 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.30 ( ( ord_less_set_nat @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_set_nat @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_le
% 5.02/5.30 thf(fact_4327_order__less__imp__le,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_le
% 5.02/5.30 thf(fact_4328_order__less__imp__le,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ord_less_num @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_num @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_le
% 5.02/5.30 thf(fact_4329_order__less__imp__le,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_le
% 5.02/5.30 thf(fact_4330_order__less__imp__le,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ord_less_int @ X2 @ Y )
% 5.02/5.30 => ( ord_less_eq_int @ X2 @ Y ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_imp_le
% 5.02/5.30 thf(fact_4331_linorder__not__less,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_eq_real @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_less
% 5.02/5.30 thf(fact_4332_linorder__not__less,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_less
% 5.02/5.30 thf(fact_4333_linorder__not__less,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_eq_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_less
% 5.02/5.30 thf(fact_4334_linorder__not__less,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_less
% 5.02/5.30 thf(fact_4335_linorder__not__less,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_eq_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_less
% 5.02/5.30 thf(fact_4336_linorder__not__le,axiom,
% 5.02/5.30 ! [X2: real,Y: real] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_real @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_real @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_le
% 5.02/5.30 thf(fact_4337_linorder__not__le,axiom,
% 5.02/5.30 ! [X2: rat,Y: rat] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_rat @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_rat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_le
% 5.02/5.30 thf(fact_4338_linorder__not__le,axiom,
% 5.02/5.30 ! [X2: num,Y: num] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_num @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_num @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_le
% 5.02/5.30 thf(fact_4339_linorder__not__le,axiom,
% 5.02/5.30 ! [X2: nat,Y: nat] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_nat @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_nat @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_le
% 5.02/5.30 thf(fact_4340_linorder__not__le,axiom,
% 5.02/5.30 ! [X2: int,Y: int] :
% 5.02/5.30 ( ( ~ ( ord_less_eq_int @ X2 @ Y ) )
% 5.02/5.30 = ( ord_less_int @ Y @ X2 ) ) ).
% 5.02/5.30
% 5.02/5.30 % linorder_not_le
% 5.02/5.30 thf(fact_4341_order__less__le,axiom,
% 5.02/5.30 ( ord_less_real
% 5.02/5.30 = ( ^ [X: real,Y6: real] :
% 5.02/5.30 ( ( ord_less_eq_real @ X @ Y6 )
% 5.02/5.30 & ( X != Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le
% 5.02/5.30 thf(fact_4342_order__less__le,axiom,
% 5.02/5.30 ( ord_less_set_nat
% 5.02/5.30 = ( ^ [X: set_nat,Y6: set_nat] :
% 5.02/5.30 ( ( ord_less_eq_set_nat @ X @ Y6 )
% 5.02/5.30 & ( X != Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le
% 5.02/5.30 thf(fact_4343_order__less__le,axiom,
% 5.02/5.30 ( ord_less_rat
% 5.02/5.30 = ( ^ [X: rat,Y6: rat] :
% 5.02/5.30 ( ( ord_less_eq_rat @ X @ Y6 )
% 5.02/5.30 & ( X != Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le
% 5.02/5.30 thf(fact_4344_order__less__le,axiom,
% 5.02/5.30 ( ord_less_num
% 5.02/5.30 = ( ^ [X: num,Y6: num] :
% 5.02/5.30 ( ( ord_less_eq_num @ X @ Y6 )
% 5.02/5.30 & ( X != Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le
% 5.02/5.30 thf(fact_4345_order__less__le,axiom,
% 5.02/5.30 ( ord_less_nat
% 5.02/5.30 = ( ^ [X: nat,Y6: nat] :
% 5.02/5.30 ( ( ord_less_eq_nat @ X @ Y6 )
% 5.02/5.30 & ( X != Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le
% 5.02/5.30 thf(fact_4346_order__less__le,axiom,
% 5.02/5.30 ( ord_less_int
% 5.02/5.30 = ( ^ [X: int,Y6: int] :
% 5.02/5.30 ( ( ord_less_eq_int @ X @ Y6 )
% 5.02/5.30 & ( X != Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_less_le
% 5.02/5.30 thf(fact_4347_order__le__less,axiom,
% 5.02/5.30 ( ord_less_eq_real
% 5.02/5.30 = ( ^ [X: real,Y6: real] :
% 5.02/5.30 ( ( ord_less_real @ X @ Y6 )
% 5.02/5.30 | ( X = Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less
% 5.02/5.30 thf(fact_4348_order__le__less,axiom,
% 5.02/5.30 ( ord_less_eq_set_nat
% 5.02/5.30 = ( ^ [X: set_nat,Y6: set_nat] :
% 5.02/5.30 ( ( ord_less_set_nat @ X @ Y6 )
% 5.02/5.30 | ( X = Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less
% 5.02/5.30 thf(fact_4349_order__le__less,axiom,
% 5.02/5.30 ( ord_less_eq_rat
% 5.02/5.30 = ( ^ [X: rat,Y6: rat] :
% 5.02/5.30 ( ( ord_less_rat @ X @ Y6 )
% 5.02/5.30 | ( X = Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less
% 5.02/5.30 thf(fact_4350_order__le__less,axiom,
% 5.02/5.30 ( ord_less_eq_num
% 5.02/5.30 = ( ^ [X: num,Y6: num] :
% 5.02/5.30 ( ( ord_less_num @ X @ Y6 )
% 5.02/5.30 | ( X = Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less
% 5.02/5.30 thf(fact_4351_order__le__less,axiom,
% 5.02/5.30 ( ord_less_eq_nat
% 5.02/5.30 = ( ^ [X: nat,Y6: nat] :
% 5.02/5.30 ( ( ord_less_nat @ X @ Y6 )
% 5.02/5.30 | ( X = Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less
% 5.02/5.30 thf(fact_4352_order__le__less,axiom,
% 5.02/5.30 ( ord_less_eq_int
% 5.02/5.30 = ( ^ [X: int,Y6: int] :
% 5.02/5.30 ( ( ord_less_int @ X @ Y6 )
% 5.02/5.30 | ( X = Y6 ) ) ) ) ).
% 5.02/5.30
% 5.02/5.30 % order_le_less
% 5.02/5.30 thf(fact_4353_dual__order_Ostrict__implies__order,axiom,
% 5.02/5.30 ! [B: real,A: real] :
% 5.02/5.30 ( ( ord_less_real @ B @ A )
% 5.02/5.30 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_implies_order
% 5.02/5.30 thf(fact_4354_dual__order_Ostrict__implies__order,axiom,
% 5.02/5.30 ! [B: set_nat,A: set_nat] :
% 5.02/5.30 ( ( ord_less_set_nat @ B @ A )
% 5.02/5.30 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 5.02/5.30
% 5.02/5.30 % dual_order.strict_implies_order
% 5.02/5.30 thf(fact_4355_dual__order_Ostrict__implies__order,axiom,
% 5.02/5.30 ! [B: rat,A: rat] :
% 5.02/5.30 ( ( ord_less_rat @ B @ A )
% 5.02/5.31 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_implies_order
% 5.02/5.31 thf(fact_4356_dual__order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [B: num,A: num] :
% 5.02/5.31 ( ( ord_less_num @ B @ A )
% 5.02/5.31 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_implies_order
% 5.02/5.31 thf(fact_4357_dual__order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [B: nat,A: nat] :
% 5.02/5.31 ( ( ord_less_nat @ B @ A )
% 5.02/5.31 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_implies_order
% 5.02/5.31 thf(fact_4358_dual__order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [B: int,A: int] :
% 5.02/5.31 ( ( ord_less_int @ B @ A )
% 5.02/5.31 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_implies_order
% 5.02/5.31 thf(fact_4359_order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ord_less_real @ A @ B )
% 5.02/5.31 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_implies_order
% 5.02/5.31 thf(fact_4360_order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [A: set_nat,B: set_nat] :
% 5.02/5.31 ( ( ord_less_set_nat @ A @ B )
% 5.02/5.31 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_implies_order
% 5.02/5.31 thf(fact_4361_order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ord_less_rat @ A @ B )
% 5.02/5.31 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_implies_order
% 5.02/5.31 thf(fact_4362_order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [A: num,B: num] :
% 5.02/5.31 ( ( ord_less_num @ A @ B )
% 5.02/5.31 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_implies_order
% 5.02/5.31 thf(fact_4363_order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [A: nat,B: nat] :
% 5.02/5.31 ( ( ord_less_nat @ A @ B )
% 5.02/5.31 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_implies_order
% 5.02/5.31 thf(fact_4364_order_Ostrict__implies__order,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ord_less_int @ A @ B )
% 5.02/5.31 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_implies_order
% 5.02/5.31 thf(fact_4365_dual__order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_real
% 5.02/5.31 = ( ^ [B5: real,A5: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ B5 @ A5 )
% 5.02/5.31 & ~ ( ord_less_eq_real @ A5 @ B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_not
% 5.02/5.31 thf(fact_4366_dual__order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_set_nat
% 5.02/5.31 = ( ^ [B5: set_nat,A5: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ B5 @ A5 )
% 5.02/5.31 & ~ ( ord_less_eq_set_nat @ A5 @ B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_not
% 5.02/5.31 thf(fact_4367_dual__order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_rat
% 5.02/5.31 = ( ^ [B5: rat,A5: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ B5 @ A5 )
% 5.02/5.31 & ~ ( ord_less_eq_rat @ A5 @ B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_not
% 5.02/5.31 thf(fact_4368_dual__order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_num
% 5.02/5.31 = ( ^ [B5: num,A5: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ B5 @ A5 )
% 5.02/5.31 & ~ ( ord_less_eq_num @ A5 @ B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_not
% 5.02/5.31 thf(fact_4369_dual__order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_nat
% 5.02/5.31 = ( ^ [B5: nat,A5: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ B5 @ A5 )
% 5.02/5.31 & ~ ( ord_less_eq_nat @ A5 @ B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_not
% 5.02/5.31 thf(fact_4370_dual__order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_int
% 5.02/5.31 = ( ^ [B5: int,A5: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ B5 @ A5 )
% 5.02/5.31 & ~ ( ord_less_eq_int @ A5 @ B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_not
% 5.02/5.31 thf(fact_4371_dual__order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [B: real,A: real,C: real] :
% 5.02/5.31 ( ( ord_less_real @ B @ A )
% 5.02/5.31 => ( ( ord_less_eq_real @ C @ B )
% 5.02/5.31 => ( ord_less_real @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans2
% 5.02/5.31 thf(fact_4372_dual__order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.02/5.31 ( ( ord_less_set_nat @ B @ A )
% 5.02/5.31 => ( ( ord_less_eq_set_nat @ C @ B )
% 5.02/5.31 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans2
% 5.02/5.31 thf(fact_4373_dual__order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [B: rat,A: rat,C: rat] :
% 5.02/5.31 ( ( ord_less_rat @ B @ A )
% 5.02/5.31 => ( ( ord_less_eq_rat @ C @ B )
% 5.02/5.31 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans2
% 5.02/5.31 thf(fact_4374_dual__order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [B: num,A: num,C: num] :
% 5.02/5.31 ( ( ord_less_num @ B @ A )
% 5.02/5.31 => ( ( ord_less_eq_num @ C @ B )
% 5.02/5.31 => ( ord_less_num @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans2
% 5.02/5.31 thf(fact_4375_dual__order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [B: nat,A: nat,C: nat] :
% 5.02/5.31 ( ( ord_less_nat @ B @ A )
% 5.02/5.31 => ( ( ord_less_eq_nat @ C @ B )
% 5.02/5.31 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans2
% 5.02/5.31 thf(fact_4376_dual__order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [B: int,A: int,C: int] :
% 5.02/5.31 ( ( ord_less_int @ B @ A )
% 5.02/5.31 => ( ( ord_less_eq_int @ C @ B )
% 5.02/5.31 => ( ord_less_int @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans2
% 5.02/5.31 thf(fact_4377_dual__order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [B: real,A: real,C: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ B @ A )
% 5.02/5.31 => ( ( ord_less_real @ C @ B )
% 5.02/5.31 => ( ord_less_real @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans1
% 5.02/5.31 thf(fact_4378_dual__order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ B @ A )
% 5.02/5.31 => ( ( ord_less_set_nat @ C @ B )
% 5.02/5.31 => ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans1
% 5.02/5.31 thf(fact_4379_dual__order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [B: rat,A: rat,C: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ B @ A )
% 5.02/5.31 => ( ( ord_less_rat @ C @ B )
% 5.02/5.31 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans1
% 5.02/5.31 thf(fact_4380_dual__order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [B: num,A: num,C: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ B @ A )
% 5.02/5.31 => ( ( ord_less_num @ C @ B )
% 5.02/5.31 => ( ord_less_num @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans1
% 5.02/5.31 thf(fact_4381_dual__order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [B: nat,A: nat,C: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ B @ A )
% 5.02/5.31 => ( ( ord_less_nat @ C @ B )
% 5.02/5.31 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans1
% 5.02/5.31 thf(fact_4382_dual__order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [B: int,A: int,C: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ B @ A )
% 5.02/5.31 => ( ( ord_less_int @ C @ B )
% 5.02/5.31 => ( ord_less_int @ C @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_trans1
% 5.02/5.31 thf(fact_4383_dual__order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_real
% 5.02/5.31 = ( ^ [B5: real,A5: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ B5 @ A5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_order
% 5.02/5.31 thf(fact_4384_dual__order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_set_nat
% 5.02/5.31 = ( ^ [B5: set_nat,A5: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ B5 @ A5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_order
% 5.02/5.31 thf(fact_4385_dual__order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_rat
% 5.02/5.31 = ( ^ [B5: rat,A5: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ B5 @ A5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_order
% 5.02/5.31 thf(fact_4386_dual__order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_num
% 5.02/5.31 = ( ^ [B5: num,A5: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ B5 @ A5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_order
% 5.02/5.31 thf(fact_4387_dual__order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_nat
% 5.02/5.31 = ( ^ [B5: nat,A5: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ B5 @ A5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_order
% 5.02/5.31 thf(fact_4388_dual__order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_int
% 5.02/5.31 = ( ^ [B5: int,A5: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ B5 @ A5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.strict_iff_order
% 5.02/5.31 thf(fact_4389_dual__order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_real
% 5.02/5.31 = ( ^ [B5: real,A5: real] :
% 5.02/5.31 ( ( ord_less_real @ B5 @ A5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.order_iff_strict
% 5.02/5.31 thf(fact_4390_dual__order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_set_nat
% 5.02/5.31 = ( ^ [B5: set_nat,A5: set_nat] :
% 5.02/5.31 ( ( ord_less_set_nat @ B5 @ A5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.order_iff_strict
% 5.02/5.31 thf(fact_4391_dual__order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_rat
% 5.02/5.31 = ( ^ [B5: rat,A5: rat] :
% 5.02/5.31 ( ( ord_less_rat @ B5 @ A5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.order_iff_strict
% 5.02/5.31 thf(fact_4392_dual__order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_num
% 5.02/5.31 = ( ^ [B5: num,A5: num] :
% 5.02/5.31 ( ( ord_less_num @ B5 @ A5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.order_iff_strict
% 5.02/5.31 thf(fact_4393_dual__order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_nat
% 5.02/5.31 = ( ^ [B5: nat,A5: nat] :
% 5.02/5.31 ( ( ord_less_nat @ B5 @ A5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.order_iff_strict
% 5.02/5.31 thf(fact_4394_dual__order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_int
% 5.02/5.31 = ( ^ [B5: int,A5: int] :
% 5.02/5.31 ( ( ord_less_int @ B5 @ A5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dual_order.order_iff_strict
% 5.02/5.31 thf(fact_4395_dense__le__bounded,axiom,
% 5.02/5.31 ! [X2: real,Y: real,Z: real] :
% 5.02/5.31 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.31 => ( ! [W2: real] :
% 5.02/5.31 ( ( ord_less_real @ X2 @ W2 )
% 5.02/5.31 => ( ( ord_less_real @ W2 @ Y )
% 5.02/5.31 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.02/5.31 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dense_le_bounded
% 5.02/5.31 thf(fact_4396_dense__le__bounded,axiom,
% 5.02/5.31 ! [X2: rat,Y: rat,Z: rat] :
% 5.02/5.31 ( ( ord_less_rat @ X2 @ Y )
% 5.02/5.31 => ( ! [W2: rat] :
% 5.02/5.31 ( ( ord_less_rat @ X2 @ W2 )
% 5.02/5.31 => ( ( ord_less_rat @ W2 @ Y )
% 5.02/5.31 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 5.02/5.31 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dense_le_bounded
% 5.02/5.31 thf(fact_4397_dense__ge__bounded,axiom,
% 5.02/5.31 ! [Z: real,X2: real,Y: real] :
% 5.02/5.31 ( ( ord_less_real @ Z @ X2 )
% 5.02/5.31 => ( ! [W2: real] :
% 5.02/5.31 ( ( ord_less_real @ Z @ W2 )
% 5.02/5.31 => ( ( ord_less_real @ W2 @ X2 )
% 5.02/5.31 => ( ord_less_eq_real @ Y @ W2 ) ) )
% 5.02/5.31 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dense_ge_bounded
% 5.02/5.31 thf(fact_4398_dense__ge__bounded,axiom,
% 5.02/5.31 ! [Z: rat,X2: rat,Y: rat] :
% 5.02/5.31 ( ( ord_less_rat @ Z @ X2 )
% 5.02/5.31 => ( ! [W2: rat] :
% 5.02/5.31 ( ( ord_less_rat @ Z @ W2 )
% 5.02/5.31 => ( ( ord_less_rat @ W2 @ X2 )
% 5.02/5.31 => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 5.02/5.31 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dense_ge_bounded
% 5.02/5.31 thf(fact_4399_order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_real
% 5.02/5.31 = ( ^ [A5: real,B5: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ A5 @ B5 )
% 5.02/5.31 & ~ ( ord_less_eq_real @ B5 @ A5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_not
% 5.02/5.31 thf(fact_4400_order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_set_nat
% 5.02/5.31 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 5.02/5.31 & ~ ( ord_less_eq_set_nat @ B5 @ A5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_not
% 5.02/5.31 thf(fact_4401_order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_rat
% 5.02/5.31 = ( ^ [A5: rat,B5: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.02/5.31 & ~ ( ord_less_eq_rat @ B5 @ A5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_not
% 5.02/5.31 thf(fact_4402_order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_num
% 5.02/5.31 = ( ^ [A5: num,B5: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.02/5.31 & ~ ( ord_less_eq_num @ B5 @ A5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_not
% 5.02/5.31 thf(fact_4403_order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_nat
% 5.02/5.31 = ( ^ [A5: nat,B5: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.02/5.31 & ~ ( ord_less_eq_nat @ B5 @ A5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_not
% 5.02/5.31 thf(fact_4404_order_Ostrict__iff__not,axiom,
% 5.02/5.31 ( ord_less_int
% 5.02/5.31 = ( ^ [A5: int,B5: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.02/5.31 & ~ ( ord_less_eq_int @ B5 @ A5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_not
% 5.02/5.31 thf(fact_4405_order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [A: real,B: real,C: real] :
% 5.02/5.31 ( ( ord_less_real @ A @ B )
% 5.02/5.31 => ( ( ord_less_eq_real @ B @ C )
% 5.02/5.31 => ( ord_less_real @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans2
% 5.02/5.31 thf(fact_4406_order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.02/5.31 ( ( ord_less_set_nat @ A @ B )
% 5.02/5.31 => ( ( ord_less_eq_set_nat @ B @ C )
% 5.02/5.31 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans2
% 5.02/5.31 thf(fact_4407_order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [A: rat,B: rat,C: rat] :
% 5.02/5.31 ( ( ord_less_rat @ A @ B )
% 5.02/5.31 => ( ( ord_less_eq_rat @ B @ C )
% 5.02/5.31 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans2
% 5.02/5.31 thf(fact_4408_order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [A: num,B: num,C: num] :
% 5.02/5.31 ( ( ord_less_num @ A @ B )
% 5.02/5.31 => ( ( ord_less_eq_num @ B @ C )
% 5.02/5.31 => ( ord_less_num @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans2
% 5.02/5.31 thf(fact_4409_order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [A: nat,B: nat,C: nat] :
% 5.02/5.31 ( ( ord_less_nat @ A @ B )
% 5.02/5.31 => ( ( ord_less_eq_nat @ B @ C )
% 5.02/5.31 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans2
% 5.02/5.31 thf(fact_4410_order_Ostrict__trans2,axiom,
% 5.02/5.31 ! [A: int,B: int,C: int] :
% 5.02/5.31 ( ( ord_less_int @ A @ B )
% 5.02/5.31 => ( ( ord_less_eq_int @ B @ C )
% 5.02/5.31 => ( ord_less_int @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans2
% 5.02/5.31 thf(fact_4411_order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [A: real,B: real,C: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.02/5.31 => ( ( ord_less_real @ B @ C )
% 5.02/5.31 => ( ord_less_real @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans1
% 5.02/5.31 thf(fact_4412_order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.31 => ( ( ord_less_set_nat @ B @ C )
% 5.02/5.31 => ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans1
% 5.02/5.31 thf(fact_4413_order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [A: rat,B: rat,C: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.31 => ( ( ord_less_rat @ B @ C )
% 5.02/5.31 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans1
% 5.02/5.31 thf(fact_4414_order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [A: num,B: num,C: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ A @ B )
% 5.02/5.31 => ( ( ord_less_num @ B @ C )
% 5.02/5.31 => ( ord_less_num @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans1
% 5.02/5.31 thf(fact_4415_order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [A: nat,B: nat,C: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.31 => ( ( ord_less_nat @ B @ C )
% 5.02/5.31 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans1
% 5.02/5.31 thf(fact_4416_order_Ostrict__trans1,axiom,
% 5.02/5.31 ! [A: int,B: int,C: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.02/5.31 => ( ( ord_less_int @ B @ C )
% 5.02/5.31 => ( ord_less_int @ A @ C ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_trans1
% 5.02/5.31 thf(fact_4417_order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_real
% 5.02/5.31 = ( ^ [A5: real,B5: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ A5 @ B5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_order
% 5.02/5.31 thf(fact_4418_order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_set_nat
% 5.02/5.31 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ A5 @ B5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_order
% 5.02/5.31 thf(fact_4419_order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_rat
% 5.02/5.31 = ( ^ [A5: rat,B5: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_order
% 5.02/5.31 thf(fact_4420_order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_num
% 5.02/5.31 = ( ^ [A5: num,B5: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_order
% 5.02/5.31 thf(fact_4421_order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_nat
% 5.02/5.31 = ( ^ [A5: nat,B5: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_order
% 5.02/5.31 thf(fact_4422_order_Ostrict__iff__order,axiom,
% 5.02/5.31 ( ord_less_int
% 5.02/5.31 = ( ^ [A5: int,B5: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.02/5.31 & ( A5 != B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.strict_iff_order
% 5.02/5.31 thf(fact_4423_order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_real
% 5.02/5.31 = ( ^ [A5: real,B5: real] :
% 5.02/5.31 ( ( ord_less_real @ A5 @ B5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.order_iff_strict
% 5.02/5.31 thf(fact_4424_order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_set_nat
% 5.02/5.31 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.02/5.31 ( ( ord_less_set_nat @ A5 @ B5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.order_iff_strict
% 5.02/5.31 thf(fact_4425_order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_rat
% 5.02/5.31 = ( ^ [A5: rat,B5: rat] :
% 5.02/5.31 ( ( ord_less_rat @ A5 @ B5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.order_iff_strict
% 5.02/5.31 thf(fact_4426_order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_num
% 5.02/5.31 = ( ^ [A5: num,B5: num] :
% 5.02/5.31 ( ( ord_less_num @ A5 @ B5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.order_iff_strict
% 5.02/5.31 thf(fact_4427_order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_nat
% 5.02/5.31 = ( ^ [A5: nat,B5: nat] :
% 5.02/5.31 ( ( ord_less_nat @ A5 @ B5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.order_iff_strict
% 5.02/5.31 thf(fact_4428_order_Oorder__iff__strict,axiom,
% 5.02/5.31 ( ord_less_eq_int
% 5.02/5.31 = ( ^ [A5: int,B5: int] :
% 5.02/5.31 ( ( ord_less_int @ A5 @ B5 )
% 5.02/5.31 | ( A5 = B5 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % order.order_iff_strict
% 5.02/5.31 thf(fact_4429_not__le__imp__less,axiom,
% 5.02/5.31 ! [Y: real,X2: real] :
% 5.02/5.31 ( ~ ( ord_less_eq_real @ Y @ X2 )
% 5.02/5.31 => ( ord_less_real @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_le_imp_less
% 5.02/5.31 thf(fact_4430_not__le__imp__less,axiom,
% 5.02/5.31 ! [Y: rat,X2: rat] :
% 5.02/5.31 ( ~ ( ord_less_eq_rat @ Y @ X2 )
% 5.02/5.31 => ( ord_less_rat @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_le_imp_less
% 5.02/5.31 thf(fact_4431_not__le__imp__less,axiom,
% 5.02/5.31 ! [Y: num,X2: num] :
% 5.02/5.31 ( ~ ( ord_less_eq_num @ Y @ X2 )
% 5.02/5.31 => ( ord_less_num @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_le_imp_less
% 5.02/5.31 thf(fact_4432_not__le__imp__less,axiom,
% 5.02/5.31 ! [Y: nat,X2: nat] :
% 5.02/5.31 ( ~ ( ord_less_eq_nat @ Y @ X2 )
% 5.02/5.31 => ( ord_less_nat @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_le_imp_less
% 5.02/5.31 thf(fact_4433_not__le__imp__less,axiom,
% 5.02/5.31 ! [Y: int,X2: int] :
% 5.02/5.31 ( ~ ( ord_less_eq_int @ Y @ X2 )
% 5.02/5.31 => ( ord_less_int @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_le_imp_less
% 5.02/5.31 thf(fact_4434_less__le__not__le,axiom,
% 5.02/5.31 ( ord_less_real
% 5.02/5.31 = ( ^ [X: real,Y6: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ X @ Y6 )
% 5.02/5.31 & ~ ( ord_less_eq_real @ Y6 @ X ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_le_not_le
% 5.02/5.31 thf(fact_4435_less__le__not__le,axiom,
% 5.02/5.31 ( ord_less_set_nat
% 5.02/5.31 = ( ^ [X: set_nat,Y6: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ X @ Y6 )
% 5.02/5.31 & ~ ( ord_less_eq_set_nat @ Y6 @ X ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_le_not_le
% 5.02/5.31 thf(fact_4436_less__le__not__le,axiom,
% 5.02/5.31 ( ord_less_rat
% 5.02/5.31 = ( ^ [X: rat,Y6: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ X @ Y6 )
% 5.02/5.31 & ~ ( ord_less_eq_rat @ Y6 @ X ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_le_not_le
% 5.02/5.31 thf(fact_4437_less__le__not__le,axiom,
% 5.02/5.31 ( ord_less_num
% 5.02/5.31 = ( ^ [X: num,Y6: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ X @ Y6 )
% 5.02/5.31 & ~ ( ord_less_eq_num @ Y6 @ X ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_le_not_le
% 5.02/5.31 thf(fact_4438_less__le__not__le,axiom,
% 5.02/5.31 ( ord_less_nat
% 5.02/5.31 = ( ^ [X: nat,Y6: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ X @ Y6 )
% 5.02/5.31 & ~ ( ord_less_eq_nat @ Y6 @ X ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_le_not_le
% 5.02/5.31 thf(fact_4439_less__le__not__le,axiom,
% 5.02/5.31 ( ord_less_int
% 5.02/5.31 = ( ^ [X: int,Y6: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ X @ Y6 )
% 5.02/5.31 & ~ ( ord_less_eq_int @ Y6 @ X ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_le_not_le
% 5.02/5.31 thf(fact_4440_dense__le,axiom,
% 5.02/5.31 ! [Y: real,Z: real] :
% 5.02/5.31 ( ! [X5: real] :
% 5.02/5.31 ( ( ord_less_real @ X5 @ Y )
% 5.02/5.31 => ( ord_less_eq_real @ X5 @ Z ) )
% 5.02/5.31 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % dense_le
% 5.02/5.31 thf(fact_4441_dense__le,axiom,
% 5.02/5.31 ! [Y: rat,Z: rat] :
% 5.02/5.31 ( ! [X5: rat] :
% 5.02/5.31 ( ( ord_less_rat @ X5 @ Y )
% 5.02/5.31 => ( ord_less_eq_rat @ X5 @ Z ) )
% 5.02/5.31 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % dense_le
% 5.02/5.31 thf(fact_4442_dense__ge,axiom,
% 5.02/5.31 ! [Z: real,Y: real] :
% 5.02/5.31 ( ! [X5: real] :
% 5.02/5.31 ( ( ord_less_real @ Z @ X5 )
% 5.02/5.31 => ( ord_less_eq_real @ Y @ X5 ) )
% 5.02/5.31 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % dense_ge
% 5.02/5.31 thf(fact_4443_dense__ge,axiom,
% 5.02/5.31 ! [Z: rat,Y: rat] :
% 5.02/5.31 ( ! [X5: rat] :
% 5.02/5.31 ( ( ord_less_rat @ Z @ X5 )
% 5.02/5.31 => ( ord_less_eq_rat @ Y @ X5 ) )
% 5.02/5.31 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % dense_ge
% 5.02/5.31 thf(fact_4444_antisym__conv2,axiom,
% 5.02/5.31 ! [X2: real,Y: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.31 => ( ( ~ ( ord_less_real @ X2 @ Y ) )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv2
% 5.02/5.31 thf(fact_4445_antisym__conv2,axiom,
% 5.02/5.31 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.31 => ( ( ~ ( ord_less_set_nat @ X2 @ Y ) )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv2
% 5.02/5.31 thf(fact_4446_antisym__conv2,axiom,
% 5.02/5.31 ! [X2: rat,Y: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.31 => ( ( ~ ( ord_less_rat @ X2 @ Y ) )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv2
% 5.02/5.31 thf(fact_4447_antisym__conv2,axiom,
% 5.02/5.31 ! [X2: num,Y: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.31 => ( ( ~ ( ord_less_num @ X2 @ Y ) )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv2
% 5.02/5.31 thf(fact_4448_antisym__conv2,axiom,
% 5.02/5.31 ! [X2: nat,Y: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.31 => ( ( ~ ( ord_less_nat @ X2 @ Y ) )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv2
% 5.02/5.31 thf(fact_4449_antisym__conv2,axiom,
% 5.02/5.31 ! [X2: int,Y: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.31 => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv2
% 5.02/5.31 thf(fact_4450_antisym__conv1,axiom,
% 5.02/5.31 ! [X2: real,Y: real] :
% 5.02/5.31 ( ~ ( ord_less_real @ X2 @ Y )
% 5.02/5.31 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv1
% 5.02/5.31 thf(fact_4451_antisym__conv1,axiom,
% 5.02/5.31 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.31 ( ~ ( ord_less_set_nat @ X2 @ Y )
% 5.02/5.31 => ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv1
% 5.02/5.31 thf(fact_4452_antisym__conv1,axiom,
% 5.02/5.31 ! [X2: rat,Y: rat] :
% 5.02/5.31 ( ~ ( ord_less_rat @ X2 @ Y )
% 5.02/5.31 => ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv1
% 5.02/5.31 thf(fact_4453_antisym__conv1,axiom,
% 5.02/5.31 ! [X2: num,Y: num] :
% 5.02/5.31 ( ~ ( ord_less_num @ X2 @ Y )
% 5.02/5.31 => ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv1
% 5.02/5.31 thf(fact_4454_antisym__conv1,axiom,
% 5.02/5.31 ! [X2: nat,Y: nat] :
% 5.02/5.31 ( ~ ( ord_less_nat @ X2 @ Y )
% 5.02/5.31 => ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv1
% 5.02/5.31 thf(fact_4455_antisym__conv1,axiom,
% 5.02/5.31 ! [X2: int,Y: int] :
% 5.02/5.31 ( ~ ( ord_less_int @ X2 @ Y )
% 5.02/5.31 => ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.31 = ( X2 = Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % antisym_conv1
% 5.02/5.31 thf(fact_4456_nless__le,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.02/5.31 | ( A = B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % nless_le
% 5.02/5.31 thf(fact_4457_nless__le,axiom,
% 5.02/5.31 ! [A: set_nat,B: set_nat] :
% 5.02/5.31 ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.31 | ( A = B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % nless_le
% 5.02/5.31 thf(fact_4458_nless__le,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.02/5.31 | ( A = B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % nless_le
% 5.02/5.31 thf(fact_4459_nless__le,axiom,
% 5.02/5.31 ! [A: num,B: num] :
% 5.02/5.31 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.02/5.31 | ( A = B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % nless_le
% 5.02/5.31 thf(fact_4460_nless__le,axiom,
% 5.02/5.31 ! [A: nat,B: nat] :
% 5.02/5.31 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.02/5.31 | ( A = B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % nless_le
% 5.02/5.31 thf(fact_4461_nless__le,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.02/5.31 | ( A = B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % nless_le
% 5.02/5.31 thf(fact_4462_leI,axiom,
% 5.02/5.31 ! [X2: real,Y: real] :
% 5.02/5.31 ( ~ ( ord_less_real @ X2 @ Y )
% 5.02/5.31 => ( ord_less_eq_real @ Y @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % leI
% 5.02/5.31 thf(fact_4463_leI,axiom,
% 5.02/5.31 ! [X2: rat,Y: rat] :
% 5.02/5.31 ( ~ ( ord_less_rat @ X2 @ Y )
% 5.02/5.31 => ( ord_less_eq_rat @ Y @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % leI
% 5.02/5.31 thf(fact_4464_leI,axiom,
% 5.02/5.31 ! [X2: num,Y: num] :
% 5.02/5.31 ( ~ ( ord_less_num @ X2 @ Y )
% 5.02/5.31 => ( ord_less_eq_num @ Y @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % leI
% 5.02/5.31 thf(fact_4465_leI,axiom,
% 5.02/5.31 ! [X2: nat,Y: nat] :
% 5.02/5.31 ( ~ ( ord_less_nat @ X2 @ Y )
% 5.02/5.31 => ( ord_less_eq_nat @ Y @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % leI
% 5.02/5.31 thf(fact_4466_leI,axiom,
% 5.02/5.31 ! [X2: int,Y: int] :
% 5.02/5.31 ( ~ ( ord_less_int @ X2 @ Y )
% 5.02/5.31 => ( ord_less_eq_int @ Y @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % leI
% 5.02/5.31 thf(fact_4467_leD,axiom,
% 5.02/5.31 ! [Y: real,X2: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ Y @ X2 )
% 5.02/5.31 => ~ ( ord_less_real @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % leD
% 5.02/5.31 thf(fact_4468_leD,axiom,
% 5.02/5.31 ! [Y: set_nat,X2: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ Y @ X2 )
% 5.02/5.31 => ~ ( ord_less_set_nat @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % leD
% 5.02/5.31 thf(fact_4469_leD,axiom,
% 5.02/5.31 ! [Y: rat,X2: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ Y @ X2 )
% 5.02/5.31 => ~ ( ord_less_rat @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % leD
% 5.02/5.31 thf(fact_4470_leD,axiom,
% 5.02/5.31 ! [Y: num,X2: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ Y @ X2 )
% 5.02/5.31 => ~ ( ord_less_num @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % leD
% 5.02/5.31 thf(fact_4471_leD,axiom,
% 5.02/5.31 ! [Y: nat,X2: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ Y @ X2 )
% 5.02/5.31 => ~ ( ord_less_nat @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % leD
% 5.02/5.31 thf(fact_4472_leD,axiom,
% 5.02/5.31 ! [Y: int,X2: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ Y @ X2 )
% 5.02/5.31 => ~ ( ord_less_int @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % leD
% 5.02/5.31 thf(fact_4473_bot_Oextremum,axiom,
% 5.02/5.31 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum
% 5.02/5.31 thf(fact_4474_bot_Oextremum,axiom,
% 5.02/5.31 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum
% 5.02/5.31 thf(fact_4475_bot_Oextremum,axiom,
% 5.02/5.31 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum
% 5.02/5.31 thf(fact_4476_bot_Oextremum,axiom,
% 5.02/5.31 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum
% 5.02/5.31 thf(fact_4477_bot_Oextremum__unique,axiom,
% 5.02/5.31 ! [A: set_int] :
% 5.02/5.31 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.02/5.31 = ( A = bot_bot_set_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_unique
% 5.02/5.31 thf(fact_4478_bot_Oextremum__unique,axiom,
% 5.02/5.31 ! [A: set_real] :
% 5.02/5.31 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.02/5.31 = ( A = bot_bot_set_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_unique
% 5.02/5.31 thf(fact_4479_bot_Oextremum__unique,axiom,
% 5.02/5.31 ! [A: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.02/5.31 = ( A = bot_bot_set_nat ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_unique
% 5.02/5.31 thf(fact_4480_bot_Oextremum__unique,axiom,
% 5.02/5.31 ! [A: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.02/5.31 = ( A = bot_bot_nat ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_unique
% 5.02/5.31 thf(fact_4481_bot_Oextremum__uniqueI,axiom,
% 5.02/5.31 ! [A: set_int] :
% 5.02/5.31 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.02/5.31 => ( A = bot_bot_set_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_uniqueI
% 5.02/5.31 thf(fact_4482_bot_Oextremum__uniqueI,axiom,
% 5.02/5.31 ! [A: set_real] :
% 5.02/5.31 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.02/5.31 => ( A = bot_bot_set_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_uniqueI
% 5.02/5.31 thf(fact_4483_bot_Oextremum__uniqueI,axiom,
% 5.02/5.31 ! [A: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.02/5.31 => ( A = bot_bot_set_nat ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_uniqueI
% 5.02/5.31 thf(fact_4484_bot_Oextremum__uniqueI,axiom,
% 5.02/5.31 ! [A: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.02/5.31 => ( A = bot_bot_nat ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_uniqueI
% 5.02/5.31 thf(fact_4485_bot_Onot__eq__extremum,axiom,
% 5.02/5.31 ! [A: set_nat] :
% 5.02/5.31 ( ( A != bot_bot_set_nat )
% 5.02/5.31 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.not_eq_extremum
% 5.02/5.31 thf(fact_4486_bot_Onot__eq__extremum,axiom,
% 5.02/5.31 ! [A: set_int] :
% 5.02/5.31 ( ( A != bot_bot_set_int )
% 5.02/5.31 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.not_eq_extremum
% 5.02/5.31 thf(fact_4487_bot_Onot__eq__extremum,axiom,
% 5.02/5.31 ! [A: set_real] :
% 5.02/5.31 ( ( A != bot_bot_set_real )
% 5.02/5.31 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.not_eq_extremum
% 5.02/5.31 thf(fact_4488_bot_Onot__eq__extremum,axiom,
% 5.02/5.31 ! [A: nat] :
% 5.02/5.31 ( ( A != bot_bot_nat )
% 5.02/5.31 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % bot.not_eq_extremum
% 5.02/5.31 thf(fact_4489_bot_Oextremum__strict,axiom,
% 5.02/5.31 ! [A: set_nat] :
% 5.02/5.31 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_strict
% 5.02/5.31 thf(fact_4490_bot_Oextremum__strict,axiom,
% 5.02/5.31 ! [A: set_int] :
% 5.02/5.31 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_strict
% 5.02/5.31 thf(fact_4491_bot_Oextremum__strict,axiom,
% 5.02/5.31 ! [A: set_real] :
% 5.02/5.31 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_strict
% 5.02/5.31 thf(fact_4492_bot_Oextremum__strict,axiom,
% 5.02/5.31 ! [A: nat] :
% 5.02/5.31 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.02/5.31
% 5.02/5.31 % bot.extremum_strict
% 5.02/5.31 thf(fact_4493_list__decode_Ocases,axiom,
% 5.02/5.31 ! [X2: nat] :
% 5.02/5.31 ( ( X2 != zero_zero_nat )
% 5.02/5.31 => ~ ! [N: nat] :
% 5.02/5.31 ( X2
% 5.02/5.31 != ( suc @ N ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % list_decode.cases
% 5.02/5.31 thf(fact_4494_max__absorb2,axiom,
% 5.02/5.31 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.31 => ( ( ord_max_set_nat @ X2 @ Y )
% 5.02/5.31 = Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb2
% 5.02/5.31 thf(fact_4495_max__absorb2,axiom,
% 5.02/5.31 ! [X2: rat,Y: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.31 => ( ( ord_max_rat @ X2 @ Y )
% 5.02/5.31 = Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb2
% 5.02/5.31 thf(fact_4496_max__absorb2,axiom,
% 5.02/5.31 ! [X2: num,Y: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ X2 @ Y )
% 5.02/5.31 => ( ( ord_max_num @ X2 @ Y )
% 5.02/5.31 = Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb2
% 5.02/5.31 thf(fact_4497_max__absorb2,axiom,
% 5.02/5.31 ! [X2: nat,Y: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ X2 @ Y )
% 5.02/5.31 => ( ( ord_max_nat @ X2 @ Y )
% 5.02/5.31 = Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb2
% 5.02/5.31 thf(fact_4498_max__absorb2,axiom,
% 5.02/5.31 ! [X2: int,Y: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.31 => ( ( ord_max_int @ X2 @ Y )
% 5.02/5.31 = Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb2
% 5.02/5.31 thf(fact_4499_max__absorb1,axiom,
% 5.02/5.31 ! [Y: set_nat,X2: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ Y @ X2 )
% 5.02/5.31 => ( ( ord_max_set_nat @ X2 @ Y )
% 5.02/5.31 = X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb1
% 5.02/5.31 thf(fact_4500_max__absorb1,axiom,
% 5.02/5.31 ! [Y: rat,X2: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ Y @ X2 )
% 5.02/5.31 => ( ( ord_max_rat @ X2 @ Y )
% 5.02/5.31 = X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb1
% 5.02/5.31 thf(fact_4501_max__absorb1,axiom,
% 5.02/5.31 ! [Y: num,X2: num] :
% 5.02/5.31 ( ( ord_less_eq_num @ Y @ X2 )
% 5.02/5.31 => ( ( ord_max_num @ X2 @ Y )
% 5.02/5.31 = X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb1
% 5.02/5.31 thf(fact_4502_max__absorb1,axiom,
% 5.02/5.31 ! [Y: nat,X2: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ Y @ X2 )
% 5.02/5.31 => ( ( ord_max_nat @ X2 @ Y )
% 5.02/5.31 = X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb1
% 5.02/5.31 thf(fact_4503_max__absorb1,axiom,
% 5.02/5.31 ! [Y: int,X2: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ Y @ X2 )
% 5.02/5.31 => ( ( ord_max_int @ X2 @ Y )
% 5.02/5.31 = X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_absorb1
% 5.02/5.31 thf(fact_4504_max__def,axiom,
% 5.02/5.31 ( ord_max_set_nat
% 5.02/5.31 = ( ^ [A5: set_nat,B5: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_def
% 5.02/5.31 thf(fact_4505_max__def,axiom,
% 5.02/5.31 ( ord_max_rat
% 5.02/5.31 = ( ^ [A5: rat,B5: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_def
% 5.02/5.31 thf(fact_4506_max__def,axiom,
% 5.02/5.31 ( ord_max_num
% 5.02/5.31 = ( ^ [A5: num,B5: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_def
% 5.02/5.31 thf(fact_4507_max__def,axiom,
% 5.02/5.31 ( ord_max_nat
% 5.02/5.31 = ( ^ [A5: nat,B5: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_def
% 5.02/5.31 thf(fact_4508_max__def,axiom,
% 5.02/5.31 ( ord_max_int
% 5.02/5.31 = ( ^ [A5: int,B5: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B5 ) @ B5 @ A5 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_def
% 5.02/5.31 thf(fact_4509_mult__exp__mod__exp__eq,axiom,
% 5.02/5.31 ! [M: nat,N2: nat,A: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.31 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_exp_mod_exp_eq
% 5.02/5.31 thf(fact_4510_mult__exp__mod__exp__eq,axiom,
% 5.02/5.31 ! [M: nat,N2: nat,A: int] :
% 5.02/5.31 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.31 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_exp_mod_exp_eq
% 5.02/5.31 thf(fact_4511_even__mod__4__div__2,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.31 = ( suc @ zero_zero_nat ) )
% 5.02/5.31 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % even_mod_4_div_2
% 5.02/5.31 thf(fact_4512_int__power__div__base,axiom,
% 5.02/5.31 ! [M: nat,K: int] :
% 5.02/5.31 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.31 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.02/5.31 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.02/5.31 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % int_power_div_base
% 5.02/5.31 thf(fact_4513_even__mult__exp__div__exp__iff,axiom,
% 5.02/5.31 ! [A: code_integer,M: nat,N2: nat] :
% 5.02/5.31 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.31 = ( ( ord_less_nat @ N2 @ M )
% 5.02/5.31 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 = zero_z3403309356797280102nteger )
% 5.02/5.31 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.31 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % even_mult_exp_div_exp_iff
% 5.02/5.31 thf(fact_4514_even__mult__exp__div__exp__iff,axiom,
% 5.02/5.31 ! [A: nat,M: nat,N2: nat] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.31 = ( ( ord_less_nat @ N2 @ M )
% 5.02/5.31 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 = zero_zero_nat )
% 5.02/5.31 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.31 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % even_mult_exp_div_exp_iff
% 5.02/5.31 thf(fact_4515_even__mult__exp__div__exp__iff,axiom,
% 5.02/5.31 ! [A: int,M: nat,N2: nat] :
% 5.02/5.31 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.31 = ( ( ord_less_nat @ N2 @ M )
% 5.02/5.31 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 = zero_zero_int )
% 5.02/5.31 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.31 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % even_mult_exp_div_exp_iff
% 5.02/5.31 thf(fact_4516_real__average__minus__first,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.02/5.31 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % real_average_minus_first
% 5.02/5.31 thf(fact_4517_real__average__minus__second,axiom,
% 5.02/5.31 ! [B: real,A: real] :
% 5.02/5.31 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.02/5.31 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % real_average_minus_second
% 5.02/5.31 thf(fact_4518_vebt__member_Opelims_I1_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.02/5.31 ( ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.02/5.31 = Y )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [A4: $o,B3: $o] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.31 => A4 )
% 5.02/5.31 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.31 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.31 => B3 )
% 5.02/5.31 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.02/5.31 => ( ~ Y
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.02/5.31 => ( ~ Y
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.02/5.31 => ( ~ Y
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( ( Xa2 != Mi2 )
% 5.02/5.31 => ( ( Xa2 != Ma2 )
% 5.02/5.31 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.31 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.31 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.31 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.31 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % vebt_member.pelims(1)
% 5.02/5.31 thf(fact_4519_vebt__member_Opelims_I3_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.31 ( ~ ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [A4: $o,B3: $o] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 5.02/5.31 => ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.31 => A4 )
% 5.02/5.31 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.31 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.31 => B3 )
% 5.02/5.31 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.02/5.31 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.02/5.31 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.02/5.31 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.02/5.31 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.02/5.31 => ( ( Xa2 != Mi2 )
% 5.02/5.31 => ( ( Xa2 != Ma2 )
% 5.02/5.31 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.31 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.31 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.31 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.31 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % vebt_member.pelims(3)
% 5.02/5.31 thf(fact_4520_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.02/5.31 ( ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.02/5.31 = Y )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [A4: $o,B3: $o] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.31 => A4 )
% 5.02/5.31 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.31 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.31 => B3 )
% 5.02/5.31 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.02/5.31 => ( ~ Y
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % VEBT_internal.naive_member.pelims(1)
% 5.02/5.31 thf(fact_4521_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.31 ( ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [A4: $o,B3: $o] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 5.02/5.31 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.31 => A4 )
% 5.02/5.31 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.31 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.31 => B3 )
% 5.02/5.31 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.02/5.31 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) )
% 5.02/5.31 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % VEBT_internal.naive_member.pelims(2)
% 5.02/5.31 thf(fact_4522_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.31 ( ~ ( vEBT_V5719532721284313246member @ X2 @ Xa2 )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [A4: $o,B3: $o] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 5.02/5.31 => ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.31 => A4 )
% 5.02/5.31 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.31 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.31 => B3 )
% 5.02/5.31 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.02/5.31 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.02/5.31 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S ) @ Xa2 ) )
% 5.02/5.31 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % VEBT_internal.naive_member.pelims(3)
% 5.02/5.31 thf(fact_4523_vebt__member_Opelims_I2_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.31 ( ( vEBT_vebt_member @ X2 @ Xa2 )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [A4: $o,B3: $o] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Leaf @ A4 @ B3 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A4 @ B3 ) @ Xa2 ) )
% 5.02/5.31 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.31 => A4 )
% 5.02/5.31 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.31 => ( ( ( Xa2 = one_one_nat )
% 5.02/5.31 => B3 )
% 5.02/5.31 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.02/5.31 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.02/5.31 => ~ ( ( Xa2 != Mi2 )
% 5.02/5.31 => ( ( Xa2 != Ma2 )
% 5.02/5.31 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.31 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.02/5.31 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.31 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.02/5.31 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % vebt_member.pelims(2)
% 5.02/5.31 thf(fact_4524_diff__commute,axiom,
% 5.02/5.31 ! [I3: nat,J: nat,K: nat] :
% 5.02/5.31 ( ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J ) @ K )
% 5.02/5.31 = ( minus_minus_nat @ ( minus_minus_nat @ I3 @ K ) @ J ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_commute
% 5.02/5.31 thf(fact_4525_mult__commute__abs,axiom,
% 5.02/5.31 ! [C: real] :
% 5.02/5.31 ( ( ^ [X: real] : ( times_times_real @ X @ C ) )
% 5.02/5.31 = ( times_times_real @ C ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_commute_abs
% 5.02/5.31 thf(fact_4526_mult__commute__abs,axiom,
% 5.02/5.31 ! [C: rat] :
% 5.02/5.31 ( ( ^ [X: rat] : ( times_times_rat @ X @ C ) )
% 5.02/5.31 = ( times_times_rat @ C ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_commute_abs
% 5.02/5.31 thf(fact_4527_mult__commute__abs,axiom,
% 5.02/5.31 ! [C: nat] :
% 5.02/5.31 ( ( ^ [X: nat] : ( times_times_nat @ X @ C ) )
% 5.02/5.31 = ( times_times_nat @ C ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_commute_abs
% 5.02/5.31 thf(fact_4528_mult__commute__abs,axiom,
% 5.02/5.31 ! [C: int] :
% 5.02/5.31 ( ( ^ [X: int] : ( times_times_int @ X @ C ) )
% 5.02/5.31 = ( times_times_int @ C ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_commute_abs
% 5.02/5.31 thf(fact_4529_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.31 ( ~ ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [Uu2: $o,Uv2: $o] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.02/5.31 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.02/5.31 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.02/5.31 => ( ( Xa2 = Mi2 )
% 5.02/5.31 | ( Xa2 = Ma2 ) ) ) )
% 5.02/5.31 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 5.02/5.31 => ( ( Xa2 = Mi2 )
% 5.02/5.31 | ( Xa2 = Ma2 )
% 5.02/5.31 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.02/5.31 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) @ Xa2 ) )
% 5.02/5.31 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % VEBT_internal.membermima.pelims(3)
% 5.02/5.31 thf(fact_4530_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.02/5.31 ( ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.02/5.31 = Y )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [Uu2: $o,Uv2: $o] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.31 => ( ~ Y
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.02/5.31 => ( ~ Y
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( ( Xa2 = Mi2 )
% 5.02/5.31 | ( Xa2 = Ma2 ) ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( ( Xa2 = Mi2 )
% 5.02/5.31 | ( Xa2 = Ma2 )
% 5.02/5.31 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.02/5.31 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) )
% 5.02/5.31 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % VEBT_internal.membermima.pelims(1)
% 5.02/5.31 thf(fact_4531_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.31 ( ( vEBT_VEBT_membermima @ X2 @ Xa2 )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.31 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.02/5.31 => ~ ( ( Xa2 = Mi2 )
% 5.02/5.31 | ( Xa2 = Ma2 ) ) ) )
% 5.02/5.31 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc2 ) @ Xa2 ) )
% 5.02/5.31 => ~ ( ( Xa2 = Mi2 )
% 5.02/5.31 | ( Xa2 = Ma2 )
% 5.02/5.31 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) )
% 5.02/5.31 => ~ ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) )
% 5.02/5.31 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd ) @ Xa2 ) )
% 5.02/5.31 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.02/5.31 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.31 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % VEBT_internal.membermima.pelims(2)
% 5.02/5.31 thf(fact_4532_inrange,axiom,
% 5.02/5.31 ! [T2: vEBT_VEBT,N2: nat] :
% 5.02/5.31 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 5.02/5.31 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % inrange
% 5.02/5.31 thf(fact_4533_vebt__buildup_Oelims,axiom,
% 5.02/5.31 ! [X2: nat,Y: vEBT_VEBT] :
% 5.02/5.31 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.02/5.31 = Y )
% 5.02/5.31 => ( ( ( X2 = zero_zero_nat )
% 5.02/5.31 => ( Y
% 5.02/5.31 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.02/5.31 => ( ( ( X2
% 5.02/5.31 = ( suc @ zero_zero_nat ) )
% 5.02/5.31 => ( Y
% 5.02/5.31 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.02/5.31 => ~ ! [Va: nat] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( suc @ ( suc @ Va ) ) )
% 5.02/5.31 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.02/5.31 => ( Y
% 5.02/5.31 = ( 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 ) ) ) ) ) ) )
% 5.02/5.31 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.02/5.31 => ( Y
% 5.02/5.31 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % vebt_buildup.elims
% 5.02/5.31 thf(fact_4534_triangle__def,axiom,
% 5.02/5.31 ( nat_triangle
% 5.02/5.31 = ( ^ [N3: nat] : ( divide_divide_nat @ ( times_times_nat @ N3 @ ( suc @ N3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % triangle_def
% 5.02/5.31 thf(fact_4535_intind,axiom,
% 5.02/5.31 ! [I3: nat,N2: nat,P: nat > $o,X2: nat] :
% 5.02/5.31 ( ( ord_less_nat @ I3 @ N2 )
% 5.02/5.31 => ( ( P @ X2 )
% 5.02/5.31 => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X2 ) @ I3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % intind
% 5.02/5.31 thf(fact_4536_intind,axiom,
% 5.02/5.31 ! [I3: nat,N2: nat,P: int > $o,X2: int] :
% 5.02/5.31 ( ( ord_less_nat @ I3 @ N2 )
% 5.02/5.31 => ( ( P @ X2 )
% 5.02/5.31 => ( P @ ( nth_int @ ( replicate_int @ N2 @ X2 ) @ I3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % intind
% 5.02/5.31 thf(fact_4537_intind,axiom,
% 5.02/5.31 ! [I3: nat,N2: nat,P: vEBT_VEBT > $o,X2: vEBT_VEBT] :
% 5.02/5.31 ( ( ord_less_nat @ I3 @ N2 )
% 5.02/5.31 => ( ( P @ X2 )
% 5.02/5.31 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X2 ) @ I3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % intind
% 5.02/5.31 thf(fact_4538_atLeastAtMost__iff,axiom,
% 5.02/5.31 ! [I3: set_nat,L: set_nat,U: set_nat] :
% 5.02/5.31 ( ( member_set_nat @ I3 @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 5.02/5.31 = ( ( ord_less_eq_set_nat @ L @ I3 )
% 5.02/5.31 & ( ord_less_eq_set_nat @ I3 @ U ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastAtMost_iff
% 5.02/5.31 thf(fact_4539_atLeastAtMost__iff,axiom,
% 5.02/5.31 ! [I3: rat,L: rat,U: rat] :
% 5.02/5.31 ( ( member_rat @ I3 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.02/5.31 = ( ( ord_less_eq_rat @ L @ I3 )
% 5.02/5.31 & ( ord_less_eq_rat @ I3 @ U ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastAtMost_iff
% 5.02/5.31 thf(fact_4540_atLeastAtMost__iff,axiom,
% 5.02/5.31 ! [I3: num,L: num,U: num] :
% 5.02/5.31 ( ( member_num @ I3 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.02/5.31 = ( ( ord_less_eq_num @ L @ I3 )
% 5.02/5.31 & ( ord_less_eq_num @ I3 @ U ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastAtMost_iff
% 5.02/5.31 thf(fact_4541_atLeastAtMost__iff,axiom,
% 5.02/5.31 ! [I3: nat,L: nat,U: nat] :
% 5.02/5.31 ( ( member_nat @ I3 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.02/5.31 = ( ( ord_less_eq_nat @ L @ I3 )
% 5.02/5.31 & ( ord_less_eq_nat @ I3 @ U ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastAtMost_iff
% 5.02/5.31 thf(fact_4542_atLeastAtMost__iff,axiom,
% 5.02/5.31 ! [I3: int,L: int,U: int] :
% 5.02/5.31 ( ( member_int @ I3 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.02/5.31 = ( ( ord_less_eq_int @ L @ I3 )
% 5.02/5.31 & ( ord_less_eq_int @ I3 @ U ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastAtMost_iff
% 5.02/5.31 thf(fact_4543_atLeastAtMost__iff,axiom,
% 5.02/5.31 ! [I3: real,L: real,U: real] :
% 5.02/5.31 ( ( member_real @ I3 @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.02/5.31 = ( ( ord_less_eq_real @ L @ I3 )
% 5.02/5.31 & ( ord_less_eq_real @ I3 @ U ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastAtMost_iff
% 5.02/5.31 thf(fact_4544_Icc__eq__Icc,axiom,
% 5.02/5.31 ! [L: set_nat,H2: set_nat,L3: set_nat,H3: set_nat] :
% 5.02/5.31 ( ( ( set_or4548717258645045905et_nat @ L @ H2 )
% 5.02/5.31 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 5.02/5.31 = ( ( ( L = L3 )
% 5.02/5.31 & ( H2 = H3 ) )
% 5.02/5.31 | ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 5.02/5.31 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Icc_eq_Icc
% 5.02/5.31 thf(fact_4545_Icc__eq__Icc,axiom,
% 5.02/5.31 ! [L: rat,H2: rat,L3: rat,H3: rat] :
% 5.02/5.31 ( ( ( set_or633870826150836451st_rat @ L @ H2 )
% 5.02/5.31 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.02/5.31 = ( ( ( L = L3 )
% 5.02/5.31 & ( H2 = H3 ) )
% 5.02/5.31 | ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.02/5.31 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Icc_eq_Icc
% 5.02/5.31 thf(fact_4546_Icc__eq__Icc,axiom,
% 5.02/5.31 ! [L: num,H2: num,L3: num,H3: num] :
% 5.02/5.31 ( ( ( set_or7049704709247886629st_num @ L @ H2 )
% 5.02/5.31 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.02/5.31 = ( ( ( L = L3 )
% 5.02/5.31 & ( H2 = H3 ) )
% 5.02/5.31 | ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.02/5.31 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Icc_eq_Icc
% 5.02/5.31 thf(fact_4547_Icc__eq__Icc,axiom,
% 5.02/5.31 ! [L: nat,H2: nat,L3: nat,H3: nat] :
% 5.02/5.31 ( ( ( set_or1269000886237332187st_nat @ L @ H2 )
% 5.02/5.31 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.02/5.31 = ( ( ( L = L3 )
% 5.02/5.31 & ( H2 = H3 ) )
% 5.02/5.31 | ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.02/5.31 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Icc_eq_Icc
% 5.02/5.31 thf(fact_4548_Icc__eq__Icc,axiom,
% 5.02/5.31 ! [L: int,H2: int,L3: int,H3: int] :
% 5.02/5.31 ( ( ( set_or1266510415728281911st_int @ L @ H2 )
% 5.02/5.31 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.02/5.31 = ( ( ( L = L3 )
% 5.02/5.31 & ( H2 = H3 ) )
% 5.02/5.31 | ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.02/5.31 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Icc_eq_Icc
% 5.02/5.31 thf(fact_4549_Icc__eq__Icc,axiom,
% 5.02/5.31 ! [L: real,H2: real,L3: real,H3: real] :
% 5.02/5.31 ( ( ( set_or1222579329274155063t_real @ L @ H2 )
% 5.02/5.31 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.02/5.31 = ( ( ( L = L3 )
% 5.02/5.31 & ( H2 = H3 ) )
% 5.02/5.31 | ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.02/5.31 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Icc_eq_Icc
% 5.02/5.31 thf(fact_4550_replicate__eq__replicate,axiom,
% 5.02/5.31 ! [M: nat,X2: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.02/5.31 ( ( ( replicate_VEBT_VEBT @ M @ X2 )
% 5.02/5.31 = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 5.02/5.31 = ( ( M = N2 )
% 5.02/5.31 & ( ( M != zero_zero_nat )
% 5.02/5.31 => ( X2 = Y ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_eq_replicate
% 5.02/5.31 thf(fact_4551_length__replicate,axiom,
% 5.02/5.31 ! [N2: nat,X2: vEBT_VEBT] :
% 5.02/5.31 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X2 ) )
% 5.02/5.31 = N2 ) ).
% 5.02/5.31
% 5.02/5.31 % length_replicate
% 5.02/5.31 thf(fact_4552_length__replicate,axiom,
% 5.02/5.31 ! [N2: nat,X2: $o] :
% 5.02/5.31 ( ( size_size_list_o @ ( replicate_o @ N2 @ X2 ) )
% 5.02/5.31 = N2 ) ).
% 5.02/5.31
% 5.02/5.31 % length_replicate
% 5.02/5.31 thf(fact_4553_length__replicate,axiom,
% 5.02/5.31 ! [N2: nat,X2: nat] :
% 5.02/5.31 ( ( size_size_list_nat @ ( replicate_nat @ N2 @ X2 ) )
% 5.02/5.31 = N2 ) ).
% 5.02/5.31
% 5.02/5.31 % length_replicate
% 5.02/5.31 thf(fact_4554_length__replicate,axiom,
% 5.02/5.31 ! [N2: nat,X2: int] :
% 5.02/5.31 ( ( size_size_list_int @ ( replicate_int @ N2 @ X2 ) )
% 5.02/5.31 = N2 ) ).
% 5.02/5.31
% 5.02/5.31 % length_replicate
% 5.02/5.31 thf(fact_4555_triangle__0,axiom,
% 5.02/5.31 ( ( nat_triangle @ zero_zero_nat )
% 5.02/5.31 = zero_zero_nat ) ).
% 5.02/5.31
% 5.02/5.31 % triangle_0
% 5.02/5.31 thf(fact_4556_atLeastatMost__empty__iff2,axiom,
% 5.02/5.31 ! [A: set_nat,B: set_nat] :
% 5.02/5.31 ( ( bot_bot_set_set_nat
% 5.02/5.31 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff2
% 5.02/5.31 thf(fact_4557_atLeastatMost__empty__iff2,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( bot_bot_set_rat
% 5.02/5.31 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff2
% 5.02/5.31 thf(fact_4558_atLeastatMost__empty__iff2,axiom,
% 5.02/5.31 ! [A: num,B: num] :
% 5.02/5.31 ( ( bot_bot_set_num
% 5.02/5.31 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff2
% 5.02/5.31 thf(fact_4559_atLeastatMost__empty__iff2,axiom,
% 5.02/5.31 ! [A: nat,B: nat] :
% 5.02/5.31 ( ( bot_bot_set_nat
% 5.02/5.31 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff2
% 5.02/5.31 thf(fact_4560_atLeastatMost__empty__iff2,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( bot_bot_set_int
% 5.02/5.31 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff2
% 5.02/5.31 thf(fact_4561_atLeastatMost__empty__iff2,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( bot_bot_set_real
% 5.02/5.31 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff2
% 5.02/5.31 thf(fact_4562_atLeastatMost__empty__iff,axiom,
% 5.02/5.31 ! [A: set_nat,B: set_nat] :
% 5.02/5.31 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 5.02/5.31 = bot_bot_set_set_nat )
% 5.02/5.31 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff
% 5.02/5.31 thf(fact_4563_atLeastatMost__empty__iff,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.02/5.31 = bot_bot_set_rat )
% 5.02/5.31 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff
% 5.02/5.31 thf(fact_4564_atLeastatMost__empty__iff,axiom,
% 5.02/5.31 ! [A: num,B: num] :
% 5.02/5.31 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.02/5.31 = bot_bot_set_num )
% 5.02/5.31 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff
% 5.02/5.31 thf(fact_4565_atLeastatMost__empty__iff,axiom,
% 5.02/5.31 ! [A: nat,B: nat] :
% 5.02/5.31 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.02/5.31 = bot_bot_set_nat )
% 5.02/5.31 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff
% 5.02/5.31 thf(fact_4566_atLeastatMost__empty__iff,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.02/5.31 = bot_bot_set_int )
% 5.02/5.31 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff
% 5.02/5.31 thf(fact_4567_atLeastatMost__empty__iff,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.02/5.31 = bot_bot_set_real )
% 5.02/5.31 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty_iff
% 5.02/5.31 thf(fact_4568_atLeastatMost__subset__iff,axiom,
% 5.02/5.31 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.02/5.31 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.02/5.31 & ( ord_less_eq_set_nat @ B @ D ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_subset_iff
% 5.02/5.31 thf(fact_4569_atLeastatMost__subset__iff,axiom,
% 5.02/5.31 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.02/5.31 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_rat @ C @ A )
% 5.02/5.31 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_subset_iff
% 5.02/5.31 thf(fact_4570_atLeastatMost__subset__iff,axiom,
% 5.02/5.31 ! [A: num,B: num,C: num,D: num] :
% 5.02/5.31 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_num @ C @ A )
% 5.02/5.31 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_subset_iff
% 5.02/5.31 thf(fact_4571_atLeastatMost__subset__iff,axiom,
% 5.02/5.31 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_nat @ C @ A )
% 5.02/5.31 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_subset_iff
% 5.02/5.31 thf(fact_4572_atLeastatMost__subset__iff,axiom,
% 5.02/5.31 ! [A: int,B: int,C: int,D: int] :
% 5.02/5.31 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_int @ C @ A )
% 5.02/5.31 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_subset_iff
% 5.02/5.31 thf(fact_4573_atLeastatMost__subset__iff,axiom,
% 5.02/5.31 ! [A: real,B: real,C: real,D: real] :
% 5.02/5.31 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.02/5.31 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_real @ C @ A )
% 5.02/5.31 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_subset_iff
% 5.02/5.31 thf(fact_4574_atLeastatMost__empty,axiom,
% 5.02/5.31 ! [B: rat,A: rat] :
% 5.02/5.31 ( ( ord_less_rat @ B @ A )
% 5.02/5.31 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.02/5.31 = bot_bot_set_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty
% 5.02/5.31 thf(fact_4575_atLeastatMost__empty,axiom,
% 5.02/5.31 ! [B: num,A: num] :
% 5.02/5.31 ( ( ord_less_num @ B @ A )
% 5.02/5.31 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.02/5.31 = bot_bot_set_num ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty
% 5.02/5.31 thf(fact_4576_atLeastatMost__empty,axiom,
% 5.02/5.31 ! [B: nat,A: nat] :
% 5.02/5.31 ( ( ord_less_nat @ B @ A )
% 5.02/5.31 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.02/5.31 = bot_bot_set_nat ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty
% 5.02/5.31 thf(fact_4577_atLeastatMost__empty,axiom,
% 5.02/5.31 ! [B: int,A: int] :
% 5.02/5.31 ( ( ord_less_int @ B @ A )
% 5.02/5.31 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.02/5.31 = bot_bot_set_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty
% 5.02/5.31 thf(fact_4578_atLeastatMost__empty,axiom,
% 5.02/5.31 ! [B: real,A: real] :
% 5.02/5.31 ( ( ord_less_real @ B @ A )
% 5.02/5.31 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.02/5.31 = bot_bot_set_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_empty
% 5.02/5.31 thf(fact_4579_Ball__set__replicate,axiom,
% 5.02/5.31 ! [N2: nat,A: int,P: int > $o] :
% 5.02/5.31 ( ( ! [X: int] :
% 5.02/5.31 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.02/5.31 => ( P @ X ) ) )
% 5.02/5.31 = ( ( P @ A )
% 5.02/5.31 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Ball_set_replicate
% 5.02/5.31 thf(fact_4580_Ball__set__replicate,axiom,
% 5.02/5.31 ! [N2: nat,A: nat,P: nat > $o] :
% 5.02/5.31 ( ( ! [X: nat] :
% 5.02/5.31 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 5.02/5.31 => ( P @ X ) ) )
% 5.02/5.31 = ( ( P @ A )
% 5.02/5.31 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Ball_set_replicate
% 5.02/5.31 thf(fact_4581_Ball__set__replicate,axiom,
% 5.02/5.31 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.02/5.31 ( ( ! [X: vEBT_VEBT] :
% 5.02/5.31 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.02/5.31 => ( P @ X ) ) )
% 5.02/5.31 = ( ( P @ A )
% 5.02/5.31 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Ball_set_replicate
% 5.02/5.31 thf(fact_4582_Bex__set__replicate,axiom,
% 5.02/5.31 ! [N2: nat,A: int,P: int > $o] :
% 5.02/5.31 ( ( ? [X: int] :
% 5.02/5.31 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.02/5.31 & ( P @ X ) ) )
% 5.02/5.31 = ( ( P @ A )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Bex_set_replicate
% 5.02/5.31 thf(fact_4583_Bex__set__replicate,axiom,
% 5.02/5.31 ! [N2: nat,A: nat,P: nat > $o] :
% 5.02/5.31 ( ( ? [X: nat] :
% 5.02/5.31 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 5.02/5.31 & ( P @ X ) ) )
% 5.02/5.31 = ( ( P @ A )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Bex_set_replicate
% 5.02/5.31 thf(fact_4584_Bex__set__replicate,axiom,
% 5.02/5.31 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.02/5.31 ( ( ? [X: vEBT_VEBT] :
% 5.02/5.31 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.02/5.31 & ( P @ X ) ) )
% 5.02/5.31 = ( ( P @ A )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Bex_set_replicate
% 5.02/5.31 thf(fact_4585_in__set__replicate,axiom,
% 5.02/5.31 ! [X2: complex,N2: nat,Y: complex] :
% 5.02/5.31 ( ( member_complex @ X2 @ ( set_complex2 @ ( replicate_complex @ N2 @ Y ) ) )
% 5.02/5.31 = ( ( X2 = Y )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % in_set_replicate
% 5.02/5.31 thf(fact_4586_in__set__replicate,axiom,
% 5.02/5.31 ! [X2: real,N2: nat,Y: real] :
% 5.02/5.31 ( ( member_real @ X2 @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 5.02/5.31 = ( ( X2 = Y )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % in_set_replicate
% 5.02/5.31 thf(fact_4587_in__set__replicate,axiom,
% 5.02/5.31 ! [X2: set_nat,N2: nat,Y: set_nat] :
% 5.02/5.31 ( ( member_set_nat @ X2 @ ( set_set_nat2 @ ( replicate_set_nat @ N2 @ Y ) ) )
% 5.02/5.31 = ( ( X2 = Y )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % in_set_replicate
% 5.02/5.31 thf(fact_4588_in__set__replicate,axiom,
% 5.02/5.31 ! [X2: int,N2: nat,Y: int] :
% 5.02/5.31 ( ( member_int @ X2 @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 5.02/5.31 = ( ( X2 = Y )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % in_set_replicate
% 5.02/5.31 thf(fact_4589_in__set__replicate,axiom,
% 5.02/5.31 ! [X2: nat,N2: nat,Y: nat] :
% 5.02/5.31 ( ( member_nat @ X2 @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 5.02/5.31 = ( ( X2 = Y )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % in_set_replicate
% 5.02/5.31 thf(fact_4590_in__set__replicate,axiom,
% 5.02/5.31 ! [X2: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.02/5.31 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 5.02/5.31 = ( ( X2 = Y )
% 5.02/5.31 & ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % in_set_replicate
% 5.02/5.31 thf(fact_4591_nth__replicate,axiom,
% 5.02/5.31 ! [I3: nat,N2: nat,X2: nat] :
% 5.02/5.31 ( ( ord_less_nat @ I3 @ N2 )
% 5.02/5.31 => ( ( nth_nat @ ( replicate_nat @ N2 @ X2 ) @ I3 )
% 5.02/5.31 = X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % nth_replicate
% 5.02/5.31 thf(fact_4592_nth__replicate,axiom,
% 5.02/5.31 ! [I3: nat,N2: nat,X2: int] :
% 5.02/5.31 ( ( ord_less_nat @ I3 @ N2 )
% 5.02/5.31 => ( ( nth_int @ ( replicate_int @ N2 @ X2 ) @ I3 )
% 5.02/5.31 = X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % nth_replicate
% 5.02/5.31 thf(fact_4593_nth__replicate,axiom,
% 5.02/5.31 ! [I3: nat,N2: nat,X2: vEBT_VEBT] :
% 5.02/5.31 ( ( ord_less_nat @ I3 @ N2 )
% 5.02/5.31 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X2 ) @ I3 )
% 5.02/5.31 = X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % nth_replicate
% 5.02/5.31 thf(fact_4594_triangle__Suc,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( nat_triangle @ ( suc @ N2 ) )
% 5.02/5.31 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % triangle_Suc
% 5.02/5.31 thf(fact_4595_all__nat__less,axiom,
% 5.02/5.31 ! [N2: nat,P: nat > $o] :
% 5.02/5.31 ( ( ! [M6: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.02/5.31 => ( P @ M6 ) ) )
% 5.02/5.31 = ( ! [X: nat] :
% 5.02/5.31 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.31 => ( P @ X ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % all_nat_less
% 5.02/5.31 thf(fact_4596_ex__nat__less,axiom,
% 5.02/5.31 ! [N2: nat,P: nat > $o] :
% 5.02/5.31 ( ( ? [M6: nat] :
% 5.02/5.31 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.02/5.31 & ( P @ M6 ) ) )
% 5.02/5.31 = ( ? [X: nat] :
% 5.02/5.31 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.31 & ( P @ X ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % ex_nat_less
% 5.02/5.31 thf(fact_4597_replicate__length__same,axiom,
% 5.02/5.31 ! [Xs: list_VEBT_VEBT,X2: vEBT_VEBT] :
% 5.02/5.31 ( ! [X5: vEBT_VEBT] :
% 5.02/5.31 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.02/5.31 => ( X5 = X2 ) )
% 5.02/5.31 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X2 )
% 5.02/5.31 = Xs ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_length_same
% 5.02/5.31 thf(fact_4598_replicate__length__same,axiom,
% 5.02/5.31 ! [Xs: list_o,X2: $o] :
% 5.02/5.31 ( ! [X5: $o] :
% 5.02/5.31 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 5.02/5.31 => ( X5 = X2 ) )
% 5.02/5.31 => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X2 )
% 5.02/5.31 = Xs ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_length_same
% 5.02/5.31 thf(fact_4599_replicate__length__same,axiom,
% 5.02/5.31 ! [Xs: list_nat,X2: nat] :
% 5.02/5.31 ( ! [X5: nat] :
% 5.02/5.31 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 5.02/5.31 => ( X5 = X2 ) )
% 5.02/5.31 => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X2 )
% 5.02/5.31 = Xs ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_length_same
% 5.02/5.31 thf(fact_4600_replicate__length__same,axiom,
% 5.02/5.31 ! [Xs: list_int,X2: int] :
% 5.02/5.31 ( ! [X5: int] :
% 5.02/5.31 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 5.02/5.31 => ( X5 = X2 ) )
% 5.02/5.31 => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X2 )
% 5.02/5.31 = Xs ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_length_same
% 5.02/5.31 thf(fact_4601_replicate__eqI,axiom,
% 5.02/5.31 ! [Xs: list_complex,N2: nat,X2: complex] :
% 5.02/5.31 ( ( ( size_s3451745648224563538omplex @ Xs )
% 5.02/5.31 = N2 )
% 5.02/5.31 => ( ! [Y3: complex] :
% 5.02/5.31 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs ) )
% 5.02/5.31 => ( Y3 = X2 ) )
% 5.02/5.31 => ( Xs
% 5.02/5.31 = ( replicate_complex @ N2 @ X2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_eqI
% 5.02/5.31 thf(fact_4602_replicate__eqI,axiom,
% 5.02/5.31 ! [Xs: list_real,N2: nat,X2: real] :
% 5.02/5.31 ( ( ( size_size_list_real @ Xs )
% 5.02/5.31 = N2 )
% 5.02/5.31 => ( ! [Y3: real] :
% 5.02/5.31 ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 5.02/5.31 => ( Y3 = X2 ) )
% 5.02/5.31 => ( Xs
% 5.02/5.31 = ( replicate_real @ N2 @ X2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_eqI
% 5.02/5.31 thf(fact_4603_replicate__eqI,axiom,
% 5.02/5.31 ! [Xs: list_set_nat,N2: nat,X2: set_nat] :
% 5.02/5.31 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 5.02/5.31 = N2 )
% 5.02/5.31 => ( ! [Y3: set_nat] :
% 5.02/5.31 ( ( member_set_nat @ Y3 @ ( set_set_nat2 @ Xs ) )
% 5.02/5.31 => ( Y3 = X2 ) )
% 5.02/5.31 => ( Xs
% 5.02/5.31 = ( replicate_set_nat @ N2 @ X2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_eqI
% 5.02/5.31 thf(fact_4604_replicate__eqI,axiom,
% 5.02/5.31 ! [Xs: list_VEBT_VEBT,N2: nat,X2: vEBT_VEBT] :
% 5.02/5.31 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.02/5.31 = N2 )
% 5.02/5.31 => ( ! [Y3: vEBT_VEBT] :
% 5.02/5.31 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.02/5.31 => ( Y3 = X2 ) )
% 5.02/5.31 => ( Xs
% 5.02/5.31 = ( replicate_VEBT_VEBT @ N2 @ X2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_eqI
% 5.02/5.31 thf(fact_4605_replicate__eqI,axiom,
% 5.02/5.31 ! [Xs: list_o,N2: nat,X2: $o] :
% 5.02/5.31 ( ( ( size_size_list_o @ Xs )
% 5.02/5.31 = N2 )
% 5.02/5.31 => ( ! [Y3: $o] :
% 5.02/5.31 ( ( member_o @ Y3 @ ( set_o2 @ Xs ) )
% 5.02/5.31 => ( Y3 = X2 ) )
% 5.02/5.31 => ( Xs
% 5.02/5.31 = ( replicate_o @ N2 @ X2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_eqI
% 5.02/5.31 thf(fact_4606_replicate__eqI,axiom,
% 5.02/5.31 ! [Xs: list_nat,N2: nat,X2: nat] :
% 5.02/5.31 ( ( ( size_size_list_nat @ Xs )
% 5.02/5.31 = N2 )
% 5.02/5.31 => ( ! [Y3: nat] :
% 5.02/5.31 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 5.02/5.31 => ( Y3 = X2 ) )
% 5.02/5.31 => ( Xs
% 5.02/5.31 = ( replicate_nat @ N2 @ X2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_eqI
% 5.02/5.31 thf(fact_4607_replicate__eqI,axiom,
% 5.02/5.31 ! [Xs: list_int,N2: nat,X2: int] :
% 5.02/5.31 ( ( ( size_size_list_int @ Xs )
% 5.02/5.31 = N2 )
% 5.02/5.31 => ( ! [Y3: int] :
% 5.02/5.31 ( ( member_int @ Y3 @ ( set_int2 @ Xs ) )
% 5.02/5.31 => ( Y3 = X2 ) )
% 5.02/5.31 => ( Xs
% 5.02/5.31 = ( replicate_int @ N2 @ X2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % replicate_eqI
% 5.02/5.31 thf(fact_4608_atLeastatMost__psubset__iff,axiom,
% 5.02/5.31 ! [A: set_nat,B: set_nat,C: set_nat,D: set_nat] :
% 5.02/5.31 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C @ D ) )
% 5.02/5.31 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_set_nat @ C @ A )
% 5.02/5.31 & ( ord_less_eq_set_nat @ B @ D )
% 5.02/5.31 & ( ( ord_less_set_nat @ C @ A )
% 5.02/5.31 | ( ord_less_set_nat @ B @ D ) ) ) )
% 5.02/5.31 & ( ord_less_eq_set_nat @ C @ D ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_psubset_iff
% 5.02/5.31 thf(fact_4609_atLeastatMost__psubset__iff,axiom,
% 5.02/5.31 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.02/5.31 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.02/5.31 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_rat @ C @ A )
% 5.02/5.31 & ( ord_less_eq_rat @ B @ D )
% 5.02/5.31 & ( ( ord_less_rat @ C @ A )
% 5.02/5.31 | ( ord_less_rat @ B @ D ) ) ) )
% 5.02/5.31 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_psubset_iff
% 5.02/5.31 thf(fact_4610_atLeastatMost__psubset__iff,axiom,
% 5.02/5.31 ! [A: num,B: num,C: num,D: num] :
% 5.02/5.31 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.02/5.31 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_num @ C @ A )
% 5.02/5.31 & ( ord_less_eq_num @ B @ D )
% 5.02/5.31 & ( ( ord_less_num @ C @ A )
% 5.02/5.31 | ( ord_less_num @ B @ D ) ) ) )
% 5.02/5.31 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_psubset_iff
% 5.02/5.31 thf(fact_4611_atLeastatMost__psubset__iff,axiom,
% 5.02/5.31 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.02/5.31 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.02/5.31 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_nat @ C @ A )
% 5.02/5.31 & ( ord_less_eq_nat @ B @ D )
% 5.02/5.31 & ( ( ord_less_nat @ C @ A )
% 5.02/5.31 | ( ord_less_nat @ B @ D ) ) ) )
% 5.02/5.31 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_psubset_iff
% 5.02/5.31 thf(fact_4612_atLeastatMost__psubset__iff,axiom,
% 5.02/5.31 ! [A: int,B: int,C: int,D: int] :
% 5.02/5.31 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.02/5.31 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_int @ C @ A )
% 5.02/5.31 & ( ord_less_eq_int @ B @ D )
% 5.02/5.31 & ( ( ord_less_int @ C @ A )
% 5.02/5.31 | ( ord_less_int @ B @ D ) ) ) )
% 5.02/5.31 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_psubset_iff
% 5.02/5.31 thf(fact_4613_atLeastatMost__psubset__iff,axiom,
% 5.02/5.31 ! [A: real,B: real,C: real,D: real] :
% 5.02/5.31 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.02/5.31 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.02/5.31 | ( ( ord_less_eq_real @ C @ A )
% 5.02/5.31 & ( ord_less_eq_real @ B @ D )
% 5.02/5.31 & ( ( ord_less_real @ C @ A )
% 5.02/5.31 | ( ord_less_real @ B @ D ) ) ) )
% 5.02/5.31 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % atLeastatMost_psubset_iff
% 5.02/5.31 thf(fact_4614_vebt__buildup_Osimps_I3_J,axiom,
% 5.02/5.31 ! [Va2: nat] :
% 5.02/5.31 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.02/5.31 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.02/5.31 = ( 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 ) ) ) ) ) ) )
% 5.02/5.31 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.02/5.31 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va2 ) ) )
% 5.02/5.31 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % vebt_buildup.simps(3)
% 5.02/5.31 thf(fact_4615_signed__take__bit__rec,axiom,
% 5.02/5.31 ( bit_ri6519982836138164636nteger
% 5.02/5.31 = ( ^ [N3: nat,A5: code_integer] : ( if_Code_integer @ ( N3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % signed_take_bit_rec
% 5.02/5.31 thf(fact_4616_signed__take__bit__rec,axiom,
% 5.02/5.31 ( bit_ri631733984087533419it_int
% 5.02/5.31 = ( ^ [N3: nat,A5: int] : ( if_int @ ( N3 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % signed_take_bit_rec
% 5.02/5.31 thf(fact_4617_concat__bit__Suc,axiom,
% 5.02/5.31 ! [N2: nat,K: int,L: int] :
% 5.02/5.31 ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L )
% 5.02/5.31 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % concat_bit_Suc
% 5.02/5.31 thf(fact_4618_vebt__buildup_Opelims,axiom,
% 5.02/5.31 ! [X2: nat,Y: vEBT_VEBT] :
% 5.02/5.31 ( ( ( vEBT_vebt_buildup @ X2 )
% 5.02/5.31 = Y )
% 5.02/5.31 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X2 )
% 5.02/5.31 => ( ( ( X2 = zero_zero_nat )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( vEBT_Leaf @ $false @ $false ) )
% 5.02/5.31 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.02/5.31 => ( ( ( X2
% 5.02/5.31 = ( suc @ zero_zero_nat ) )
% 5.02/5.31 => ( ( Y
% 5.02/5.31 = ( vEBT_Leaf @ $false @ $false ) )
% 5.02/5.31 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.02/5.31 => ~ ! [Va: nat] :
% 5.02/5.31 ( ( X2
% 5.02/5.31 = ( suc @ ( suc @ Va ) ) )
% 5.02/5.31 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.02/5.31 => ( Y
% 5.02/5.31 = ( 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 ) ) ) ) ) ) )
% 5.02/5.31 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.02/5.31 => ( Y
% 5.02/5.31 = ( 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 ) ) ) ) ) ) ) ) )
% 5.02/5.31 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % vebt_buildup.pelims
% 5.02/5.31 thf(fact_4619_flip__bit__0,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.02/5.31 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % flip_bit_0
% 5.02/5.31 thf(fact_4620_flip__bit__0,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.02/5.31 = ( 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 ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % flip_bit_0
% 5.02/5.31 thf(fact_4621_flip__bit__0,axiom,
% 5.02/5.31 ! [A: nat] :
% 5.02/5.31 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.02/5.31 = ( 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 ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % flip_bit_0
% 5.02/5.31 thf(fact_4622_set__decode__0,axiom,
% 5.02/5.31 ! [X2: nat] :
% 5.02/5.31 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X2 ) )
% 5.02/5.31 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % set_decode_0
% 5.02/5.31 thf(fact_4623_set__decode__Suc,axiom,
% 5.02/5.31 ! [N2: nat,X2: nat] :
% 5.02/5.31 ( ( member_nat @ ( suc @ N2 ) @ ( nat_set_decode @ X2 ) )
% 5.02/5.31 = ( member_nat @ N2 @ ( nat_set_decode @ ( divide_divide_nat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % set_decode_Suc
% 5.02/5.31 thf(fact_4624_diff__shunt__var,axiom,
% 5.02/5.31 ! [X2: set_int,Y: set_int] :
% 5.02/5.31 ( ( ( minus_minus_set_int @ X2 @ Y )
% 5.02/5.31 = bot_bot_set_int )
% 5.02/5.31 = ( ord_less_eq_set_int @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_shunt_var
% 5.02/5.31 thf(fact_4625_diff__shunt__var,axiom,
% 5.02/5.31 ! [X2: set_real,Y: set_real] :
% 5.02/5.31 ( ( ( minus_minus_set_real @ X2 @ Y )
% 5.02/5.31 = bot_bot_set_real )
% 5.02/5.31 = ( ord_less_eq_set_real @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_shunt_var
% 5.02/5.31 thf(fact_4626_diff__shunt__var,axiom,
% 5.02/5.31 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.31 ( ( ( minus_minus_set_nat @ X2 @ Y )
% 5.02/5.31 = bot_bot_set_nat )
% 5.02/5.31 = ( ord_less_eq_set_nat @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_shunt_var
% 5.02/5.31 thf(fact_4627_neg__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ( uminus_uminus_real @ A )
% 5.02/5.31 = ( uminus_uminus_real @ B ) )
% 5.02/5.31 = ( A = B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_iff_equal
% 5.02/5.31 thf(fact_4628_neg__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ( uminus_uminus_int @ A )
% 5.02/5.31 = ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( A = B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_iff_equal
% 5.02/5.31 thf(fact_4629_neg__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( ( uminus1482373934393186551omplex @ A )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.31 = ( A = B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_iff_equal
% 5.02/5.31 thf(fact_4630_neg__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ( uminus_uminus_rat @ A )
% 5.02/5.31 = ( uminus_uminus_rat @ B ) )
% 5.02/5.31 = ( A = B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_iff_equal
% 5.02/5.31 thf(fact_4631_neg__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( ( uminus1351360451143612070nteger @ A )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( A = B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_iff_equal
% 5.02/5.31 thf(fact_4632_add_Oinverse__inverse,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_inverse
% 5.02/5.31 thf(fact_4633_add_Oinverse__inverse,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_inverse
% 5.02/5.31 thf(fact_4634_add_Oinverse__inverse,axiom,
% 5.02/5.31 ! [A: complex] :
% 5.02/5.31 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_inverse
% 5.02/5.31 thf(fact_4635_add_Oinverse__inverse,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_inverse
% 5.02/5.31 thf(fact_4636_add_Oinverse__inverse,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_inverse
% 5.02/5.31 thf(fact_4637_Compl__subset__Compl__iff,axiom,
% 5.02/5.31 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ ( uminus5710092332889474511et_nat @ B4 ) )
% 5.02/5.31 = ( ord_less_eq_set_nat @ B4 @ A3 ) ) ).
% 5.02/5.31
% 5.02/5.31 % Compl_subset_Compl_iff
% 5.02/5.31 thf(fact_4638_Compl__anti__mono,axiom,
% 5.02/5.31 ! [A3: set_nat,B4: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.31 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ B4 ) @ ( uminus5710092332889474511et_nat @ A3 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Compl_anti_mono
% 5.02/5.31 thf(fact_4639_compl__le__compl__iff,axiom,
% 5.02/5.31 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 5.02/5.31 = ( ord_less_eq_set_nat @ Y @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % compl_le_compl_iff
% 5.02/5.31 thf(fact_4640_neg__le__iff__le,axiom,
% 5.02/5.31 ! [B: real,A: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_le_iff_le
% 5.02/5.31 thf(fact_4641_neg__le__iff__le,axiom,
% 5.02/5.31 ! [B: code_integer,A: code_integer] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_le_iff_le
% 5.02/5.31 thf(fact_4642_neg__le__iff__le,axiom,
% 5.02/5.31 ! [B: rat,A: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_le_iff_le
% 5.02/5.31 thf(fact_4643_neg__le__iff__le,axiom,
% 5.02/5.31 ! [B: int,A: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.02/5.31 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_le_iff_le
% 5.02/5.31 thf(fact_4644_add_Oinverse__neutral,axiom,
% 5.02/5.31 ( ( uminus_uminus_real @ zero_zero_real )
% 5.02/5.31 = zero_zero_real ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_neutral
% 5.02/5.31 thf(fact_4645_add_Oinverse__neutral,axiom,
% 5.02/5.31 ( ( uminus_uminus_int @ zero_zero_int )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_neutral
% 5.02/5.31 thf(fact_4646_add_Oinverse__neutral,axiom,
% 5.02/5.31 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.02/5.31 = zero_zero_complex ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_neutral
% 5.02/5.31 thf(fact_4647_add_Oinverse__neutral,axiom,
% 5.02/5.31 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.02/5.31 = zero_zero_rat ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_neutral
% 5.02/5.31 thf(fact_4648_add_Oinverse__neutral,axiom,
% 5.02/5.31 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % add.inverse_neutral
% 5.02/5.31 thf(fact_4649_neg__0__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( zero_zero_real
% 5.02/5.31 = ( uminus_uminus_real @ A ) )
% 5.02/5.31 = ( zero_zero_real = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_equal_iff_equal
% 5.02/5.31 thf(fact_4650_neg__0__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( zero_zero_int
% 5.02/5.31 = ( uminus_uminus_int @ A ) )
% 5.02/5.31 = ( zero_zero_int = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_equal_iff_equal
% 5.02/5.31 thf(fact_4651_neg__0__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: complex] :
% 5.02/5.31 ( ( zero_zero_complex
% 5.02/5.31 = ( uminus1482373934393186551omplex @ A ) )
% 5.02/5.31 = ( zero_zero_complex = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_equal_iff_equal
% 5.02/5.31 thf(fact_4652_neg__0__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( zero_zero_rat
% 5.02/5.31 = ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = ( zero_zero_rat = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_equal_iff_equal
% 5.02/5.31 thf(fact_4653_neg__0__equal__iff__equal,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( zero_z3403309356797280102nteger
% 5.02/5.31 = ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_equal_iff_equal
% 5.02/5.31 thf(fact_4654_neg__equal__0__iff__equal,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ( uminus_uminus_real @ A )
% 5.02/5.31 = zero_zero_real )
% 5.02/5.31 = ( A = zero_zero_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_0_iff_equal
% 5.02/5.31 thf(fact_4655_neg__equal__0__iff__equal,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ( uminus_uminus_int @ A )
% 5.02/5.31 = zero_zero_int )
% 5.02/5.31 = ( A = zero_zero_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_0_iff_equal
% 5.02/5.31 thf(fact_4656_neg__equal__0__iff__equal,axiom,
% 5.02/5.31 ! [A: complex] :
% 5.02/5.31 ( ( ( uminus1482373934393186551omplex @ A )
% 5.02/5.31 = zero_zero_complex )
% 5.02/5.31 = ( A = zero_zero_complex ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_0_iff_equal
% 5.02/5.31 thf(fact_4657_neg__equal__0__iff__equal,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ( uminus_uminus_rat @ A )
% 5.02/5.31 = zero_zero_rat )
% 5.02/5.31 = ( A = zero_zero_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_0_iff_equal
% 5.02/5.31 thf(fact_4658_neg__equal__0__iff__equal,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ( uminus1351360451143612070nteger @ A )
% 5.02/5.31 = zero_z3403309356797280102nteger )
% 5.02/5.31 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_0_iff_equal
% 5.02/5.31 thf(fact_4659_equal__neg__zero,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus_uminus_real @ A ) )
% 5.02/5.31 = ( A = zero_zero_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % equal_neg_zero
% 5.02/5.31 thf(fact_4660_equal__neg__zero,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus_uminus_int @ A ) )
% 5.02/5.31 = ( A = zero_zero_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % equal_neg_zero
% 5.02/5.31 thf(fact_4661_equal__neg__zero,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = ( A = zero_zero_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % equal_neg_zero
% 5.02/5.31 thf(fact_4662_equal__neg__zero,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.31
% 5.02/5.31 % equal_neg_zero
% 5.02/5.31 thf(fact_4663_neg__equal__zero,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ( uminus_uminus_real @ A )
% 5.02/5.31 = A )
% 5.02/5.31 = ( A = zero_zero_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_zero
% 5.02/5.31 thf(fact_4664_neg__equal__zero,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ( uminus_uminus_int @ A )
% 5.02/5.31 = A )
% 5.02/5.31 = ( A = zero_zero_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_zero
% 5.02/5.31 thf(fact_4665_neg__equal__zero,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ( uminus_uminus_rat @ A )
% 5.02/5.31 = A )
% 5.02/5.31 = ( A = zero_zero_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_zero
% 5.02/5.31 thf(fact_4666_neg__equal__zero,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ( uminus1351360451143612070nteger @ A )
% 5.02/5.31 = A )
% 5.02/5.31 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_equal_zero
% 5.02/5.31 thf(fact_4667_neg__less__iff__less,axiom,
% 5.02/5.31 ! [B: real,A: real] :
% 5.02/5.31 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = ( ord_less_real @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_iff_less
% 5.02/5.31 thf(fact_4668_neg__less__iff__less,axiom,
% 5.02/5.31 ! [B: int,A: int] :
% 5.02/5.31 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.02/5.31 = ( ord_less_int @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_iff_less
% 5.02/5.31 thf(fact_4669_neg__less__iff__less,axiom,
% 5.02/5.31 ! [B: rat,A: rat] :
% 5.02/5.31 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = ( ord_less_rat @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_iff_less
% 5.02/5.31 thf(fact_4670_neg__less__iff__less,axiom,
% 5.02/5.31 ! [B: code_integer,A: code_integer] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_iff_less
% 5.02/5.31 thf(fact_4671_neg__numeral__eq__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( M = N2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_eq_iff
% 5.02/5.31 thf(fact_4672_neg__numeral__eq__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( M = N2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_eq_iff
% 5.02/5.31 thf(fact_4673_neg__numeral__eq__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.02/5.31 = ( M = N2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_eq_iff
% 5.02/5.31 thf(fact_4674_neg__numeral__eq__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( M = N2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_eq_iff
% 5.02/5.31 thf(fact_4675_neg__numeral__eq__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( M = N2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_eq_iff
% 5.02/5.31 thf(fact_4676_mult__minus__right,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_right
% 5.02/5.31 thf(fact_4677_mult__minus__right,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_right
% 5.02/5.31 thf(fact_4678_mult__minus__right,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_right
% 5.02/5.31 thf(fact_4679_mult__minus__right,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_right
% 5.02/5.31 thf(fact_4680_mult__minus__right,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_right
% 5.02/5.31 thf(fact_4681_minus__mult__minus,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.02/5.31 = ( times_times_real @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_mult_minus
% 5.02/5.31 thf(fact_4682_minus__mult__minus,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( times_times_int @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_mult_minus
% 5.02/5.31 thf(fact_4683_minus__mult__minus,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.31 = ( times_times_complex @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_mult_minus
% 5.02/5.31 thf(fact_4684_minus__mult__minus,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.02/5.31 = ( times_times_rat @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_mult_minus
% 5.02/5.31 thf(fact_4685_minus__mult__minus,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_mult_minus
% 5.02/5.31 thf(fact_4686_mult__minus__left,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.02/5.31 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_left
% 5.02/5.31 thf(fact_4687_mult__minus__left,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.31 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_left
% 5.02/5.31 thf(fact_4688_mult__minus__left,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_left
% 5.02/5.31 thf(fact_4689_mult__minus__left,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.02/5.31 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_left
% 5.02/5.31 thf(fact_4690_mult__minus__left,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus_left
% 5.02/5.31 thf(fact_4691_add__minus__cancel,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % add_minus_cancel
% 5.02/5.31 thf(fact_4692_add__minus__cancel,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % add_minus_cancel
% 5.02/5.31 thf(fact_4693_add__minus__cancel,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % add_minus_cancel
% 5.02/5.31 thf(fact_4694_add__minus__cancel,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % add_minus_cancel
% 5.02/5.31 thf(fact_4695_add__minus__cancel,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % add_minus_cancel
% 5.02/5.31 thf(fact_4696_minus__add__cancel,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_cancel
% 5.02/5.31 thf(fact_4697_minus__add__cancel,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_cancel
% 5.02/5.31 thf(fact_4698_minus__add__cancel,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_cancel
% 5.02/5.31 thf(fact_4699_minus__add__cancel,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_cancel
% 5.02/5.31 thf(fact_4700_minus__add__cancel,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.02/5.31 = B ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_cancel
% 5.02/5.31 thf(fact_4701_minus__add__distrib,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.02/5.31 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_distrib
% 5.02/5.31 thf(fact_4702_minus__add__distrib,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.02/5.31 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_distrib
% 5.02/5.31 thf(fact_4703_minus__add__distrib,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.02/5.31 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_distrib
% 5.02/5.31 thf(fact_4704_minus__add__distrib,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.02/5.31 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_distrib
% 5.02/5.31 thf(fact_4705_minus__add__distrib,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.02/5.31 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_add_distrib
% 5.02/5.31 thf(fact_4706_minus__diff__eq,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.02/5.31 = ( minus_minus_real @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_diff_eq
% 5.02/5.31 thf(fact_4707_minus__diff__eq,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.02/5.31 = ( minus_minus_int @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_diff_eq
% 5.02/5.31 thf(fact_4708_minus__diff__eq,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.02/5.31 = ( minus_minus_complex @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_diff_eq
% 5.02/5.31 thf(fact_4709_minus__diff__eq,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.02/5.31 = ( minus_minus_rat @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_diff_eq
% 5.02/5.31 thf(fact_4710_minus__diff__eq,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.02/5.31 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_diff_eq
% 5.02/5.31 thf(fact_4711_div__minus__minus,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( divide_divide_int @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % div_minus_minus
% 5.02/5.31 thf(fact_4712_div__minus__minus,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % div_minus_minus
% 5.02/5.31 thf(fact_4713_minus__dvd__iff,axiom,
% 5.02/5.31 ! [X2: real,Y: real] :
% 5.02/5.31 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X2 ) @ Y )
% 5.02/5.31 = ( dvd_dvd_real @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_dvd_iff
% 5.02/5.31 thf(fact_4714_minus__dvd__iff,axiom,
% 5.02/5.31 ! [X2: int,Y: int] :
% 5.02/5.31 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X2 ) @ Y )
% 5.02/5.31 = ( dvd_dvd_int @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_dvd_iff
% 5.02/5.31 thf(fact_4715_minus__dvd__iff,axiom,
% 5.02/5.31 ! [X2: complex,Y: complex] :
% 5.02/5.31 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y )
% 5.02/5.31 = ( dvd_dvd_complex @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_dvd_iff
% 5.02/5.31 thf(fact_4716_minus__dvd__iff,axiom,
% 5.02/5.31 ! [X2: rat,Y: rat] :
% 5.02/5.31 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X2 ) @ Y )
% 5.02/5.31 = ( dvd_dvd_rat @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_dvd_iff
% 5.02/5.31 thf(fact_4717_minus__dvd__iff,axiom,
% 5.02/5.31 ! [X2: code_integer,Y: code_integer] :
% 5.02/5.31 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X2 ) @ Y )
% 5.02/5.31 = ( dvd_dvd_Code_integer @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_dvd_iff
% 5.02/5.31 thf(fact_4718_dvd__minus__iff,axiom,
% 5.02/5.31 ! [X2: real,Y: real] :
% 5.02/5.31 ( ( dvd_dvd_real @ X2 @ ( uminus_uminus_real @ Y ) )
% 5.02/5.31 = ( dvd_dvd_real @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % dvd_minus_iff
% 5.02/5.31 thf(fact_4719_dvd__minus__iff,axiom,
% 5.02/5.31 ! [X2: int,Y: int] :
% 5.02/5.31 ( ( dvd_dvd_int @ X2 @ ( uminus_uminus_int @ Y ) )
% 5.02/5.31 = ( dvd_dvd_int @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % dvd_minus_iff
% 5.02/5.31 thf(fact_4720_dvd__minus__iff,axiom,
% 5.02/5.31 ! [X2: complex,Y: complex] :
% 5.02/5.31 ( ( dvd_dvd_complex @ X2 @ ( uminus1482373934393186551omplex @ Y ) )
% 5.02/5.31 = ( dvd_dvd_complex @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % dvd_minus_iff
% 5.02/5.31 thf(fact_4721_dvd__minus__iff,axiom,
% 5.02/5.31 ! [X2: rat,Y: rat] :
% 5.02/5.31 ( ( dvd_dvd_rat @ X2 @ ( uminus_uminus_rat @ Y ) )
% 5.02/5.31 = ( dvd_dvd_rat @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % dvd_minus_iff
% 5.02/5.31 thf(fact_4722_dvd__minus__iff,axiom,
% 5.02/5.31 ! [X2: code_integer,Y: code_integer] :
% 5.02/5.31 ( ( dvd_dvd_Code_integer @ X2 @ ( uminus1351360451143612070nteger @ Y ) )
% 5.02/5.31 = ( dvd_dvd_Code_integer @ X2 @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % dvd_minus_iff
% 5.02/5.31 thf(fact_4723_mod__minus__minus,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mod_minus_minus
% 5.02/5.31 thf(fact_4724_mod__minus__minus,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mod_minus_minus
% 5.02/5.31 thf(fact_4725_of__bool__less__eq__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.02/5.31 = ( P
% 5.02/5.31 => Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_eq_iff
% 5.02/5.31 thf(fact_4726_of__bool__less__eq__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.02/5.31 = ( P
% 5.02/5.31 => Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_eq_iff
% 5.02/5.31 thf(fact_4727_of__bool__less__eq__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.02/5.31 = ( P
% 5.02/5.31 => Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_eq_iff
% 5.02/5.31 thf(fact_4728_of__bool__less__eq__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.02/5.31 = ( P
% 5.02/5.31 => Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_eq_iff
% 5.02/5.31 thf(fact_4729_of__bool__eq_I1_J,axiom,
% 5.02/5.31 ( ( zero_n1201886186963655149omplex @ $false )
% 5.02/5.31 = zero_zero_complex ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(1)
% 5.02/5.31 thf(fact_4730_of__bool__eq_I1_J,axiom,
% 5.02/5.31 ( ( zero_n3304061248610475627l_real @ $false )
% 5.02/5.31 = zero_zero_real ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(1)
% 5.02/5.31 thf(fact_4731_of__bool__eq_I1_J,axiom,
% 5.02/5.31 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.02/5.31 = zero_zero_rat ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(1)
% 5.02/5.31 thf(fact_4732_of__bool__eq_I1_J,axiom,
% 5.02/5.31 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.02/5.31 = zero_zero_nat ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(1)
% 5.02/5.31 thf(fact_4733_of__bool__eq_I1_J,axiom,
% 5.02/5.31 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(1)
% 5.02/5.31 thf(fact_4734_of__bool__eq_I1_J,axiom,
% 5.02/5.31 ( ( zero_n356916108424825756nteger @ $false )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(1)
% 5.02/5.31 thf(fact_4735_of__bool__eq__0__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.02/5.31 = zero_zero_complex )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_0_iff
% 5.02/5.31 thf(fact_4736_of__bool__eq__0__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.02/5.31 = zero_zero_real )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_0_iff
% 5.02/5.31 thf(fact_4737_of__bool__eq__0__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.02/5.31 = zero_zero_rat )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_0_iff
% 5.02/5.31 thf(fact_4738_of__bool__eq__0__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.02/5.31 = zero_zero_nat )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_0_iff
% 5.02/5.31 thf(fact_4739_of__bool__eq__0__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.02/5.31 = zero_zero_int )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_0_iff
% 5.02/5.31 thf(fact_4740_of__bool__eq__0__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n356916108424825756nteger @ P )
% 5.02/5.31 = zero_z3403309356797280102nteger )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_0_iff
% 5.02/5.31 thf(fact_4741_real__add__minus__iff,axiom,
% 5.02/5.31 ! [X2: real,A: real] :
% 5.02/5.31 ( ( ( plus_plus_real @ X2 @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = zero_zero_real )
% 5.02/5.31 = ( X2 = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % real_add_minus_iff
% 5.02/5.31 thf(fact_4742_of__bool__less__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.02/5.31 = ( ~ P
% 5.02/5.31 & Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_iff
% 5.02/5.31 thf(fact_4743_of__bool__less__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.02/5.31 = ( ~ P
% 5.02/5.31 & Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_iff
% 5.02/5.31 thf(fact_4744_of__bool__less__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.02/5.31 = ( ~ P
% 5.02/5.31 & Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_iff
% 5.02/5.31 thf(fact_4745_of__bool__less__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.02/5.31 = ( ~ P
% 5.02/5.31 & Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_iff
% 5.02/5.31 thf(fact_4746_of__bool__less__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.02/5.31 = ( ~ P
% 5.02/5.31 & Q ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_iff
% 5.02/5.31 thf(fact_4747_of__bool__eq_I2_J,axiom,
% 5.02/5.31 ( ( zero_n1201886186963655149omplex @ $true )
% 5.02/5.31 = one_one_complex ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(2)
% 5.02/5.31 thf(fact_4748_of__bool__eq_I2_J,axiom,
% 5.02/5.31 ( ( zero_n3304061248610475627l_real @ $true )
% 5.02/5.31 = one_one_real ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(2)
% 5.02/5.31 thf(fact_4749_of__bool__eq_I2_J,axiom,
% 5.02/5.31 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.02/5.31 = one_one_rat ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(2)
% 5.02/5.31 thf(fact_4750_of__bool__eq_I2_J,axiom,
% 5.02/5.31 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.02/5.31 = one_one_nat ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(2)
% 5.02/5.31 thf(fact_4751_of__bool__eq_I2_J,axiom,
% 5.02/5.31 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.02/5.31 = one_one_int ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(2)
% 5.02/5.31 thf(fact_4752_of__bool__eq_I2_J,axiom,
% 5.02/5.31 ( ( zero_n356916108424825756nteger @ $true )
% 5.02/5.31 = one_one_Code_integer ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq(2)
% 5.02/5.31 thf(fact_4753_of__bool__eq__1__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.02/5.31 = one_one_complex )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_1_iff
% 5.02/5.31 thf(fact_4754_of__bool__eq__1__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.02/5.31 = one_one_real )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_1_iff
% 5.02/5.31 thf(fact_4755_of__bool__eq__1__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.02/5.31 = one_one_rat )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_1_iff
% 5.02/5.31 thf(fact_4756_of__bool__eq__1__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.02/5.31 = one_one_nat )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_1_iff
% 5.02/5.31 thf(fact_4757_of__bool__eq__1__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.02/5.31 = one_one_int )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_1_iff
% 5.02/5.31 thf(fact_4758_of__bool__eq__1__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ( zero_n356916108424825756nteger @ P )
% 5.02/5.31 = one_one_Code_integer )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_1_iff
% 5.02/5.31 thf(fact_4759_of__bool__or__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( zero_n2687167440665602831ol_nat
% 5.02/5.31 @ ( P
% 5.02/5.31 | Q ) )
% 5.02/5.31 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_or_iff
% 5.02/5.31 thf(fact_4760_of__bool__or__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( zero_n2684676970156552555ol_int
% 5.02/5.31 @ ( P
% 5.02/5.31 | Q ) )
% 5.02/5.31 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_or_iff
% 5.02/5.31 thf(fact_4761_of__bool__or__iff,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( zero_n356916108424825756nteger
% 5.02/5.31 @ ( P
% 5.02/5.31 | Q ) )
% 5.02/5.31 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_or_iff
% 5.02/5.31 thf(fact_4762_concat__bit__0,axiom,
% 5.02/5.31 ! [K: int,L: int] :
% 5.02/5.31 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 5.02/5.31 = L ) ).
% 5.02/5.31
% 5.02/5.31 % concat_bit_0
% 5.02/5.31 thf(fact_4763_neg__0__le__iff__le,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_le_iff_le
% 5.02/5.31 thf(fact_4764_neg__0__le__iff__le,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_le_iff_le
% 5.02/5.31 thf(fact_4765_neg__0__le__iff__le,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_le_iff_le
% 5.02/5.31 thf(fact_4766_neg__0__le__iff__le,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.02/5.31 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_le_iff_le
% 5.02/5.31 thf(fact_4767_neg__le__0__iff__le,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.02/5.31 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_le_0_iff_le
% 5.02/5.31 thf(fact_4768_neg__le__0__iff__le,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.02/5.31 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_le_0_iff_le
% 5.02/5.31 thf(fact_4769_neg__le__0__iff__le,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.02/5.31 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_le_0_iff_le
% 5.02/5.31 thf(fact_4770_neg__le__0__iff__le,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.02/5.31 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_le_0_iff_le
% 5.02/5.31 thf(fact_4771_less__eq__neg__nonpos,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_eq_neg_nonpos
% 5.02/5.31 thf(fact_4772_less__eq__neg__nonpos,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_eq_neg_nonpos
% 5.02/5.31 thf(fact_4773_less__eq__neg__nonpos,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_eq_neg_nonpos
% 5.02/5.31 thf(fact_4774_less__eq__neg__nonpos,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.02/5.31 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_eq_neg_nonpos
% 5.02/5.31 thf(fact_4775_neg__less__eq__nonneg,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.02/5.31 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_eq_nonneg
% 5.02/5.31 thf(fact_4776_neg__less__eq__nonneg,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.02/5.31 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_eq_nonneg
% 5.02/5.31 thf(fact_4777_neg__less__eq__nonneg,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.02/5.31 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_eq_nonneg
% 5.02/5.31 thf(fact_4778_neg__less__eq__nonneg,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.02/5.31 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_eq_nonneg
% 5.02/5.31 thf(fact_4779_less__neg__neg,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_neg_neg
% 5.02/5.31 thf(fact_4780_less__neg__neg,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.02/5.31 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_neg_neg
% 5.02/5.31 thf(fact_4781_less__neg__neg,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_neg_neg
% 5.02/5.31 thf(fact_4782_less__neg__neg,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_neg_neg
% 5.02/5.31 thf(fact_4783_neg__less__pos,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.02/5.31 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_pos
% 5.02/5.31 thf(fact_4784_neg__less__pos,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.02/5.31 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_pos
% 5.02/5.31 thf(fact_4785_neg__less__pos,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.02/5.31 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_pos
% 5.02/5.31 thf(fact_4786_neg__less__pos,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.02/5.31 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_pos
% 5.02/5.31 thf(fact_4787_neg__0__less__iff__less,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_less_iff_less
% 5.02/5.31 thf(fact_4788_neg__0__less__iff__less,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.02/5.31 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_less_iff_less
% 5.02/5.31 thf(fact_4789_neg__0__less__iff__less,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_less_iff_less
% 5.02/5.31 thf(fact_4790_neg__0__less__iff__less,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_0_less_iff_less
% 5.02/5.31 thf(fact_4791_neg__less__0__iff__less,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.02/5.31 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_0_iff_less
% 5.02/5.31 thf(fact_4792_neg__less__0__iff__less,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.02/5.31 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_0_iff_less
% 5.02/5.31 thf(fact_4793_neg__less__0__iff__less,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.02/5.31 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_0_iff_less
% 5.02/5.31 thf(fact_4794_neg__less__0__iff__less,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.02/5.31 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_less_0_iff_less
% 5.02/5.31 thf(fact_4795_add_Oright__inverse,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.02/5.31 = zero_zero_real ) ).
% 5.02/5.31
% 5.02/5.31 % add.right_inverse
% 5.02/5.31 thf(fact_4796_add_Oright__inverse,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % add.right_inverse
% 5.02/5.31 thf(fact_4797_add_Oright__inverse,axiom,
% 5.02/5.31 ! [A: complex] :
% 5.02/5.31 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.02/5.31 = zero_zero_complex ) ).
% 5.02/5.31
% 5.02/5.31 % add.right_inverse
% 5.02/5.31 thf(fact_4798_add_Oright__inverse,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.02/5.31 = zero_zero_rat ) ).
% 5.02/5.31
% 5.02/5.31 % add.right_inverse
% 5.02/5.31 thf(fact_4799_add_Oright__inverse,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % add.right_inverse
% 5.02/5.31 thf(fact_4800_ab__left__minus,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.02/5.31 = zero_zero_real ) ).
% 5.02/5.31
% 5.02/5.31 % ab_left_minus
% 5.02/5.31 thf(fact_4801_ab__left__minus,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % ab_left_minus
% 5.02/5.31 thf(fact_4802_ab__left__minus,axiom,
% 5.02/5.31 ! [A: complex] :
% 5.02/5.31 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.02/5.31 = zero_zero_complex ) ).
% 5.02/5.31
% 5.02/5.31 % ab_left_minus
% 5.02/5.31 thf(fact_4803_ab__left__minus,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.02/5.31 = zero_zero_rat ) ).
% 5.02/5.31
% 5.02/5.31 % ab_left_minus
% 5.02/5.31 thf(fact_4804_ab__left__minus,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % ab_left_minus
% 5.02/5.31 thf(fact_4805_verit__minus__simplify_I3_J,axiom,
% 5.02/5.31 ! [B: real] :
% 5.02/5.31 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.02/5.31 = ( uminus_uminus_real @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % verit_minus_simplify(3)
% 5.02/5.31 thf(fact_4806_verit__minus__simplify_I3_J,axiom,
% 5.02/5.31 ! [B: int] :
% 5.02/5.31 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.02/5.31 = ( uminus_uminus_int @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % verit_minus_simplify(3)
% 5.02/5.31 thf(fact_4807_verit__minus__simplify_I3_J,axiom,
% 5.02/5.31 ! [B: complex] :
% 5.02/5.31 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % verit_minus_simplify(3)
% 5.02/5.31 thf(fact_4808_verit__minus__simplify_I3_J,axiom,
% 5.02/5.31 ! [B: rat] :
% 5.02/5.31 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.02/5.31 = ( uminus_uminus_rat @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % verit_minus_simplify(3)
% 5.02/5.31 thf(fact_4809_verit__minus__simplify_I3_J,axiom,
% 5.02/5.31 ! [B: code_integer] :
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % verit_minus_simplify(3)
% 5.02/5.31 thf(fact_4810_diff__0,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.02/5.31 = ( uminus_uminus_real @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_0
% 5.02/5.31 thf(fact_4811_diff__0,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.02/5.31 = ( uminus_uminus_int @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_0
% 5.02/5.31 thf(fact_4812_diff__0,axiom,
% 5.02/5.31 ! [A: complex] :
% 5.02/5.31 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_0
% 5.02/5.31 thf(fact_4813_diff__0,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.02/5.31 = ( uminus_uminus_rat @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_0
% 5.02/5.31 thf(fact_4814_diff__0,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_0
% 5.02/5.31 thf(fact_4815_add__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4816_add__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4817_add__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4818_add__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4819_add__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4820_mult__minus1,axiom,
% 5.02/5.31 ! [Z: real] :
% 5.02/5.31 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.02/5.31 = ( uminus_uminus_real @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1
% 5.02/5.31 thf(fact_4821_mult__minus1,axiom,
% 5.02/5.31 ! [Z: int] :
% 5.02/5.31 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.02/5.31 = ( uminus_uminus_int @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1
% 5.02/5.31 thf(fact_4822_mult__minus1,axiom,
% 5.02/5.31 ! [Z: complex] :
% 5.02/5.31 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1
% 5.02/5.31 thf(fact_4823_mult__minus1,axiom,
% 5.02/5.31 ! [Z: rat] :
% 5.02/5.31 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.02/5.31 = ( uminus_uminus_rat @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1
% 5.02/5.31 thf(fact_4824_mult__minus1,axiom,
% 5.02/5.31 ! [Z: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1
% 5.02/5.31 thf(fact_4825_mult__minus1__right,axiom,
% 5.02/5.31 ! [Z: real] :
% 5.02/5.31 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = ( uminus_uminus_real @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1_right
% 5.02/5.31 thf(fact_4826_mult__minus1__right,axiom,
% 5.02/5.31 ! [Z: int] :
% 5.02/5.31 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = ( uminus_uminus_int @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1_right
% 5.02/5.31 thf(fact_4827_mult__minus1__right,axiom,
% 5.02/5.31 ! [Z: complex] :
% 5.02/5.31 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1_right
% 5.02/5.31 thf(fact_4828_mult__minus1__right,axiom,
% 5.02/5.31 ! [Z: rat] :
% 5.02/5.31 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = ( uminus_uminus_rat @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1_right
% 5.02/5.31 thf(fact_4829_mult__minus1__right,axiom,
% 5.02/5.31 ! [Z: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_minus1_right
% 5.02/5.31 thf(fact_4830_diff__minus__eq__add,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.02/5.31 = ( plus_plus_real @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_minus_eq_add
% 5.02/5.31 thf(fact_4831_diff__minus__eq__add,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( plus_plus_int @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_minus_eq_add
% 5.02/5.31 thf(fact_4832_diff__minus__eq__add,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.31 = ( plus_plus_complex @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_minus_eq_add
% 5.02/5.31 thf(fact_4833_diff__minus__eq__add,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.02/5.31 = ( plus_plus_rat @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_minus_eq_add
% 5.02/5.31 thf(fact_4834_diff__minus__eq__add,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_minus_eq_add
% 5.02/5.31 thf(fact_4835_uminus__add__conv__diff,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.02/5.31 = ( minus_minus_real @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % uminus_add_conv_diff
% 5.02/5.31 thf(fact_4836_uminus__add__conv__diff,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.31 = ( minus_minus_int @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % uminus_add_conv_diff
% 5.02/5.31 thf(fact_4837_uminus__add__conv__diff,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.02/5.31 = ( minus_minus_complex @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % uminus_add_conv_diff
% 5.02/5.31 thf(fact_4838_uminus__add__conv__diff,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.02/5.31 = ( minus_minus_rat @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % uminus_add_conv_diff
% 5.02/5.31 thf(fact_4839_uminus__add__conv__diff,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.02/5.31 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % uminus_add_conv_diff
% 5.02/5.31 thf(fact_4840_divide__minus1,axiom,
% 5.02/5.31 ! [X2: real] :
% 5.02/5.31 ( ( divide_divide_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = ( uminus_uminus_real @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_minus1
% 5.02/5.31 thf(fact_4841_divide__minus1,axiom,
% 5.02/5.31 ! [X2: complex] :
% 5.02/5.31 ( ( divide1717551699836669952omplex @ X2 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_minus1
% 5.02/5.31 thf(fact_4842_divide__minus1,axiom,
% 5.02/5.31 ! [X2: rat] :
% 5.02/5.31 ( ( divide_divide_rat @ X2 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = ( uminus_uminus_rat @ X2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_minus1
% 5.02/5.31 thf(fact_4843_div__minus1__right,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = ( uminus_uminus_int @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % div_minus1_right
% 5.02/5.31 thf(fact_4844_div__minus1__right,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % div_minus1_right
% 5.02/5.31 thf(fact_4845_minus__mod__self1,axiom,
% 5.02/5.31 ! [B: int,A: int] :
% 5.02/5.31 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.02/5.31 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_mod_self1
% 5.02/5.31 thf(fact_4846_minus__mod__self1,axiom,
% 5.02/5.31 ! [B: code_integer,A: code_integer] :
% 5.02/5.31 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.02/5.31 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_mod_self1
% 5.02/5.31 thf(fact_4847_zero__less__of__bool__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % zero_less_of_bool_iff
% 5.02/5.31 thf(fact_4848_zero__less__of__bool__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % zero_less_of_bool_iff
% 5.02/5.31 thf(fact_4849_zero__less__of__bool__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % zero_less_of_bool_iff
% 5.02/5.31 thf(fact_4850_zero__less__of__bool__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % zero_less_of_bool_iff
% 5.02/5.31 thf(fact_4851_zero__less__of__bool__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.02/5.31 = P ) ).
% 5.02/5.31
% 5.02/5.31 % zero_less_of_bool_iff
% 5.02/5.31 thf(fact_4852_of__bool__less__one__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_one_iff
% 5.02/5.31 thf(fact_4853_of__bool__less__one__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_one_iff
% 5.02/5.31 thf(fact_4854_of__bool__less__one__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_one_iff
% 5.02/5.31 thf(fact_4855_of__bool__less__one__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_one_iff
% 5.02/5.31 thf(fact_4856_of__bool__less__one__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.02/5.31 = ~ P ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_less_one_iff
% 5.02/5.31 thf(fact_4857_of__bool__not__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.02/5.31 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_not_iff
% 5.02/5.31 thf(fact_4858_of__bool__not__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.02/5.31 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_not_iff
% 5.02/5.31 thf(fact_4859_of__bool__not__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.02/5.31 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_not_iff
% 5.02/5.31 thf(fact_4860_of__bool__not__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.02/5.31 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_not_iff
% 5.02/5.31 thf(fact_4861_of__bool__not__iff,axiom,
% 5.02/5.31 ! [P: $o] :
% 5.02/5.31 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.02/5.31 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_not_iff
% 5.02/5.31 thf(fact_4862_Suc__0__mod__eq,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.02/5.31 = ( zero_n2687167440665602831ol_nat
% 5.02/5.31 @ ( N2
% 5.02/5.31 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Suc_0_mod_eq
% 5.02/5.31 thf(fact_4863_signed__take__bit__of__minus__1,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.31
% 5.02/5.31 % signed_take_bit_of_minus_1
% 5.02/5.31 thf(fact_4864_signed__take__bit__of__minus__1,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % signed_take_bit_of_minus_1
% 5.02/5.31 thf(fact_4865_concat__bit__nonnegative__iff,axiom,
% 5.02/5.31 ! [N2: nat,K: int,L: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K @ L ) )
% 5.02/5.31 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.02/5.31
% 5.02/5.31 % concat_bit_nonnegative_iff
% 5.02/5.31 thf(fact_4866_concat__bit__negative__iff,axiom,
% 5.02/5.31 ! [N2: nat,K: int,L: int] :
% 5.02/5.31 ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K @ L ) @ zero_zero_int )
% 5.02/5.31 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % concat_bit_negative_iff
% 5.02/5.31 thf(fact_4867_dbl__simps_I1_J,axiom,
% 5.02/5.31 ! [K: num] :
% 5.02/5.31 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(1)
% 5.02/5.31 thf(fact_4868_dbl__simps_I1_J,axiom,
% 5.02/5.31 ! [K: num] :
% 5.02/5.31 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(1)
% 5.02/5.31 thf(fact_4869_dbl__simps_I1_J,axiom,
% 5.02/5.31 ! [K: num] :
% 5.02/5.31 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(1)
% 5.02/5.31 thf(fact_4870_dbl__simps_I1_J,axiom,
% 5.02/5.31 ! [K: num] :
% 5.02/5.31 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(1)
% 5.02/5.31 thf(fact_4871_dbl__simps_I1_J,axiom,
% 5.02/5.31 ! [K: num] :
% 5.02/5.31 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(1)
% 5.02/5.31 thf(fact_4872_set__decode__zero,axiom,
% 5.02/5.31 ( ( nat_set_decode @ zero_zero_nat )
% 5.02/5.31 = bot_bot_set_nat ) ).
% 5.02/5.31
% 5.02/5.31 % set_decode_zero
% 5.02/5.31 thf(fact_4873_add__neg__numeral__special_I8_J,axiom,
% 5.02/5.31 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.02/5.31 = zero_zero_real ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(8)
% 5.02/5.31 thf(fact_4874_add__neg__numeral__special_I8_J,axiom,
% 5.02/5.31 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(8)
% 5.02/5.31 thf(fact_4875_add__neg__numeral__special_I8_J,axiom,
% 5.02/5.31 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.02/5.31 = zero_zero_complex ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(8)
% 5.02/5.31 thf(fact_4876_add__neg__numeral__special_I8_J,axiom,
% 5.02/5.31 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.02/5.31 = zero_zero_rat ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(8)
% 5.02/5.31 thf(fact_4877_add__neg__numeral__special_I8_J,axiom,
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(8)
% 5.02/5.31 thf(fact_4878_add__neg__numeral__special_I7_J,axiom,
% 5.02/5.31 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = zero_zero_real ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(7)
% 5.02/5.31 thf(fact_4879_add__neg__numeral__special_I7_J,axiom,
% 5.02/5.31 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(7)
% 5.02/5.31 thf(fact_4880_add__neg__numeral__special_I7_J,axiom,
% 5.02/5.31 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.31 = zero_zero_complex ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(7)
% 5.02/5.31 thf(fact_4881_add__neg__numeral__special_I7_J,axiom,
% 5.02/5.31 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = zero_zero_rat ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(7)
% 5.02/5.31 thf(fact_4882_add__neg__numeral__special_I7_J,axiom,
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(7)
% 5.02/5.31 thf(fact_4883_diff__numeral__special_I12_J,axiom,
% 5.02/5.31 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = zero_zero_real ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(12)
% 5.02/5.31 thf(fact_4884_diff__numeral__special_I12_J,axiom,
% 5.02/5.31 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(12)
% 5.02/5.31 thf(fact_4885_diff__numeral__special_I12_J,axiom,
% 5.02/5.31 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.31 = zero_zero_complex ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(12)
% 5.02/5.31 thf(fact_4886_diff__numeral__special_I12_J,axiom,
% 5.02/5.31 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = zero_zero_rat ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(12)
% 5.02/5.31 thf(fact_4887_diff__numeral__special_I12_J,axiom,
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(12)
% 5.02/5.31 thf(fact_4888_neg__one__eq__numeral__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_real @ one_one_real )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_eq_numeral_iff
% 5.02/5.31 thf(fact_4889_neg__one__eq__numeral__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_int @ one_one_int )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_eq_numeral_iff
% 5.02/5.31 thf(fact_4890_neg__one__eq__numeral__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_eq_numeral_iff
% 5.02/5.31 thf(fact_4891_neg__one__eq__numeral__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_eq_numeral_iff
% 5.02/5.31 thf(fact_4892_neg__one__eq__numeral__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_eq_numeral_iff
% 5.02/5.31 thf(fact_4893_numeral__eq__neg__one__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % numeral_eq_neg_one_iff
% 5.02/5.31 thf(fact_4894_numeral__eq__neg__one__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % numeral_eq_neg_one_iff
% 5.02/5.31 thf(fact_4895_numeral__eq__neg__one__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % numeral_eq_neg_one_iff
% 5.02/5.31 thf(fact_4896_numeral__eq__neg__one__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % numeral_eq_neg_one_iff
% 5.02/5.31 thf(fact_4897_numeral__eq__neg__one__iff,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = ( N2 = one ) ) ).
% 5.02/5.31
% 5.02/5.31 % numeral_eq_neg_one_iff
% 5.02/5.31 thf(fact_4898_left__minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat,A: real] :
% 5.02/5.31 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % left_minus_one_mult_self
% 5.02/5.31 thf(fact_4899_left__minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat,A: int] :
% 5.02/5.31 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % left_minus_one_mult_self
% 5.02/5.31 thf(fact_4900_left__minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat,A: complex] :
% 5.02/5.31 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % left_minus_one_mult_self
% 5.02/5.31 thf(fact_4901_left__minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat,A: rat] :
% 5.02/5.31 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % left_minus_one_mult_self
% 5.02/5.31 thf(fact_4902_left__minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat,A: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 5.02/5.31 = A ) ).
% 5.02/5.31
% 5.02/5.31 % left_minus_one_mult_self
% 5.02/5.31 thf(fact_4903_minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) )
% 5.02/5.31 = one_one_real ) ).
% 5.02/5.31
% 5.02/5.31 % minus_one_mult_self
% 5.02/5.31 thf(fact_4904_minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 5.02/5.31 = one_one_int ) ).
% 5.02/5.31
% 5.02/5.31 % minus_one_mult_self
% 5.02/5.31 thf(fact_4905_minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) )
% 5.02/5.31 = one_one_complex ) ).
% 5.02/5.31
% 5.02/5.31 % minus_one_mult_self
% 5.02/5.31 thf(fact_4906_minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 5.02/5.31 = one_one_rat ) ).
% 5.02/5.31
% 5.02/5.31 % minus_one_mult_self
% 5.02/5.31 thf(fact_4907_minus__one__mult__self,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 5.02/5.31 = one_one_Code_integer ) ).
% 5.02/5.31
% 5.02/5.31 % minus_one_mult_self
% 5.02/5.31 thf(fact_4908_mod__minus1__right,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % mod_minus1_right
% 5.02/5.31 thf(fact_4909_mod__minus1__right,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % mod_minus1_right
% 5.02/5.31 thf(fact_4910_max__number__of_I4_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(4)
% 5.02/5.31 thf(fact_4911_max__number__of_I4_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.02/5.31 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(4)
% 5.02/5.31 thf(fact_4912_max__number__of_I4_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(4)
% 5.02/5.31 thf(fact_4913_max__number__of_I4_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(4)
% 5.02/5.31 thf(fact_4914_max__number__of_I3_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.02/5.31 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.02/5.31 = ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.02/5.31 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(3)
% 5.02/5.31 thf(fact_4915_max__number__of_I3_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.02/5.31 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.02/5.31 = ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.02/5.31 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(3)
% 5.02/5.31 thf(fact_4916_max__number__of_I3_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.02/5.31 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.02/5.31 = ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.02/5.31 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(3)
% 5.02/5.31 thf(fact_4917_max__number__of_I3_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.02/5.31 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.02/5.31 = ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.02/5.31 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(3)
% 5.02/5.31 thf(fact_4918_max__number__of_I2_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.02/5.31 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(2)
% 5.02/5.31 thf(fact_4919_max__number__of_I2_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.02/5.31 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.02/5.31 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(2)
% 5.02/5.31 thf(fact_4920_max__number__of_I2_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.02/5.31 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(2)
% 5.02/5.31 thf(fact_4921_max__number__of_I2_J,axiom,
% 5.02/5.31 ! [U: num,V: num] :
% 5.02/5.31 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.02/5.31 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.02/5.31 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % max_number_of(2)
% 5.02/5.31 thf(fact_4922_semiring__norm_I168_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: real] :
% 5.02/5.31 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.02/5.31 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(168)
% 5.02/5.31 thf(fact_4923_semiring__norm_I168_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: int] :
% 5.02/5.31 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.02/5.31 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(168)
% 5.02/5.31 thf(fact_4924_semiring__norm_I168_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: complex] :
% 5.02/5.31 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.02/5.31 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(168)
% 5.02/5.31 thf(fact_4925_semiring__norm_I168_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: rat] :
% 5.02/5.31 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.02/5.31 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(168)
% 5.02/5.31 thf(fact_4926_semiring__norm_I168_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: code_integer] :
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.02/5.31 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(168)
% 5.02/5.31 thf(fact_4927_diff__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(2)
% 5.02/5.31 thf(fact_4928_diff__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(2)
% 5.02/5.31 thf(fact_4929_diff__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.02/5.31 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(2)
% 5.02/5.31 thf(fact_4930_diff__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(2)
% 5.02/5.31 thf(fact_4931_diff__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(2)
% 5.02/5.31 thf(fact_4932_diff__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(3)
% 5.02/5.31 thf(fact_4933_diff__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(3)
% 5.02/5.31 thf(fact_4934_diff__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(3)
% 5.02/5.31 thf(fact_4935_diff__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(3)
% 5.02/5.31 thf(fact_4936_diff__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_simps(3)
% 5.02/5.31 thf(fact_4937_mult__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4938_mult__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4939_mult__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4940_mult__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4941_mult__neg__numeral__simps_I3_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(3)
% 5.02/5.31 thf(fact_4942_mult__neg__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(2)
% 5.02/5.31 thf(fact_4943_mult__neg__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(2)
% 5.02/5.31 thf(fact_4944_mult__neg__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(2)
% 5.02/5.31 thf(fact_4945_mult__neg__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(2)
% 5.02/5.31 thf(fact_4946_mult__neg__numeral__simps_I2_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(2)
% 5.02/5.31 thf(fact_4947_mult__neg__numeral__simps_I1_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(1)
% 5.02/5.31 thf(fact_4948_mult__neg__numeral__simps_I1_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(1)
% 5.02/5.31 thf(fact_4949_mult__neg__numeral__simps_I1_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.02/5.31 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(1)
% 5.02/5.31 thf(fact_4950_mult__neg__numeral__simps_I1_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(1)
% 5.02/5.31 thf(fact_4951_mult__neg__numeral__simps_I1_J,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % mult_neg_numeral_simps(1)
% 5.02/5.31 thf(fact_4952_semiring__norm_I170_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: real] :
% 5.02/5.31 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 5.02/5.31 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(170)
% 5.02/5.31 thf(fact_4953_semiring__norm_I170_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: int] :
% 5.02/5.31 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 5.02/5.31 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(170)
% 5.02/5.31 thf(fact_4954_semiring__norm_I170_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: complex] :
% 5.02/5.31 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 5.02/5.31 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(170)
% 5.02/5.31 thf(fact_4955_semiring__norm_I170_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: rat] :
% 5.02/5.31 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 5.02/5.31 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(170)
% 5.02/5.31 thf(fact_4956_semiring__norm_I170_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 5.02/5.31 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(170)
% 5.02/5.31 thf(fact_4957_semiring__norm_I171_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: real] :
% 5.02/5.31 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(171)
% 5.02/5.31 thf(fact_4958_semiring__norm_I171_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: int] :
% 5.02/5.31 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(171)
% 5.02/5.31 thf(fact_4959_semiring__norm_I171_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: complex] :
% 5.02/5.31 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(171)
% 5.02/5.31 thf(fact_4960_semiring__norm_I171_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: rat] :
% 5.02/5.31 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(171)
% 5.02/5.31 thf(fact_4961_semiring__norm_I171_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(171)
% 5.02/5.31 thf(fact_4962_semiring__norm_I172_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: real] :
% 5.02/5.31 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(172)
% 5.02/5.31 thf(fact_4963_semiring__norm_I172_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: int] :
% 5.02/5.31 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(172)
% 5.02/5.31 thf(fact_4964_semiring__norm_I172_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: complex] :
% 5.02/5.31 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(172)
% 5.02/5.31 thf(fact_4965_semiring__norm_I172_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: rat] :
% 5.02/5.31 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(172)
% 5.02/5.31 thf(fact_4966_semiring__norm_I172_J,axiom,
% 5.02/5.31 ! [V: num,W: num,Y: code_integer] :
% 5.02/5.31 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.02/5.31 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % semiring_norm(172)
% 5.02/5.31 thf(fact_4967_neg__numeral__le__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_le_iff
% 5.02/5.31 thf(fact_4968_neg__numeral__le__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_le_iff
% 5.02/5.31 thf(fact_4969_neg__numeral__le__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_le_iff
% 5.02/5.31 thf(fact_4970_neg__numeral__le__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_le_iff
% 5.02/5.31 thf(fact_4971_neg__numeral__less__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( ord_less_num @ N2 @ M ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_less_iff
% 5.02/5.31 thf(fact_4972_neg__numeral__less__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( ord_less_num @ N2 @ M ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_less_iff
% 5.02/5.31 thf(fact_4973_neg__numeral__less__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( ord_less_num @ N2 @ M ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_less_iff
% 5.02/5.31 thf(fact_4974_neg__numeral__less__iff,axiom,
% 5.02/5.31 ! [M: num,N2: num] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( ord_less_num @ N2 @ M ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_less_iff
% 5.02/5.31 thf(fact_4975_not__neg__one__le__neg__numeral__iff,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.02/5.31 = ( M != one ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_neg_one_le_neg_numeral_iff
% 5.02/5.31 thf(fact_4976_not__neg__one__le__neg__numeral__iff,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.02/5.31 = ( M != one ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_neg_one_le_neg_numeral_iff
% 5.02/5.31 thf(fact_4977_not__neg__one__le__neg__numeral__iff,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.02/5.31 = ( M != one ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_neg_one_le_neg_numeral_iff
% 5.02/5.31 thf(fact_4978_not__neg__one__le__neg__numeral__iff,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.02/5.31 = ( M != one ) ) ).
% 5.02/5.31
% 5.02/5.31 % not_neg_one_le_neg_numeral_iff
% 5.02/5.31 thf(fact_4979_divide__le__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [B: real,W: num,A: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.02/5.31 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_le_eq_numeral1(2)
% 5.02/5.31 thf(fact_4980_divide__le__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [B: rat,W: num,A: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.02/5.31 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_le_eq_numeral1(2)
% 5.02/5.31 thf(fact_4981_le__divide__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [A: real,B: real,W: num] :
% 5.02/5.31 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.02/5.31 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_divide_eq_numeral1(2)
% 5.02/5.31 thf(fact_4982_le__divide__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [A: rat,B: rat,W: num] :
% 5.02/5.31 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.02/5.31 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_divide_eq_numeral1(2)
% 5.02/5.31 thf(fact_4983_divide__eq__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [B: real,W: num,A: real] :
% 5.02/5.31 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.31 = A )
% 5.02/5.31 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.31 != zero_zero_real )
% 5.02/5.31 => ( B
% 5.02/5.31 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.02/5.31 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.31 = zero_zero_real )
% 5.02/5.31 => ( A = zero_zero_real ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_eq_eq_numeral1(2)
% 5.02/5.31 thf(fact_4984_divide__eq__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [B: complex,W: num,A: complex] :
% 5.02/5.31 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.02/5.31 = A )
% 5.02/5.31 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.31 != zero_zero_complex )
% 5.02/5.31 => ( B
% 5.02/5.31 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.02/5.31 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.31 = zero_zero_complex )
% 5.02/5.31 => ( A = zero_zero_complex ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_eq_eq_numeral1(2)
% 5.02/5.31 thf(fact_4985_divide__eq__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [B: rat,W: num,A: rat] :
% 5.02/5.31 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.02/5.31 = A )
% 5.02/5.31 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.02/5.31 != zero_zero_rat )
% 5.02/5.31 => ( B
% 5.02/5.31 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.02/5.31 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.02/5.31 = zero_zero_rat )
% 5.02/5.31 => ( A = zero_zero_rat ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_eq_eq_numeral1(2)
% 5.02/5.31 thf(fact_4986_eq__divide__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [A: real,B: real,W: num] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.02/5.31 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.31 != zero_zero_real )
% 5.02/5.31 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.31 = B ) )
% 5.02/5.31 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.31 = zero_zero_real )
% 5.02/5.31 => ( A = zero_zero_real ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % eq_divide_eq_numeral1(2)
% 5.02/5.31 thf(fact_4987_eq__divide__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [A: complex,B: complex,W: num] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.02/5.31 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.31 != zero_zero_complex )
% 5.02/5.31 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.02/5.31 = B ) )
% 5.02/5.31 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.31 = zero_zero_complex )
% 5.02/5.31 => ( A = zero_zero_complex ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % eq_divide_eq_numeral1(2)
% 5.02/5.31 thf(fact_4988_eq__divide__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [A: rat,B: rat,W: num] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.02/5.31 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.02/5.31 != zero_zero_rat )
% 5.02/5.31 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.02/5.31 = B ) )
% 5.02/5.31 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.02/5.31 = zero_zero_rat )
% 5.02/5.31 => ( A = zero_zero_rat ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % eq_divide_eq_numeral1(2)
% 5.02/5.31 thf(fact_4989_neg__numeral__less__neg__one__iff,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = ( M != one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_less_neg_one_iff
% 5.02/5.31 thf(fact_4990_neg__numeral__less__neg__one__iff,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = ( M != one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_less_neg_one_iff
% 5.02/5.31 thf(fact_4991_neg__numeral__less__neg__one__iff,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = ( M != one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_less_neg_one_iff
% 5.02/5.31 thf(fact_4992_neg__numeral__less__neg__one__iff,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = ( M != one ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_numeral_less_neg_one_iff
% 5.02/5.31 thf(fact_4993_divide__less__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [B: real,W: num,A: real] :
% 5.02/5.31 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.02/5.31 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_less_eq_numeral1(2)
% 5.02/5.31 thf(fact_4994_divide__less__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [B: rat,W: num,A: rat] :
% 5.02/5.31 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.02/5.31 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.02/5.31
% 5.02/5.31 % divide_less_eq_numeral1(2)
% 5.02/5.31 thf(fact_4995_less__divide__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [A: real,B: real,W: num] :
% 5.02/5.31 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.02/5.31 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_divide_eq_numeral1(2)
% 5.02/5.31 thf(fact_4996_less__divide__eq__numeral1_I2_J,axiom,
% 5.02/5.31 ! [A: rat,B: rat,W: num] :
% 5.02/5.31 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.02/5.31 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_divide_eq_numeral1(2)
% 5.02/5.31 thf(fact_4997_power2__minus,axiom,
% 5.02/5.31 ! [A: real] :
% 5.02/5.31 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.31 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power2_minus
% 5.02/5.31 thf(fact_4998_power2__minus,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.31 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power2_minus
% 5.02/5.31 thf(fact_4999_power2__minus,axiom,
% 5.02/5.31 ! [A: complex] :
% 5.02/5.31 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.31 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power2_minus
% 5.02/5.31 thf(fact_5000_power2__minus,axiom,
% 5.02/5.31 ! [A: rat] :
% 5.02/5.31 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.31 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power2_minus
% 5.02/5.31 thf(fact_5001_power2__minus,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.31 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power2_minus
% 5.02/5.31 thf(fact_5002_odd__of__bool__self,axiom,
% 5.02/5.31 ! [P2: $o] :
% 5.02/5.31 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 5.02/5.31 = P2 ) ).
% 5.02/5.31
% 5.02/5.31 % odd_of_bool_self
% 5.02/5.31 thf(fact_5003_odd__of__bool__self,axiom,
% 5.02/5.31 ! [P2: $o] :
% 5.02/5.31 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 5.02/5.31 = P2 ) ).
% 5.02/5.31
% 5.02/5.31 % odd_of_bool_self
% 5.02/5.31 thf(fact_5004_odd__of__bool__self,axiom,
% 5.02/5.31 ! [P2: $o] :
% 5.02/5.31 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 5.02/5.31 = P2 ) ).
% 5.02/5.31
% 5.02/5.31 % odd_of_bool_self
% 5.02/5.31 thf(fact_5005_add__neg__numeral__special_I9_J,axiom,
% 5.02/5.31 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(9)
% 5.02/5.31 thf(fact_5006_add__neg__numeral__special_I9_J,axiom,
% 5.02/5.31 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(9)
% 5.02/5.31 thf(fact_5007_add__neg__numeral__special_I9_J,axiom,
% 5.02/5.31 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(9)
% 5.02/5.31 thf(fact_5008_add__neg__numeral__special_I9_J,axiom,
% 5.02/5.31 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(9)
% 5.02/5.31 thf(fact_5009_add__neg__numeral__special_I9_J,axiom,
% 5.02/5.31 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % add_neg_numeral_special(9)
% 5.02/5.31 thf(fact_5010_diff__numeral__special_I11_J,axiom,
% 5.02/5.31 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(11)
% 5.02/5.31 thf(fact_5011_diff__numeral__special_I11_J,axiom,
% 5.02/5.31 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(11)
% 5.02/5.31 thf(fact_5012_diff__numeral__special_I11_J,axiom,
% 5.02/5.31 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.31 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(11)
% 5.02/5.31 thf(fact_5013_diff__numeral__special_I11_J,axiom,
% 5.02/5.31 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(11)
% 5.02/5.31 thf(fact_5014_diff__numeral__special_I11_J,axiom,
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(11)
% 5.02/5.31 thf(fact_5015_diff__numeral__special_I10_J,axiom,
% 5.02/5.31 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(10)
% 5.02/5.31 thf(fact_5016_diff__numeral__special_I10_J,axiom,
% 5.02/5.31 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(10)
% 5.02/5.31 thf(fact_5017_diff__numeral__special_I10_J,axiom,
% 5.02/5.31 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(10)
% 5.02/5.31 thf(fact_5018_diff__numeral__special_I10_J,axiom,
% 5.02/5.31 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(10)
% 5.02/5.31 thf(fact_5019_diff__numeral__special_I10_J,axiom,
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(10)
% 5.02/5.31 thf(fact_5020_minus__1__div__2__eq,axiom,
% 5.02/5.31 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.31 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_1_div_2_eq
% 5.02/5.31 thf(fact_5021_minus__1__div__2__eq,axiom,
% 5.02/5.31 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_1_div_2_eq
% 5.02/5.31 thf(fact_5022_minus__1__mod__2__eq,axiom,
% 5.02/5.31 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.31 = one_one_int ) ).
% 5.02/5.31
% 5.02/5.31 % minus_1_mod_2_eq
% 5.02/5.31 thf(fact_5023_minus__1__mod__2__eq,axiom,
% 5.02/5.31 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.31 = one_one_Code_integer ) ).
% 5.02/5.31
% 5.02/5.31 % minus_1_mod_2_eq
% 5.02/5.31 thf(fact_5024_bits__minus__1__mod__2__eq,axiom,
% 5.02/5.31 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.31 = one_one_int ) ).
% 5.02/5.31
% 5.02/5.31 % bits_minus_1_mod_2_eq
% 5.02/5.31 thf(fact_5025_bits__minus__1__mod__2__eq,axiom,
% 5.02/5.31 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.31 = one_one_Code_integer ) ).
% 5.02/5.31
% 5.02/5.31 % bits_minus_1_mod_2_eq
% 5.02/5.31 thf(fact_5026_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [A: real,N2: nat] :
% 5.02/5.31 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Power.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5027_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [A: int,N2: nat] :
% 5.02/5.31 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Power.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5028_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [A: complex,N2: nat] :
% 5.02/5.31 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Power.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5029_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [A: rat,N2: nat] :
% 5.02/5.31 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Power.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5030_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [A: code_integer,N2: nat] :
% 5.02/5.31 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Power.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5031_of__bool__half__eq__0,axiom,
% 5.02/5.31 ! [B: $o] :
% 5.02/5.31 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.31 = zero_zero_nat ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_half_eq_0
% 5.02/5.31 thf(fact_5032_of__bool__half__eq__0,axiom,
% 5.02/5.31 ! [B: $o] :
% 5.02/5.31 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.31 = zero_zero_int ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_half_eq_0
% 5.02/5.31 thf(fact_5033_of__bool__half__eq__0,axiom,
% 5.02/5.31 ! [B: $o] :
% 5.02/5.31 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.31 = zero_z3403309356797280102nteger ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_half_eq_0
% 5.02/5.31 thf(fact_5034_power__minus__odd,axiom,
% 5.02/5.31 ! [N2: nat,A: real] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.02/5.31 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus_odd
% 5.02/5.31 thf(fact_5035_power__minus__odd,axiom,
% 5.02/5.31 ! [N2: nat,A: int] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.02/5.31 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus_odd
% 5.02/5.31 thf(fact_5036_power__minus__odd,axiom,
% 5.02/5.31 ! [N2: nat,A: complex] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus_odd
% 5.02/5.31 thf(fact_5037_power__minus__odd,axiom,
% 5.02/5.31 ! [N2: nat,A: rat] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.02/5.31 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus_odd
% 5.02/5.31 thf(fact_5038_power__minus__odd,axiom,
% 5.02/5.31 ! [N2: nat,A: code_integer] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus_odd
% 5.02/5.31 thf(fact_5039_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [N2: nat,A: real] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.02/5.31 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Parity.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5040_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [N2: nat,A: int] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.02/5.31 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Parity.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5041_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [N2: nat,A: complex] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.02/5.31 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Parity.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5042_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [N2: nat,A: rat] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.02/5.31 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Parity.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5043_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.02/5.31 ! [N2: nat,A: code_integer] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.02/5.31 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % Parity.ring_1_class.power_minus_even
% 5.02/5.31 thf(fact_5044_diff__numeral__special_I4_J,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(4)
% 5.02/5.31 thf(fact_5045_diff__numeral__special_I4_J,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(4)
% 5.02/5.31 thf(fact_5046_diff__numeral__special_I4_J,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(4)
% 5.02/5.31 thf(fact_5047_diff__numeral__special_I4_J,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(4)
% 5.02/5.31 thf(fact_5048_diff__numeral__special_I4_J,axiom,
% 5.02/5.31 ! [M: num] :
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(4)
% 5.02/5.31 thf(fact_5049_diff__numeral__special_I3_J,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(3)
% 5.02/5.31 thf(fact_5050_diff__numeral__special_I3_J,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(3)
% 5.02/5.31 thf(fact_5051_diff__numeral__special_I3_J,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.02/5.31 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(3)
% 5.02/5.31 thf(fact_5052_diff__numeral__special_I3_J,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.31 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(3)
% 5.02/5.31 thf(fact_5053_diff__numeral__special_I3_J,axiom,
% 5.02/5.31 ! [N2: num] :
% 5.02/5.31 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.31 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % diff_numeral_special(3)
% 5.02/5.31 thf(fact_5054_signed__take__bit__Suc__minus__bit0,axiom,
% 5.02/5.31 ! [N2: nat,K: num] :
% 5.02/5.31 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.02/5.31 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % signed_take_bit_Suc_minus_bit0
% 5.02/5.31 thf(fact_5055_dbl__simps_I4_J,axiom,
% 5.02/5.31 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.31 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(4)
% 5.02/5.31 thf(fact_5056_dbl__simps_I4_J,axiom,
% 5.02/5.31 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.31 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(4)
% 5.02/5.31 thf(fact_5057_dbl__simps_I4_J,axiom,
% 5.02/5.31 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(4)
% 5.02/5.31 thf(fact_5058_dbl__simps_I4_J,axiom,
% 5.02/5.31 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.31 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(4)
% 5.02/5.31 thf(fact_5059_dbl__simps_I4_J,axiom,
% 5.02/5.31 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % dbl_simps(4)
% 5.02/5.31 thf(fact_5060_power__minus1__even,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = one_one_real ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus1_even
% 5.02/5.31 thf(fact_5061_power__minus1__even,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = one_one_int ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus1_even
% 5.02/5.31 thf(fact_5062_power__minus1__even,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = one_one_complex ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus1_even
% 5.02/5.31 thf(fact_5063_power__minus1__even,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = one_one_rat ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus1_even
% 5.02/5.31 thf(fact_5064_power__minus1__even,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = one_one_Code_integer ) ).
% 5.02/5.31
% 5.02/5.31 % power_minus1_even
% 5.02/5.31 thf(fact_5065_neg__one__odd__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.02/5.31 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_odd_power
% 5.02/5.31 thf(fact_5066_neg__one__odd__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.02/5.31 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_odd_power
% 5.02/5.31 thf(fact_5067_neg__one__odd__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.02/5.31 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_odd_power
% 5.02/5.31 thf(fact_5068_neg__one__odd__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.02/5.31 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_odd_power
% 5.02/5.31 thf(fact_5069_neg__one__odd__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_odd_power
% 5.02/5.31 thf(fact_5070_neg__one__even__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.02/5.31 = one_one_real ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_even_power
% 5.02/5.31 thf(fact_5071_neg__one__even__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.02/5.31 = one_one_int ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_even_power
% 5.02/5.31 thf(fact_5072_neg__one__even__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.02/5.31 = one_one_complex ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_even_power
% 5.02/5.31 thf(fact_5073_neg__one__even__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.02/5.31 = one_one_rat ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_even_power
% 5.02/5.31 thf(fact_5074_neg__one__even__power,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.31 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.02/5.31 = one_one_Code_integer ) ) ).
% 5.02/5.31
% 5.02/5.31 % neg_one_even_power
% 5.02/5.31 thf(fact_5075_signed__take__bit__0,axiom,
% 5.02/5.31 ! [A: code_integer] :
% 5.02/5.31 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.02/5.31 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % signed_take_bit_0
% 5.02/5.31 thf(fact_5076_signed__take__bit__0,axiom,
% 5.02/5.31 ! [A: int] :
% 5.02/5.31 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.02/5.31 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % signed_take_bit_0
% 5.02/5.31 thf(fact_5077_bits__1__div__exp,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % bits_1_div_exp
% 5.02/5.31 thf(fact_5078_bits__1__div__exp,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % bits_1_div_exp
% 5.02/5.31 thf(fact_5079_bits__1__div__exp,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % bits_1_div_exp
% 5.02/5.31 thf(fact_5080_one__div__2__pow__eq,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % one_div_2_pow_eq
% 5.02/5.31 thf(fact_5081_one__div__2__pow__eq,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % one_div_2_pow_eq
% 5.02/5.31 thf(fact_5082_one__div__2__pow__eq,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % one_div_2_pow_eq
% 5.02/5.31 thf(fact_5083_one__mod__2__pow__eq,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % one_mod_2_pow_eq
% 5.02/5.31 thf(fact_5084_one__mod__2__pow__eq,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % one_mod_2_pow_eq
% 5.02/5.31 thf(fact_5085_one__mod__2__pow__eq,axiom,
% 5.02/5.31 ! [N2: nat] :
% 5.02/5.31 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.31 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % one_mod_2_pow_eq
% 5.02/5.31 thf(fact_5086_compl__le__swap2,axiom,
% 5.02/5.31 ! [Y: set_nat,X2: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X2 )
% 5.02/5.31 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X2 ) @ Y ) ) ).
% 5.02/5.31
% 5.02/5.31 % compl_le_swap2
% 5.02/5.31 thf(fact_5087_compl__le__swap1,axiom,
% 5.02/5.31 ! [Y: set_nat,X2: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X2 ) )
% 5.02/5.31 => ( ord_less_eq_set_nat @ X2 @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % compl_le_swap1
% 5.02/5.31 thf(fact_5088_compl__mono,axiom,
% 5.02/5.31 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.31 ( ( ord_less_eq_set_nat @ X2 @ Y )
% 5.02/5.31 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X2 ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % compl_mono
% 5.02/5.31 thf(fact_5089_minus__equation__iff,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ( uminus_uminus_real @ A )
% 5.02/5.31 = B )
% 5.02/5.31 = ( ( uminus_uminus_real @ B )
% 5.02/5.31 = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_equation_iff
% 5.02/5.31 thf(fact_5090_minus__equation__iff,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ( uminus_uminus_int @ A )
% 5.02/5.31 = B )
% 5.02/5.31 = ( ( uminus_uminus_int @ B )
% 5.02/5.31 = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_equation_iff
% 5.02/5.31 thf(fact_5091_minus__equation__iff,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( ( uminus1482373934393186551omplex @ A )
% 5.02/5.31 = B )
% 5.02/5.31 = ( ( uminus1482373934393186551omplex @ B )
% 5.02/5.31 = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_equation_iff
% 5.02/5.31 thf(fact_5092_minus__equation__iff,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ( uminus_uminus_rat @ A )
% 5.02/5.31 = B )
% 5.02/5.31 = ( ( uminus_uminus_rat @ B )
% 5.02/5.31 = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_equation_iff
% 5.02/5.31 thf(fact_5093_minus__equation__iff,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( ( uminus1351360451143612070nteger @ A )
% 5.02/5.31 = B )
% 5.02/5.31 = ( ( uminus1351360451143612070nteger @ B )
% 5.02/5.31 = A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_equation_iff
% 5.02/5.31 thf(fact_5094_equation__minus__iff,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus_uminus_real @ B ) )
% 5.02/5.31 = ( B
% 5.02/5.31 = ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % equation_minus_iff
% 5.02/5.31 thf(fact_5095_equation__minus__iff,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( B
% 5.02/5.31 = ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % equation_minus_iff
% 5.02/5.31 thf(fact_5096_equation__minus__iff,axiom,
% 5.02/5.31 ! [A: complex,B: complex] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.31 = ( B
% 5.02/5.31 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % equation_minus_iff
% 5.02/5.31 thf(fact_5097_equation__minus__iff,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus_uminus_rat @ B ) )
% 5.02/5.31 = ( B
% 5.02/5.31 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % equation_minus_iff
% 5.02/5.31 thf(fact_5098_equation__minus__iff,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( A
% 5.02/5.31 = ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( B
% 5.02/5.31 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % equation_minus_iff
% 5.02/5.31 thf(fact_5099_of__bool__eq__iff,axiom,
% 5.02/5.31 ! [P2: $o,Q2: $o] :
% 5.02/5.31 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 5.02/5.31 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.02/5.31 = ( P2 = Q2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_iff
% 5.02/5.31 thf(fact_5100_of__bool__eq__iff,axiom,
% 5.02/5.31 ! [P2: $o,Q2: $o] :
% 5.02/5.31 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 5.02/5.31 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.02/5.31 = ( P2 = Q2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_iff
% 5.02/5.31 thf(fact_5101_of__bool__eq__iff,axiom,
% 5.02/5.31 ! [P2: $o,Q2: $o] :
% 5.02/5.31 ( ( ( zero_n356916108424825756nteger @ P2 )
% 5.02/5.31 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.02/5.31 = ( P2 = Q2 ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_eq_iff
% 5.02/5.31 thf(fact_5102_of__bool__conj,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( zero_n3304061248610475627l_real
% 5.02/5.31 @ ( P
% 5.02/5.31 & Q ) )
% 5.02/5.31 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_conj
% 5.02/5.31 thf(fact_5103_of__bool__conj,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( zero_n2052037380579107095ol_rat
% 5.02/5.31 @ ( P
% 5.02/5.31 & Q ) )
% 5.02/5.31 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_conj
% 5.02/5.31 thf(fact_5104_of__bool__conj,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( zero_n2687167440665602831ol_nat
% 5.02/5.31 @ ( P
% 5.02/5.31 & Q ) )
% 5.02/5.31 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_conj
% 5.02/5.31 thf(fact_5105_of__bool__conj,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( zero_n2684676970156552555ol_int
% 5.02/5.31 @ ( P
% 5.02/5.31 & Q ) )
% 5.02/5.31 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_conj
% 5.02/5.31 thf(fact_5106_of__bool__conj,axiom,
% 5.02/5.31 ! [P: $o,Q: $o] :
% 5.02/5.31 ( ( zero_n356916108424825756nteger
% 5.02/5.31 @ ( P
% 5.02/5.31 & Q ) )
% 5.02/5.31 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % of_bool_conj
% 5.02/5.31 thf(fact_5107_le__minus__iff,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.02/5.31 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_minus_iff
% 5.02/5.31 thf(fact_5108_le__minus__iff,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_minus_iff
% 5.02/5.31 thf(fact_5109_le__minus__iff,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.02/5.31 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_minus_iff
% 5.02/5.31 thf(fact_5110_le__minus__iff,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_minus_iff
% 5.02/5.31 thf(fact_5111_minus__le__iff,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.02/5.31 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_le_iff
% 5.02/5.31 thf(fact_5112_minus__le__iff,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.02/5.31 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_le_iff
% 5.02/5.31 thf(fact_5113_minus__le__iff,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.02/5.31 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_le_iff
% 5.02/5.31 thf(fact_5114_minus__le__iff,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.31 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.02/5.31
% 5.02/5.31 % minus_le_iff
% 5.02/5.31 thf(fact_5115_le__imp__neg__le,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ord_less_eq_real @ A @ B )
% 5.02/5.31 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_imp_neg_le
% 5.02/5.31 thf(fact_5116_le__imp__neg__le,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.02/5.31 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_imp_neg_le
% 5.02/5.31 thf(fact_5117_le__imp__neg__le,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.31 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_imp_neg_le
% 5.02/5.31 thf(fact_5118_le__imp__neg__le,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ord_less_eq_int @ A @ B )
% 5.02/5.31 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % le_imp_neg_le
% 5.02/5.31 thf(fact_5119_less__minus__iff,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.02/5.31 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_minus_iff
% 5.02/5.31 thf(fact_5120_less__minus__iff,axiom,
% 5.02/5.31 ! [A: int,B: int] :
% 5.02/5.31 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.31 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_minus_iff
% 5.02/5.31 thf(fact_5121_less__minus__iff,axiom,
% 5.02/5.31 ! [A: rat,B: rat] :
% 5.02/5.31 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.02/5.31 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_minus_iff
% 5.02/5.31 thf(fact_5122_less__minus__iff,axiom,
% 5.02/5.31 ! [A: code_integer,B: code_integer] :
% 5.02/5.31 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.31 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.31
% 5.02/5.31 % less_minus_iff
% 5.02/5.31 thf(fact_5123_minus__less__iff,axiom,
% 5.02/5.31 ! [A: real,B: real] :
% 5.02/5.31 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.02/5.31 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_less_iff
% 5.02/5.32 thf(fact_5124_minus__less__iff,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.32 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_less_iff
% 5.02/5.32 thf(fact_5125_minus__less__iff,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.02/5.32 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_less_iff
% 5.02/5.32 thf(fact_5126_minus__less__iff,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.02/5.32 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_less_iff
% 5.02/5.32 thf(fact_5127_verit__negate__coefficient_I2_J,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( ord_less_real @ A @ B )
% 5.02/5.32 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % verit_negate_coefficient(2)
% 5.02/5.32 thf(fact_5128_verit__negate__coefficient_I2_J,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( ord_less_int @ A @ B )
% 5.02/5.32 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % verit_negate_coefficient(2)
% 5.02/5.32 thf(fact_5129_verit__negate__coefficient_I2_J,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( ord_less_rat @ A @ B )
% 5.02/5.32 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % verit_negate_coefficient(2)
% 5.02/5.32 thf(fact_5130_verit__negate__coefficient_I2_J,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.02/5.32 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % verit_negate_coefficient(2)
% 5.02/5.32 thf(fact_5131_neg__numeral__neq__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.02/5.32 != ( numeral_numeral_real @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_neq_numeral
% 5.02/5.32 thf(fact_5132_neg__numeral__neq__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.02/5.32 != ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_neq_numeral
% 5.02/5.32 thf(fact_5133_neg__numeral__neq__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.02/5.32 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_neq_numeral
% 5.02/5.32 thf(fact_5134_neg__numeral__neq__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.02/5.32 != ( numeral_numeral_rat @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_neq_numeral
% 5.02/5.32 thf(fact_5135_neg__numeral__neq__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.02/5.32 != ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_neq_numeral
% 5.02/5.32 thf(fact_5136_numeral__neq__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( numeral_numeral_real @ M )
% 5.02/5.32 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_numeral
% 5.02/5.32 thf(fact_5137_numeral__neq__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( numeral_numeral_int @ M )
% 5.02/5.32 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_numeral
% 5.02/5.32 thf(fact_5138_numeral__neq__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( numera6690914467698888265omplex @ M )
% 5.02/5.32 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_numeral
% 5.02/5.32 thf(fact_5139_numeral__neq__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( numeral_numeral_rat @ M )
% 5.02/5.32 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_numeral
% 5.02/5.32 thf(fact_5140_numeral__neq__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( numera6620942414471956472nteger @ M )
% 5.02/5.32 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_numeral
% 5.02/5.32 thf(fact_5141_minus__mult__commute,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.02/5.32 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_mult_commute
% 5.02/5.32 thf(fact_5142_minus__mult__commute,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.32 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_mult_commute
% 5.02/5.32 thf(fact_5143_minus__mult__commute,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.02/5.32 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_mult_commute
% 5.02/5.32 thf(fact_5144_minus__mult__commute,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.02/5.32 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_mult_commute
% 5.02/5.32 thf(fact_5145_minus__mult__commute,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.02/5.32 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_mult_commute
% 5.02/5.32 thf(fact_5146_square__eq__iff,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( ( times_times_real @ A @ A )
% 5.02/5.32 = ( times_times_real @ B @ B ) )
% 5.02/5.32 = ( ( A = B )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_iff
% 5.02/5.32 thf(fact_5147_square__eq__iff,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( ( times_times_int @ A @ A )
% 5.02/5.32 = ( times_times_int @ B @ B ) )
% 5.02/5.32 = ( ( A = B )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_iff
% 5.02/5.32 thf(fact_5148_square__eq__iff,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( ( times_times_complex @ A @ A )
% 5.02/5.32 = ( times_times_complex @ B @ B ) )
% 5.02/5.32 = ( ( A = B )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_iff
% 5.02/5.32 thf(fact_5149_square__eq__iff,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( ( times_times_rat @ A @ A )
% 5.02/5.32 = ( times_times_rat @ B @ B ) )
% 5.02/5.32 = ( ( A = B )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_iff
% 5.02/5.32 thf(fact_5150_square__eq__iff,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.02/5.32 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.02/5.32 = ( ( A = B )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_iff
% 5.02/5.32 thf(fact_5151_one__neq__neg__one,axiom,
% 5.02/5.32 ( one_one_real
% 5.02/5.32 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_one
% 5.02/5.32 thf(fact_5152_one__neq__neg__one,axiom,
% 5.02/5.32 ( one_one_int
% 5.02/5.32 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_one
% 5.02/5.32 thf(fact_5153_one__neq__neg__one,axiom,
% 5.02/5.32 ( one_one_complex
% 5.02/5.32 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_one
% 5.02/5.32 thf(fact_5154_one__neq__neg__one,axiom,
% 5.02/5.32 ( one_one_rat
% 5.02/5.32 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_one
% 5.02/5.32 thf(fact_5155_one__neq__neg__one,axiom,
% 5.02/5.32 ( one_one_Code_integer
% 5.02/5.32 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_one
% 5.02/5.32 thf(fact_5156_is__num__normalize_I8_J,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.02/5.32 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % is_num_normalize(8)
% 5.02/5.32 thf(fact_5157_is__num__normalize_I8_J,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.02/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % is_num_normalize(8)
% 5.02/5.32 thf(fact_5158_is__num__normalize_I8_J,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.02/5.32 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % is_num_normalize(8)
% 5.02/5.32 thf(fact_5159_is__num__normalize_I8_J,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.02/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % is_num_normalize(8)
% 5.02/5.32 thf(fact_5160_is__num__normalize_I8_J,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.02/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % is_num_normalize(8)
% 5.02/5.32 thf(fact_5161_group__cancel_Oneg1,axiom,
% 5.02/5.32 ! [A3: real,K: real,A: real] :
% 5.02/5.32 ( ( A3
% 5.02/5.32 = ( plus_plus_real @ K @ A ) )
% 5.02/5.32 => ( ( uminus_uminus_real @ A3 )
% 5.02/5.32 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.neg1
% 5.02/5.32 thf(fact_5162_group__cancel_Oneg1,axiom,
% 5.02/5.32 ! [A3: int,K: int,A: int] :
% 5.02/5.32 ( ( A3
% 5.02/5.32 = ( plus_plus_int @ K @ A ) )
% 5.02/5.32 => ( ( uminus_uminus_int @ A3 )
% 5.02/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.neg1
% 5.02/5.32 thf(fact_5163_group__cancel_Oneg1,axiom,
% 5.02/5.32 ! [A3: complex,K: complex,A: complex] :
% 5.02/5.32 ( ( A3
% 5.02/5.32 = ( plus_plus_complex @ K @ A ) )
% 5.02/5.32 => ( ( uminus1482373934393186551omplex @ A3 )
% 5.02/5.32 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.neg1
% 5.02/5.32 thf(fact_5164_group__cancel_Oneg1,axiom,
% 5.02/5.32 ! [A3: rat,K: rat,A: rat] :
% 5.02/5.32 ( ( A3
% 5.02/5.32 = ( plus_plus_rat @ K @ A ) )
% 5.02/5.32 => ( ( uminus_uminus_rat @ A3 )
% 5.02/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.neg1
% 5.02/5.32 thf(fact_5165_group__cancel_Oneg1,axiom,
% 5.02/5.32 ! [A3: code_integer,K: code_integer,A: code_integer] :
% 5.02/5.32 ( ( A3
% 5.02/5.32 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.02/5.32 => ( ( uminus1351360451143612070nteger @ A3 )
% 5.02/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.neg1
% 5.02/5.32 thf(fact_5166_add_Oinverse__distrib__swap,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.02/5.32 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_distrib_swap
% 5.02/5.32 thf(fact_5167_add_Oinverse__distrib__swap,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.02/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_distrib_swap
% 5.02/5.32 thf(fact_5168_add_Oinverse__distrib__swap,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.02/5.32 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_distrib_swap
% 5.02/5.32 thf(fact_5169_add_Oinverse__distrib__swap,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.02/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_distrib_swap
% 5.02/5.32 thf(fact_5170_add_Oinverse__distrib__swap,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.02/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_distrib_swap
% 5.02/5.32 thf(fact_5171_minus__diff__commute,axiom,
% 5.02/5.32 ! [B: real,A: real] :
% 5.02/5.32 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.02/5.32 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_commute
% 5.02/5.32 thf(fact_5172_minus__diff__commute,axiom,
% 5.02/5.32 ! [B: int,A: int] :
% 5.02/5.32 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.02/5.32 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_commute
% 5.02/5.32 thf(fact_5173_minus__diff__commute,axiom,
% 5.02/5.32 ! [B: complex,A: complex] :
% 5.02/5.32 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.02/5.32 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_commute
% 5.02/5.32 thf(fact_5174_minus__diff__commute,axiom,
% 5.02/5.32 ! [B: rat,A: rat] :
% 5.02/5.32 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.02/5.32 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_commute
% 5.02/5.32 thf(fact_5175_minus__diff__commute,axiom,
% 5.02/5.32 ! [B: code_integer,A: code_integer] :
% 5.02/5.32 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.02/5.32 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_commute
% 5.02/5.32 thf(fact_5176_minus__diff__minus,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.02/5.32 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_minus
% 5.02/5.32 thf(fact_5177_minus__diff__minus,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.02/5.32 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_minus
% 5.02/5.32 thf(fact_5178_minus__diff__minus,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_minus
% 5.02/5.32 thf(fact_5179_minus__diff__minus,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.02/5.32 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_minus
% 5.02/5.32 thf(fact_5180_minus__diff__minus,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_diff_minus
% 5.02/5.32 thf(fact_5181_minus__divide__right,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.32 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_right
% 5.02/5.32 thf(fact_5182_minus__divide__right,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.32 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_right
% 5.02/5.32 thf(fact_5183_minus__divide__right,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.02/5.32 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_right
% 5.02/5.32 thf(fact_5184_minus__divide__divide,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.02/5.32 = ( divide_divide_real @ A @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_divide
% 5.02/5.32 thf(fact_5185_minus__divide__divide,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.32 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_divide
% 5.02/5.32 thf(fact_5186_minus__divide__divide,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.02/5.32 = ( divide_divide_rat @ A @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_divide
% 5.02/5.32 thf(fact_5187_minus__divide__left,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.32 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_left
% 5.02/5.32 thf(fact_5188_minus__divide__left,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.32 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_left
% 5.02/5.32 thf(fact_5189_minus__divide__left,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.02/5.32 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_left
% 5.02/5.32 thf(fact_5190_div__minus__right,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.32 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % div_minus_right
% 5.02/5.32 thf(fact_5191_div__minus__right,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.32 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % div_minus_right
% 5.02/5.32 thf(fact_5192_mod__minus__right,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.32 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % mod_minus_right
% 5.02/5.32 thf(fact_5193_mod__minus__right,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % mod_minus_right
% 5.02/5.32 thf(fact_5194_mod__minus__cong,axiom,
% 5.02/5.32 ! [A: int,B: int,A2: int] :
% 5.02/5.32 ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 = ( modulo_modulo_int @ A2 @ B ) )
% 5.02/5.32 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.32 = ( modulo_modulo_int @ ( uminus_uminus_int @ A2 ) @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % mod_minus_cong
% 5.02/5.32 thf(fact_5195_mod__minus__cong,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer,A2: code_integer] :
% 5.02/5.32 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.02/5.32 = ( modulo364778990260209775nteger @ A2 @ B ) )
% 5.02/5.32 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.02/5.32 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A2 ) @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % mod_minus_cong
% 5.02/5.32 thf(fact_5196_mod__minus__eq,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.02/5.32 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mod_minus_eq
% 5.02/5.32 thf(fact_5197_mod__minus__eq,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.02/5.32 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mod_minus_eq
% 5.02/5.32 thf(fact_5198_uminus__int__code_I1_J,axiom,
% 5.02/5.32 ( ( uminus_uminus_int @ zero_zero_int )
% 5.02/5.32 = zero_zero_int ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_int_code(1)
% 5.02/5.32 thf(fact_5199_signed__take__bit__minus,axiom,
% 5.02/5.32 ! [N2: nat,K: int] :
% 5.02/5.32 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) )
% 5.02/5.32 = ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_minus
% 5.02/5.32 thf(fact_5200_concat__bit__assoc,axiom,
% 5.02/5.32 ! [N2: nat,K: int,M: nat,L: int,R2: int] :
% 5.02/5.32 ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L @ R2 ) )
% 5.02/5.32 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L ) @ R2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % concat_bit_assoc
% 5.02/5.32 thf(fact_5201_zero__less__eq__of__bool,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_less_eq_of_bool
% 5.02/5.32 thf(fact_5202_zero__less__eq__of__bool,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_less_eq_of_bool
% 5.02/5.32 thf(fact_5203_zero__less__eq__of__bool,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_less_eq_of_bool
% 5.02/5.32 thf(fact_5204_zero__less__eq__of__bool,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_less_eq_of_bool
% 5.02/5.32 thf(fact_5205_zero__less__eq__of__bool,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_less_eq_of_bool
% 5.02/5.32 thf(fact_5206_of__bool__less__eq__one,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_less_eq_one
% 5.02/5.32 thf(fact_5207_of__bool__less__eq__one,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_less_eq_one
% 5.02/5.32 thf(fact_5208_of__bool__less__eq__one,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_less_eq_one
% 5.02/5.32 thf(fact_5209_of__bool__less__eq__one,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_less_eq_one
% 5.02/5.32 thf(fact_5210_of__bool__less__eq__one,axiom,
% 5.02/5.32 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_less_eq_one
% 5.02/5.32 thf(fact_5211_of__bool__def,axiom,
% 5.02/5.32 ( zero_n1201886186963655149omplex
% 5.02/5.32 = ( ^ [P6: $o] : ( if_complex @ P6 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_def
% 5.02/5.32 thf(fact_5212_of__bool__def,axiom,
% 5.02/5.32 ( zero_n3304061248610475627l_real
% 5.02/5.32 = ( ^ [P6: $o] : ( if_real @ P6 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_def
% 5.02/5.32 thf(fact_5213_of__bool__def,axiom,
% 5.02/5.32 ( zero_n2052037380579107095ol_rat
% 5.02/5.32 = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_def
% 5.02/5.32 thf(fact_5214_of__bool__def,axiom,
% 5.02/5.32 ( zero_n2687167440665602831ol_nat
% 5.02/5.32 = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_def
% 5.02/5.32 thf(fact_5215_of__bool__def,axiom,
% 5.02/5.32 ( zero_n2684676970156552555ol_int
% 5.02/5.32 = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_def
% 5.02/5.32 thf(fact_5216_of__bool__def,axiom,
% 5.02/5.32 ( zero_n356916108424825756nteger
% 5.02/5.32 = ( ^ [P6: $o] : ( if_Code_integer @ P6 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_def
% 5.02/5.32 thf(fact_5217_split__of__bool,axiom,
% 5.02/5.32 ! [P: complex > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.02/5.32 = ( ( P2
% 5.02/5.32 => ( P @ one_one_complex ) )
% 5.02/5.32 & ( ~ P2
% 5.02/5.32 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool
% 5.02/5.32 thf(fact_5218_split__of__bool,axiom,
% 5.02/5.32 ! [P: real > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.02/5.32 = ( ( P2
% 5.02/5.32 => ( P @ one_one_real ) )
% 5.02/5.32 & ( ~ P2
% 5.02/5.32 => ( P @ zero_zero_real ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool
% 5.02/5.32 thf(fact_5219_split__of__bool,axiom,
% 5.02/5.32 ! [P: rat > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.02/5.32 = ( ( P2
% 5.02/5.32 => ( P @ one_one_rat ) )
% 5.02/5.32 & ( ~ P2
% 5.02/5.32 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool
% 5.02/5.32 thf(fact_5220_split__of__bool,axiom,
% 5.02/5.32 ! [P: nat > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.02/5.32 = ( ( P2
% 5.02/5.32 => ( P @ one_one_nat ) )
% 5.02/5.32 & ( ~ P2
% 5.02/5.32 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool
% 5.02/5.32 thf(fact_5221_split__of__bool,axiom,
% 5.02/5.32 ! [P: int > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.02/5.32 = ( ( P2
% 5.02/5.32 => ( P @ one_one_int ) )
% 5.02/5.32 & ( ~ P2
% 5.02/5.32 => ( P @ zero_zero_int ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool
% 5.02/5.32 thf(fact_5222_split__of__bool,axiom,
% 5.02/5.32 ! [P: code_integer > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.02/5.32 = ( ( P2
% 5.02/5.32 => ( P @ one_one_Code_integer ) )
% 5.02/5.32 & ( ~ P2
% 5.02/5.32 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool
% 5.02/5.32 thf(fact_5223_split__of__bool__asm,axiom,
% 5.02/5.32 ! [P: complex > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.02/5.32 = ( ~ ( ( P2
% 5.02/5.32 & ~ ( P @ one_one_complex ) )
% 5.02/5.32 | ( ~ P2
% 5.02/5.32 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool_asm
% 5.02/5.32 thf(fact_5224_split__of__bool__asm,axiom,
% 5.02/5.32 ! [P: real > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.02/5.32 = ( ~ ( ( P2
% 5.02/5.32 & ~ ( P @ one_one_real ) )
% 5.02/5.32 | ( ~ P2
% 5.02/5.32 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool_asm
% 5.02/5.32 thf(fact_5225_split__of__bool__asm,axiom,
% 5.02/5.32 ! [P: rat > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.02/5.32 = ( ~ ( ( P2
% 5.02/5.32 & ~ ( P @ one_one_rat ) )
% 5.02/5.32 | ( ~ P2
% 5.02/5.32 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool_asm
% 5.02/5.32 thf(fact_5226_split__of__bool__asm,axiom,
% 5.02/5.32 ! [P: nat > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.02/5.32 = ( ~ ( ( P2
% 5.02/5.32 & ~ ( P @ one_one_nat ) )
% 5.02/5.32 | ( ~ P2
% 5.02/5.32 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool_asm
% 5.02/5.32 thf(fact_5227_split__of__bool__asm,axiom,
% 5.02/5.32 ! [P: int > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.02/5.32 = ( ~ ( ( P2
% 5.02/5.32 & ~ ( P @ one_one_int ) )
% 5.02/5.32 | ( ~ P2
% 5.02/5.32 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool_asm
% 5.02/5.32 thf(fact_5228_split__of__bool__asm,axiom,
% 5.02/5.32 ! [P: code_integer > $o,P2: $o] :
% 5.02/5.32 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.02/5.32 = ( ~ ( ( P2
% 5.02/5.32 & ~ ( P @ one_one_Code_integer ) )
% 5.02/5.32 | ( ~ P2
% 5.02/5.32 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % split_of_bool_asm
% 5.02/5.32 thf(fact_5229_neg__numeral__le__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_numeral
% 5.02/5.32 thf(fact_5230_neg__numeral__le__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_numeral
% 5.02/5.32 thf(fact_5231_neg__numeral__le__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_numeral
% 5.02/5.32 thf(fact_5232_neg__numeral__le__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_numeral
% 5.02/5.32 thf(fact_5233_not__numeral__le__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_le_neg_numeral
% 5.02/5.32 thf(fact_5234_not__numeral__le__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_le_neg_numeral
% 5.02/5.32 thf(fact_5235_not__numeral__le__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_le_neg_numeral
% 5.02/5.32 thf(fact_5236_not__numeral__le__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_le_neg_numeral
% 5.02/5.32 thf(fact_5237_zero__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( zero_zero_real
% 5.02/5.32 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_numeral
% 5.02/5.32 thf(fact_5238_zero__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( zero_zero_int
% 5.02/5.32 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_numeral
% 5.02/5.32 thf(fact_5239_zero__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( zero_zero_complex
% 5.02/5.32 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_numeral
% 5.02/5.32 thf(fact_5240_zero__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( zero_zero_rat
% 5.02/5.32 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_numeral
% 5.02/5.32 thf(fact_5241_zero__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( zero_z3403309356797280102nteger
% 5.02/5.32 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_numeral
% 5.02/5.32 thf(fact_5242_neg__numeral__less__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_numeral
% 5.02/5.32 thf(fact_5243_neg__numeral__less__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_numeral
% 5.02/5.32 thf(fact_5244_neg__numeral__less__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_numeral
% 5.02/5.32 thf(fact_5245_neg__numeral__less__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_numeral
% 5.02/5.32 thf(fact_5246_not__numeral__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_less_neg_numeral
% 5.02/5.32 thf(fact_5247_not__numeral__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_less_neg_numeral
% 5.02/5.32 thf(fact_5248_not__numeral__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_less_neg_numeral
% 5.02/5.32 thf(fact_5249_not__numeral__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_less_neg_numeral
% 5.02/5.32 thf(fact_5250_le__minus__one__simps_I4_J,axiom,
% 5.02/5.32 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(4)
% 5.02/5.32 thf(fact_5251_le__minus__one__simps_I4_J,axiom,
% 5.02/5.32 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(4)
% 5.02/5.32 thf(fact_5252_le__minus__one__simps_I4_J,axiom,
% 5.02/5.32 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(4)
% 5.02/5.32 thf(fact_5253_le__minus__one__simps_I4_J,axiom,
% 5.02/5.32 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(4)
% 5.02/5.32 thf(fact_5254_le__minus__one__simps_I2_J,axiom,
% 5.02/5.32 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(2)
% 5.02/5.32 thf(fact_5255_le__minus__one__simps_I2_J,axiom,
% 5.02/5.32 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(2)
% 5.02/5.32 thf(fact_5256_le__minus__one__simps_I2_J,axiom,
% 5.02/5.32 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(2)
% 5.02/5.32 thf(fact_5257_le__minus__one__simps_I2_J,axiom,
% 5.02/5.32 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(2)
% 5.02/5.32 thf(fact_5258_zero__neq__neg__one,axiom,
% 5.02/5.32 ( zero_zero_real
% 5.02/5.32 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_one
% 5.02/5.32 thf(fact_5259_zero__neq__neg__one,axiom,
% 5.02/5.32 ( zero_zero_int
% 5.02/5.32 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_one
% 5.02/5.32 thf(fact_5260_zero__neq__neg__one,axiom,
% 5.02/5.32 ( zero_zero_complex
% 5.02/5.32 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_one
% 5.02/5.32 thf(fact_5261_zero__neq__neg__one,axiom,
% 5.02/5.32 ( zero_zero_rat
% 5.02/5.32 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_one
% 5.02/5.32 thf(fact_5262_zero__neq__neg__one,axiom,
% 5.02/5.32 ( zero_z3403309356797280102nteger
% 5.02/5.32 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % zero_neq_neg_one
% 5.02/5.32 thf(fact_5263_add__eq__0__iff,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( ( plus_plus_real @ A @ B )
% 5.02/5.32 = zero_zero_real )
% 5.02/5.32 = ( B
% 5.02/5.32 = ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_eq_0_iff
% 5.02/5.32 thf(fact_5264_add__eq__0__iff,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( ( plus_plus_int @ A @ B )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 = ( B
% 5.02/5.32 = ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_eq_0_iff
% 5.02/5.32 thf(fact_5265_add__eq__0__iff,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( ( plus_plus_complex @ A @ B )
% 5.02/5.32 = zero_zero_complex )
% 5.02/5.32 = ( B
% 5.02/5.32 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_eq_0_iff
% 5.02/5.32 thf(fact_5266_add__eq__0__iff,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( ( plus_plus_rat @ A @ B )
% 5.02/5.32 = zero_zero_rat )
% 5.02/5.32 = ( B
% 5.02/5.32 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_eq_0_iff
% 5.02/5.32 thf(fact_5267_add__eq__0__iff,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.02/5.32 = zero_z3403309356797280102nteger )
% 5.02/5.32 = ( B
% 5.02/5.32 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_eq_0_iff
% 5.02/5.32 thf(fact_5268_ab__group__add__class_Oab__left__minus,axiom,
% 5.02/5.32 ! [A: real] :
% 5.02/5.32 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.02/5.32 = zero_zero_real ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_left_minus
% 5.02/5.32 thf(fact_5269_ab__group__add__class_Oab__left__minus,axiom,
% 5.02/5.32 ! [A: int] :
% 5.02/5.32 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.02/5.32 = zero_zero_int ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_left_minus
% 5.02/5.32 thf(fact_5270_ab__group__add__class_Oab__left__minus,axiom,
% 5.02/5.32 ! [A: complex] :
% 5.02/5.32 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.02/5.32 = zero_zero_complex ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_left_minus
% 5.02/5.32 thf(fact_5271_ab__group__add__class_Oab__left__minus,axiom,
% 5.02/5.32 ! [A: rat] :
% 5.02/5.32 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.02/5.32 = zero_zero_rat ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_left_minus
% 5.02/5.32 thf(fact_5272_ab__group__add__class_Oab__left__minus,axiom,
% 5.02/5.32 ! [A: code_integer] :
% 5.02/5.32 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.02/5.32 = zero_z3403309356797280102nteger ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_left_minus
% 5.02/5.32 thf(fact_5273_add_Oinverse__unique,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( ( plus_plus_real @ A @ B )
% 5.02/5.32 = zero_zero_real )
% 5.02/5.32 => ( ( uminus_uminus_real @ A )
% 5.02/5.32 = B ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_unique
% 5.02/5.32 thf(fact_5274_add_Oinverse__unique,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( ( plus_plus_int @ A @ B )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 => ( ( uminus_uminus_int @ A )
% 5.02/5.32 = B ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_unique
% 5.02/5.32 thf(fact_5275_add_Oinverse__unique,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( ( plus_plus_complex @ A @ B )
% 5.02/5.32 = zero_zero_complex )
% 5.02/5.32 => ( ( uminus1482373934393186551omplex @ A )
% 5.02/5.32 = B ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_unique
% 5.02/5.32 thf(fact_5276_add_Oinverse__unique,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( ( plus_plus_rat @ A @ B )
% 5.02/5.32 = zero_zero_rat )
% 5.02/5.32 => ( ( uminus_uminus_rat @ A )
% 5.02/5.32 = B ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_unique
% 5.02/5.32 thf(fact_5277_add_Oinverse__unique,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.02/5.32 = zero_z3403309356797280102nteger )
% 5.02/5.32 => ( ( uminus1351360451143612070nteger @ A )
% 5.02/5.32 = B ) ) ).
% 5.02/5.32
% 5.02/5.32 % add.inverse_unique
% 5.02/5.32 thf(fact_5278_eq__neg__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( A
% 5.02/5.32 = ( uminus_uminus_real @ B ) )
% 5.02/5.32 = ( ( plus_plus_real @ A @ B )
% 5.02/5.32 = zero_zero_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_neg_iff_add_eq_0
% 5.02/5.32 thf(fact_5279_eq__neg__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( A
% 5.02/5.32 = ( uminus_uminus_int @ B ) )
% 5.02/5.32 = ( ( plus_plus_int @ A @ B )
% 5.02/5.32 = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_neg_iff_add_eq_0
% 5.02/5.32 thf(fact_5280_eq__neg__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( A
% 5.02/5.32 = ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.32 = ( ( plus_plus_complex @ A @ B )
% 5.02/5.32 = zero_zero_complex ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_neg_iff_add_eq_0
% 5.02/5.32 thf(fact_5281_eq__neg__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( A
% 5.02/5.32 = ( uminus_uminus_rat @ B ) )
% 5.02/5.32 = ( ( plus_plus_rat @ A @ B )
% 5.02/5.32 = zero_zero_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_neg_iff_add_eq_0
% 5.02/5.32 thf(fact_5282_eq__neg__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( A
% 5.02/5.32 = ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.32 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.02/5.32 = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_neg_iff_add_eq_0
% 5.02/5.32 thf(fact_5283_neg__eq__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( ( uminus_uminus_real @ A )
% 5.02/5.32 = B )
% 5.02/5.32 = ( ( plus_plus_real @ A @ B )
% 5.02/5.32 = zero_zero_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_eq_iff_add_eq_0
% 5.02/5.32 thf(fact_5284_neg__eq__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( ( uminus_uminus_int @ A )
% 5.02/5.32 = B )
% 5.02/5.32 = ( ( plus_plus_int @ A @ B )
% 5.02/5.32 = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_eq_iff_add_eq_0
% 5.02/5.32 thf(fact_5285_neg__eq__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( ( uminus1482373934393186551omplex @ A )
% 5.02/5.32 = B )
% 5.02/5.32 = ( ( plus_plus_complex @ A @ B )
% 5.02/5.32 = zero_zero_complex ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_eq_iff_add_eq_0
% 5.02/5.32 thf(fact_5286_neg__eq__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( ( uminus_uminus_rat @ A )
% 5.02/5.32 = B )
% 5.02/5.32 = ( ( plus_plus_rat @ A @ B )
% 5.02/5.32 = zero_zero_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_eq_iff_add_eq_0
% 5.02/5.32 thf(fact_5287_neg__eq__iff__add__eq__0,axiom,
% 5.02/5.32 ! [A: code_integer,B: code_integer] :
% 5.02/5.32 ( ( ( uminus1351360451143612070nteger @ A )
% 5.02/5.32 = B )
% 5.02/5.32 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.02/5.32 = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_eq_iff_add_eq_0
% 5.02/5.32 thf(fact_5288_less__minus__one__simps_I4_J,axiom,
% 5.02/5.32 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(4)
% 5.02/5.32 thf(fact_5289_less__minus__one__simps_I4_J,axiom,
% 5.02/5.32 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(4)
% 5.02/5.32 thf(fact_5290_less__minus__one__simps_I4_J,axiom,
% 5.02/5.32 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(4)
% 5.02/5.32 thf(fact_5291_less__minus__one__simps_I4_J,axiom,
% 5.02/5.32 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(4)
% 5.02/5.32 thf(fact_5292_less__minus__one__simps_I2_J,axiom,
% 5.02/5.32 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(2)
% 5.02/5.32 thf(fact_5293_less__minus__one__simps_I2_J,axiom,
% 5.02/5.32 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(2)
% 5.02/5.32 thf(fact_5294_less__minus__one__simps_I2_J,axiom,
% 5.02/5.32 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(2)
% 5.02/5.32 thf(fact_5295_less__minus__one__simps_I2_J,axiom,
% 5.02/5.32 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(2)
% 5.02/5.32 thf(fact_5296_numeral__times__minus__swap,axiom,
% 5.02/5.32 ! [W: num,X2: real] :
% 5.02/5.32 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X2 ) )
% 5.02/5.32 = ( times_times_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_times_minus_swap
% 5.02/5.32 thf(fact_5297_numeral__times__minus__swap,axiom,
% 5.02/5.32 ! [W: num,X2: int] :
% 5.02/5.32 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X2 ) )
% 5.02/5.32 = ( times_times_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_times_minus_swap
% 5.02/5.32 thf(fact_5298_numeral__times__minus__swap,axiom,
% 5.02/5.32 ! [W: num,X2: complex] :
% 5.02/5.32 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.02/5.32 = ( times_times_complex @ X2 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_times_minus_swap
% 5.02/5.32 thf(fact_5299_numeral__times__minus__swap,axiom,
% 5.02/5.32 ! [W: num,X2: rat] :
% 5.02/5.32 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X2 ) )
% 5.02/5.32 = ( times_times_rat @ X2 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_times_minus_swap
% 5.02/5.32 thf(fact_5300_numeral__times__minus__swap,axiom,
% 5.02/5.32 ! [W: num,X2: code_integer] :
% 5.02/5.32 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X2 ) )
% 5.02/5.32 = ( times_3573771949741848930nteger @ X2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_times_minus_swap
% 5.02/5.32 thf(fact_5301_nonzero__minus__divide__divide,axiom,
% 5.02/5.32 ! [B: real,A: real] :
% 5.02/5.32 ( ( B != zero_zero_real )
% 5.02/5.32 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.02/5.32 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_minus_divide_divide
% 5.02/5.32 thf(fact_5302_nonzero__minus__divide__divide,axiom,
% 5.02/5.32 ! [B: complex,A: complex] :
% 5.02/5.32 ( ( B != zero_zero_complex )
% 5.02/5.32 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.32 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_minus_divide_divide
% 5.02/5.32 thf(fact_5303_nonzero__minus__divide__divide,axiom,
% 5.02/5.32 ! [B: rat,A: rat] :
% 5.02/5.32 ( ( B != zero_zero_rat )
% 5.02/5.32 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.02/5.32 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_minus_divide_divide
% 5.02/5.32 thf(fact_5304_nonzero__minus__divide__right,axiom,
% 5.02/5.32 ! [B: real,A: real] :
% 5.02/5.32 ( ( B != zero_zero_real )
% 5.02/5.32 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.32 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_minus_divide_right
% 5.02/5.32 thf(fact_5305_nonzero__minus__divide__right,axiom,
% 5.02/5.32 ! [B: complex,A: complex] :
% 5.02/5.32 ( ( B != zero_zero_complex )
% 5.02/5.32 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.32 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_minus_divide_right
% 5.02/5.32 thf(fact_5306_nonzero__minus__divide__right,axiom,
% 5.02/5.32 ! [B: rat,A: rat] :
% 5.02/5.32 ( ( B != zero_zero_rat )
% 5.02/5.32 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.02/5.32 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_minus_divide_right
% 5.02/5.32 thf(fact_5307_numeral__neq__neg__one,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( ( numeral_numeral_real @ N2 )
% 5.02/5.32 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_one
% 5.02/5.32 thf(fact_5308_numeral__neq__neg__one,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( ( numeral_numeral_int @ N2 )
% 5.02/5.32 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_one
% 5.02/5.32 thf(fact_5309_numeral__neq__neg__one,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( ( numera6690914467698888265omplex @ N2 )
% 5.02/5.32 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_one
% 5.02/5.32 thf(fact_5310_numeral__neq__neg__one,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( ( numeral_numeral_rat @ N2 )
% 5.02/5.32 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_one
% 5.02/5.32 thf(fact_5311_numeral__neq__neg__one,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( ( numera6620942414471956472nteger @ N2 )
% 5.02/5.32 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_neq_neg_one
% 5.02/5.32 thf(fact_5312_one__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( one_one_real
% 5.02/5.32 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_numeral
% 5.02/5.32 thf(fact_5313_one__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( one_one_int
% 5.02/5.32 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_numeral
% 5.02/5.32 thf(fact_5314_one__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( one_one_complex
% 5.02/5.32 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_numeral
% 5.02/5.32 thf(fact_5315_one__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( one_one_rat
% 5.02/5.32 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_numeral
% 5.02/5.32 thf(fact_5316_one__neq__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( one_one_Code_integer
% 5.02/5.32 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % one_neq_neg_numeral
% 5.02/5.32 thf(fact_5317_square__eq__1__iff,axiom,
% 5.02/5.32 ! [X2: real] :
% 5.02/5.32 ( ( ( times_times_real @ X2 @ X2 )
% 5.02/5.32 = one_one_real )
% 5.02/5.32 = ( ( X2 = one_one_real )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_1_iff
% 5.02/5.32 thf(fact_5318_square__eq__1__iff,axiom,
% 5.02/5.32 ! [X2: int] :
% 5.02/5.32 ( ( ( times_times_int @ X2 @ X2 )
% 5.02/5.32 = one_one_int )
% 5.02/5.32 = ( ( X2 = one_one_int )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_1_iff
% 5.02/5.32 thf(fact_5319_square__eq__1__iff,axiom,
% 5.02/5.32 ! [X2: complex] :
% 5.02/5.32 ( ( ( times_times_complex @ X2 @ X2 )
% 5.02/5.32 = one_one_complex )
% 5.02/5.32 = ( ( X2 = one_one_complex )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_1_iff
% 5.02/5.32 thf(fact_5320_square__eq__1__iff,axiom,
% 5.02/5.32 ! [X2: rat] :
% 5.02/5.32 ( ( ( times_times_rat @ X2 @ X2 )
% 5.02/5.32 = one_one_rat )
% 5.02/5.32 = ( ( X2 = one_one_rat )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_1_iff
% 5.02/5.32 thf(fact_5321_square__eq__1__iff,axiom,
% 5.02/5.32 ! [X2: code_integer] :
% 5.02/5.32 ( ( ( times_3573771949741848930nteger @ X2 @ X2 )
% 5.02/5.32 = one_one_Code_integer )
% 5.02/5.32 = ( ( X2 = one_one_Code_integer )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_eq_1_iff
% 5.02/5.32 thf(fact_5322_group__cancel_Osub2,axiom,
% 5.02/5.32 ! [B4: real,K: real,B: real,A: real] :
% 5.02/5.32 ( ( B4
% 5.02/5.32 = ( plus_plus_real @ K @ B ) )
% 5.02/5.32 => ( ( minus_minus_real @ A @ B4 )
% 5.02/5.32 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.sub2
% 5.02/5.32 thf(fact_5323_group__cancel_Osub2,axiom,
% 5.02/5.32 ! [B4: int,K: int,B: int,A: int] :
% 5.02/5.32 ( ( B4
% 5.02/5.32 = ( plus_plus_int @ K @ B ) )
% 5.02/5.32 => ( ( minus_minus_int @ A @ B4 )
% 5.02/5.32 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.sub2
% 5.02/5.32 thf(fact_5324_group__cancel_Osub2,axiom,
% 5.02/5.32 ! [B4: complex,K: complex,B: complex,A: complex] :
% 5.02/5.32 ( ( B4
% 5.02/5.32 = ( plus_plus_complex @ K @ B ) )
% 5.02/5.32 => ( ( minus_minus_complex @ A @ B4 )
% 5.02/5.32 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.sub2
% 5.02/5.32 thf(fact_5325_group__cancel_Osub2,axiom,
% 5.02/5.32 ! [B4: rat,K: rat,B: rat,A: rat] :
% 5.02/5.32 ( ( B4
% 5.02/5.32 = ( plus_plus_rat @ K @ B ) )
% 5.02/5.32 => ( ( minus_minus_rat @ A @ B4 )
% 5.02/5.32 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.sub2
% 5.02/5.32 thf(fact_5326_group__cancel_Osub2,axiom,
% 5.02/5.32 ! [B4: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.02/5.32 ( ( B4
% 5.02/5.32 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.02/5.32 => ( ( minus_8373710615458151222nteger @ A @ B4 )
% 5.02/5.32 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % group_cancel.sub2
% 5.02/5.32 thf(fact_5327_diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_minus_real
% 5.02/5.32 = ( ^ [A5: real,B5: real] : ( plus_plus_real @ A5 @ ( uminus_uminus_real @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % diff_conv_add_uminus
% 5.02/5.32 thf(fact_5328_diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_minus_int
% 5.02/5.32 = ( ^ [A5: int,B5: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % diff_conv_add_uminus
% 5.02/5.32 thf(fact_5329_diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_minus_complex
% 5.02/5.32 = ( ^ [A5: complex,B5: complex] : ( plus_plus_complex @ A5 @ ( uminus1482373934393186551omplex @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % diff_conv_add_uminus
% 5.02/5.32 thf(fact_5330_diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_minus_rat
% 5.02/5.32 = ( ^ [A5: rat,B5: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % diff_conv_add_uminus
% 5.02/5.32 thf(fact_5331_diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_8373710615458151222nteger
% 5.02/5.32 = ( ^ [A5: code_integer,B5: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % diff_conv_add_uminus
% 5.02/5.32 thf(fact_5332_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_minus_real
% 5.02/5.32 = ( ^ [A5: real,B5: real] : ( plus_plus_real @ A5 @ ( uminus_uminus_real @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.02/5.32 thf(fact_5333_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_minus_int
% 5.02/5.32 = ( ^ [A5: int,B5: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.02/5.32 thf(fact_5334_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_minus_complex
% 5.02/5.32 = ( ^ [A5: complex,B5: complex] : ( plus_plus_complex @ A5 @ ( uminus1482373934393186551omplex @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.02/5.32 thf(fact_5335_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_minus_rat
% 5.02/5.32 = ( ^ [A5: rat,B5: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.02/5.32 thf(fact_5336_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.02/5.32 ( minus_8373710615458151222nteger
% 5.02/5.32 = ( ^ [A5: code_integer,B5: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B5 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.02/5.32 thf(fact_5337_dvd__div__neg,axiom,
% 5.02/5.32 ! [B: real,A: real] :
% 5.02/5.32 ( ( dvd_dvd_real @ B @ A )
% 5.02/5.32 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.02/5.32 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_div_neg
% 5.02/5.32 thf(fact_5338_dvd__div__neg,axiom,
% 5.02/5.32 ! [B: int,A: int] :
% 5.02/5.32 ( ( dvd_dvd_int @ B @ A )
% 5.02/5.32 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.32 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_div_neg
% 5.02/5.32 thf(fact_5339_dvd__div__neg,axiom,
% 5.02/5.32 ! [B: complex,A: complex] :
% 5.02/5.32 ( ( dvd_dvd_complex @ B @ A )
% 5.02/5.32 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_div_neg
% 5.02/5.32 thf(fact_5340_dvd__div__neg,axiom,
% 5.02/5.32 ! [B: rat,A: rat] :
% 5.02/5.32 ( ( dvd_dvd_rat @ B @ A )
% 5.02/5.32 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.02/5.32 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_div_neg
% 5.02/5.32 thf(fact_5341_dvd__div__neg,axiom,
% 5.02/5.32 ! [B: code_integer,A: code_integer] :
% 5.02/5.32 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.02/5.32 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_div_neg
% 5.02/5.32 thf(fact_5342_dvd__neg__div,axiom,
% 5.02/5.32 ! [B: real,A: real] :
% 5.02/5.32 ( ( dvd_dvd_real @ B @ A )
% 5.02/5.32 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.02/5.32 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_neg_div
% 5.02/5.32 thf(fact_5343_dvd__neg__div,axiom,
% 5.02/5.32 ! [B: int,A: int] :
% 5.02/5.32 ( ( dvd_dvd_int @ B @ A )
% 5.02/5.32 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.32 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_neg_div
% 5.02/5.32 thf(fact_5344_dvd__neg__div,axiom,
% 5.02/5.32 ! [B: complex,A: complex] :
% 5.02/5.32 ( ( dvd_dvd_complex @ B @ A )
% 5.02/5.32 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_neg_div
% 5.02/5.32 thf(fact_5345_dvd__neg__div,axiom,
% 5.02/5.32 ! [B: rat,A: rat] :
% 5.02/5.32 ( ( dvd_dvd_rat @ B @ A )
% 5.02/5.32 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.02/5.32 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_neg_div
% 5.02/5.32 thf(fact_5346_dvd__neg__div,axiom,
% 5.02/5.32 ! [B: code_integer,A: code_integer] :
% 5.02/5.32 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.02/5.32 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % dvd_neg_div
% 5.02/5.32 thf(fact_5347_subset__Compl__self__eq,axiom,
% 5.02/5.32 ! [A3: set_int] :
% 5.02/5.32 ( ( ord_less_eq_set_int @ A3 @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.02/5.32 = ( A3 = bot_bot_set_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % subset_Compl_self_eq
% 5.02/5.32 thf(fact_5348_subset__Compl__self__eq,axiom,
% 5.02/5.32 ! [A3: set_real] :
% 5.02/5.32 ( ( ord_less_eq_set_real @ A3 @ ( uminus612125837232591019t_real @ A3 ) )
% 5.02/5.32 = ( A3 = bot_bot_set_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % subset_Compl_self_eq
% 5.02/5.32 thf(fact_5349_subset__Compl__self__eq,axiom,
% 5.02/5.32 ! [A3: set_nat] :
% 5.02/5.32 ( ( ord_less_eq_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.02/5.32 = ( A3 = bot_bot_set_nat ) ) ).
% 5.02/5.32
% 5.02/5.32 % subset_Compl_self_eq
% 5.02/5.32 thf(fact_5350_real__minus__mult__self__le,axiom,
% 5.02/5.32 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X2 @ X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_minus_mult_self_le
% 5.02/5.32 thf(fact_5351_zmult__eq__1__iff,axiom,
% 5.02/5.32 ! [M: int,N2: int] :
% 5.02/5.32 ( ( ( times_times_int @ M @ N2 )
% 5.02/5.32 = one_one_int )
% 5.02/5.32 = ( ( ( M = one_one_int )
% 5.02/5.32 & ( N2 = one_one_int ) )
% 5.02/5.32 | ( ( M
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.32 & ( N2
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zmult_eq_1_iff
% 5.02/5.32 thf(fact_5352_pos__zmult__eq__1__iff__lemma,axiom,
% 5.02/5.32 ! [M: int,N2: int] :
% 5.02/5.32 ( ( ( times_times_int @ M @ N2 )
% 5.02/5.32 = one_one_int )
% 5.02/5.32 => ( ( M = one_one_int )
% 5.02/5.32 | ( M
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_zmult_eq_1_iff_lemma
% 5.02/5.32 thf(fact_5353_minus__int__code_I2_J,axiom,
% 5.02/5.32 ! [L: int] :
% 5.02/5.32 ( ( minus_minus_int @ zero_zero_int @ L )
% 5.02/5.32 = ( uminus_uminus_int @ L ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_int_code(2)
% 5.02/5.32 thf(fact_5354_zmod__zminus2__not__zero,axiom,
% 5.02/5.32 ! [K: int,L: int] :
% 5.02/5.32 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 5.02/5.32 != zero_zero_int )
% 5.02/5.32 => ( ( modulo_modulo_int @ K @ L )
% 5.02/5.32 != zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % zmod_zminus2_not_zero
% 5.02/5.32 thf(fact_5355_zmod__zminus1__not__zero,axiom,
% 5.02/5.32 ! [K: int,L: int] :
% 5.02/5.32 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.02/5.32 != zero_zero_int )
% 5.02/5.32 => ( ( modulo_modulo_int @ K @ L )
% 5.02/5.32 != zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % zmod_zminus1_not_zero
% 5.02/5.32 thf(fact_5356_minus__real__def,axiom,
% 5.02/5.32 ( minus_minus_real
% 5.02/5.32 = ( ^ [X: real,Y6: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y6 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_real_def
% 5.02/5.32 thf(fact_5357_neg__numeral__le__zero,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_zero
% 5.02/5.32 thf(fact_5358_neg__numeral__le__zero,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_zero
% 5.02/5.32 thf(fact_5359_neg__numeral__le__zero,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_zero
% 5.02/5.32 thf(fact_5360_neg__numeral__le__zero,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_zero
% 5.02/5.32 thf(fact_5361_not__zero__le__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_zero_le_neg_numeral
% 5.02/5.32 thf(fact_5362_not__zero__le__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_zero_le_neg_numeral
% 5.02/5.32 thf(fact_5363_not__zero__le__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_zero_le_neg_numeral
% 5.02/5.32 thf(fact_5364_not__zero__le__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_zero_le_neg_numeral
% 5.02/5.32 thf(fact_5365_neg__numeral__less__zero,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_zero
% 5.02/5.32 thf(fact_5366_neg__numeral__less__zero,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_zero
% 5.02/5.32 thf(fact_5367_neg__numeral__less__zero,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_zero
% 5.02/5.32 thf(fact_5368_neg__numeral__less__zero,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_zero
% 5.02/5.32 thf(fact_5369_not__zero__less__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_zero_less_neg_numeral
% 5.02/5.32 thf(fact_5370_not__zero__less__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_zero_less_neg_numeral
% 5.02/5.32 thf(fact_5371_not__zero__less__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_zero_less_neg_numeral
% 5.02/5.32 thf(fact_5372_not__zero__less__neg__numeral,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_zero_less_neg_numeral
% 5.02/5.32 thf(fact_5373_le__minus__one__simps_I3_J,axiom,
% 5.02/5.32 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(3)
% 5.02/5.32 thf(fact_5374_le__minus__one__simps_I3_J,axiom,
% 5.02/5.32 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(3)
% 5.02/5.32 thf(fact_5375_le__minus__one__simps_I3_J,axiom,
% 5.02/5.32 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(3)
% 5.02/5.32 thf(fact_5376_le__minus__one__simps_I3_J,axiom,
% 5.02/5.32 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(3)
% 5.02/5.32 thf(fact_5377_le__minus__one__simps_I1_J,axiom,
% 5.02/5.32 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(1)
% 5.02/5.32 thf(fact_5378_le__minus__one__simps_I1_J,axiom,
% 5.02/5.32 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(1)
% 5.02/5.32 thf(fact_5379_le__minus__one__simps_I1_J,axiom,
% 5.02/5.32 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(1)
% 5.02/5.32 thf(fact_5380_le__minus__one__simps_I1_J,axiom,
% 5.02/5.32 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.02/5.32
% 5.02/5.32 % le_minus_one_simps(1)
% 5.02/5.32 thf(fact_5381_less__minus__one__simps_I3_J,axiom,
% 5.02/5.32 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(3)
% 5.02/5.32 thf(fact_5382_less__minus__one__simps_I3_J,axiom,
% 5.02/5.32 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(3)
% 5.02/5.32 thf(fact_5383_less__minus__one__simps_I3_J,axiom,
% 5.02/5.32 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(3)
% 5.02/5.32 thf(fact_5384_less__minus__one__simps_I3_J,axiom,
% 5.02/5.32 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(3)
% 5.02/5.32 thf(fact_5385_less__minus__one__simps_I1_J,axiom,
% 5.02/5.32 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(1)
% 5.02/5.32 thf(fact_5386_less__minus__one__simps_I1_J,axiom,
% 5.02/5.32 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(1)
% 5.02/5.32 thf(fact_5387_less__minus__one__simps_I1_J,axiom,
% 5.02/5.32 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(1)
% 5.02/5.32 thf(fact_5388_less__minus__one__simps_I1_J,axiom,
% 5.02/5.32 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.02/5.32
% 5.02/5.32 % less_minus_one_simps(1)
% 5.02/5.32 thf(fact_5389_neg__numeral__le__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_one
% 5.02/5.32 thf(fact_5390_neg__numeral__le__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_one
% 5.02/5.32 thf(fact_5391_neg__numeral__le__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_one
% 5.02/5.32 thf(fact_5392_neg__numeral__le__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_one
% 5.02/5.32 thf(fact_5393_neg__one__le__numeral,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_le_numeral
% 5.02/5.32 thf(fact_5394_neg__one__le__numeral,axiom,
% 5.02/5.32 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_le_numeral
% 5.02/5.32 thf(fact_5395_neg__one__le__numeral,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_le_numeral
% 5.02/5.32 thf(fact_5396_neg__one__le__numeral,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_le_numeral
% 5.02/5.32 thf(fact_5397_neg__numeral__le__neg__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_neg_one
% 5.02/5.32 thf(fact_5398_neg__numeral__le__neg__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_neg_one
% 5.02/5.32 thf(fact_5399_neg__numeral__le__neg__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_neg_one
% 5.02/5.32 thf(fact_5400_neg__numeral__le__neg__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_le_neg_one
% 5.02/5.32 thf(fact_5401_not__numeral__le__neg__one,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_le_neg_one
% 5.02/5.32 thf(fact_5402_not__numeral__le__neg__one,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_le_neg_one
% 5.02/5.32 thf(fact_5403_not__numeral__le__neg__one,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_le_neg_one
% 5.02/5.32 thf(fact_5404_not__numeral__le__neg__one,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_le_neg_one
% 5.02/5.32 thf(fact_5405_not__one__le__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_one_le_neg_numeral
% 5.02/5.32 thf(fact_5406_not__one__le__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_one_le_neg_numeral
% 5.02/5.32 thf(fact_5407_not__one__le__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_one_le_neg_numeral
% 5.02/5.32 thf(fact_5408_not__one__le__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_one_le_neg_numeral
% 5.02/5.32 thf(fact_5409_neg__numeral__less__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_one
% 5.02/5.32 thf(fact_5410_neg__numeral__less__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_one
% 5.02/5.32 thf(fact_5411_neg__numeral__less__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_one
% 5.02/5.32 thf(fact_5412_neg__numeral__less__one,axiom,
% 5.02/5.32 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_less_one
% 5.02/5.32 thf(fact_5413_neg__one__less__numeral,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_less_numeral
% 5.02/5.32 thf(fact_5414_neg__one__less__numeral,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_less_numeral
% 5.02/5.32 thf(fact_5415_neg__one__less__numeral,axiom,
% 5.02/5.32 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_less_numeral
% 5.02/5.32 thf(fact_5416_neg__one__less__numeral,axiom,
% 5.02/5.32 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_less_numeral
% 5.02/5.32 thf(fact_5417_not__numeral__less__neg__one,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_less_neg_one
% 5.02/5.32 thf(fact_5418_not__numeral__less__neg__one,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_less_neg_one
% 5.02/5.32 thf(fact_5419_not__numeral__less__neg__one,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_less_neg_one
% 5.02/5.32 thf(fact_5420_not__numeral__less__neg__one,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_numeral_less_neg_one
% 5.02/5.32 thf(fact_5421_not__one__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_one_less_neg_numeral
% 5.02/5.32 thf(fact_5422_not__one__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_one_less_neg_numeral
% 5.02/5.32 thf(fact_5423_not__one__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_one_less_neg_numeral
% 5.02/5.32 thf(fact_5424_not__one__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_one_less_neg_numeral
% 5.02/5.32 thf(fact_5425_not__neg__one__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_neg_one_less_neg_numeral
% 5.02/5.32 thf(fact_5426_not__neg__one__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_neg_one_less_neg_numeral
% 5.02/5.32 thf(fact_5427_not__neg__one__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_neg_one_less_neg_numeral
% 5.02/5.32 thf(fact_5428_not__neg__one__less__neg__numeral,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % not_neg_one_less_neg_numeral
% 5.02/5.32 thf(fact_5429_nonzero__neg__divide__eq__eq2,axiom,
% 5.02/5.32 ! [B: real,C: real,A: real] :
% 5.02/5.32 ( ( B != zero_zero_real )
% 5.02/5.32 => ( ( C
% 5.02/5.32 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.02/5.32 = ( ( times_times_real @ C @ B )
% 5.02/5.32 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_neg_divide_eq_eq2
% 5.02/5.32 thf(fact_5430_nonzero__neg__divide__eq__eq2,axiom,
% 5.02/5.32 ! [B: complex,C: complex,A: complex] :
% 5.02/5.32 ( ( B != zero_zero_complex )
% 5.02/5.32 => ( ( C
% 5.02/5.32 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.02/5.32 = ( ( times_times_complex @ C @ B )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_neg_divide_eq_eq2
% 5.02/5.32 thf(fact_5431_nonzero__neg__divide__eq__eq2,axiom,
% 5.02/5.32 ! [B: rat,C: rat,A: rat] :
% 5.02/5.32 ( ( B != zero_zero_rat )
% 5.02/5.32 => ( ( C
% 5.02/5.32 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.02/5.32 = ( ( times_times_rat @ C @ B )
% 5.02/5.32 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_neg_divide_eq_eq2
% 5.02/5.32 thf(fact_5432_nonzero__neg__divide__eq__eq,axiom,
% 5.02/5.32 ! [B: real,A: real,C: real] :
% 5.02/5.32 ( ( B != zero_zero_real )
% 5.02/5.32 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.32 = C )
% 5.02/5.32 = ( ( uminus_uminus_real @ A )
% 5.02/5.32 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_neg_divide_eq_eq
% 5.02/5.32 thf(fact_5433_nonzero__neg__divide__eq__eq,axiom,
% 5.02/5.32 ! [B: complex,A: complex,C: complex] :
% 5.02/5.32 ( ( B != zero_zero_complex )
% 5.02/5.32 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.32 = C )
% 5.02/5.32 = ( ( uminus1482373934393186551omplex @ A )
% 5.02/5.32 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_neg_divide_eq_eq
% 5.02/5.32 thf(fact_5434_nonzero__neg__divide__eq__eq,axiom,
% 5.02/5.32 ! [B: rat,A: rat,C: rat] :
% 5.02/5.32 ( ( B != zero_zero_rat )
% 5.02/5.32 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.02/5.32 = C )
% 5.02/5.32 = ( ( uminus_uminus_rat @ A )
% 5.02/5.32 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % nonzero_neg_divide_eq_eq
% 5.02/5.32 thf(fact_5435_minus__divide__eq__eq,axiom,
% 5.02/5.32 ! [B: real,C: real,A: real] :
% 5.02/5.32 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.02/5.32 = A )
% 5.02/5.32 = ( ( ( C != zero_zero_real )
% 5.02/5.32 => ( ( uminus_uminus_real @ B )
% 5.02/5.32 = ( times_times_real @ A @ C ) ) )
% 5.02/5.32 & ( ( C = zero_zero_real )
% 5.02/5.32 => ( A = zero_zero_real ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_eq_eq
% 5.02/5.32 thf(fact_5436_minus__divide__eq__eq,axiom,
% 5.02/5.32 ! [B: complex,C: complex,A: complex] :
% 5.02/5.32 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.02/5.32 = A )
% 5.02/5.32 = ( ( ( C != zero_zero_complex )
% 5.02/5.32 => ( ( uminus1482373934393186551omplex @ B )
% 5.02/5.32 = ( times_times_complex @ A @ C ) ) )
% 5.02/5.32 & ( ( C = zero_zero_complex )
% 5.02/5.32 => ( A = zero_zero_complex ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_eq_eq
% 5.02/5.32 thf(fact_5437_minus__divide__eq__eq,axiom,
% 5.02/5.32 ! [B: rat,C: rat,A: rat] :
% 5.02/5.32 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.02/5.32 = A )
% 5.02/5.32 = ( ( ( C != zero_zero_rat )
% 5.02/5.32 => ( ( uminus_uminus_rat @ B )
% 5.02/5.32 = ( times_times_rat @ A @ C ) ) )
% 5.02/5.32 & ( ( C = zero_zero_rat )
% 5.02/5.32 => ( A = zero_zero_rat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_eq_eq
% 5.02/5.32 thf(fact_5438_eq__minus__divide__eq,axiom,
% 5.02/5.32 ! [A: real,B: real,C: real] :
% 5.02/5.32 ( ( A
% 5.02/5.32 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.02/5.32 = ( ( ( C != zero_zero_real )
% 5.02/5.32 => ( ( times_times_real @ A @ C )
% 5.02/5.32 = ( uminus_uminus_real @ B ) ) )
% 5.02/5.32 & ( ( C = zero_zero_real )
% 5.02/5.32 => ( A = zero_zero_real ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_minus_divide_eq
% 5.02/5.32 thf(fact_5439_eq__minus__divide__eq,axiom,
% 5.02/5.32 ! [A: complex,B: complex,C: complex] :
% 5.02/5.32 ( ( A
% 5.02/5.32 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.02/5.32 = ( ( ( C != zero_zero_complex )
% 5.02/5.32 => ( ( times_times_complex @ A @ C )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.02/5.32 & ( ( C = zero_zero_complex )
% 5.02/5.32 => ( A = zero_zero_complex ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_minus_divide_eq
% 5.02/5.32 thf(fact_5440_eq__minus__divide__eq,axiom,
% 5.02/5.32 ! [A: rat,B: rat,C: rat] :
% 5.02/5.32 ( ( A
% 5.02/5.32 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.02/5.32 = ( ( ( C != zero_zero_rat )
% 5.02/5.32 => ( ( times_times_rat @ A @ C )
% 5.02/5.32 = ( uminus_uminus_rat @ B ) ) )
% 5.02/5.32 & ( ( C = zero_zero_rat )
% 5.02/5.32 => ( A = zero_zero_rat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_minus_divide_eq
% 5.02/5.32 thf(fact_5441_mult__1s__ring__1_I2_J,axiom,
% 5.02/5.32 ! [B: real] :
% 5.02/5.32 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.02/5.32 = ( uminus_uminus_real @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(2)
% 5.02/5.32 thf(fact_5442_mult__1s__ring__1_I2_J,axiom,
% 5.02/5.32 ! [B: int] :
% 5.02/5.32 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.02/5.32 = ( uminus_uminus_int @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(2)
% 5.02/5.32 thf(fact_5443_mult__1s__ring__1_I2_J,axiom,
% 5.02/5.32 ! [B: complex] :
% 5.02/5.32 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(2)
% 5.02/5.32 thf(fact_5444_mult__1s__ring__1_I2_J,axiom,
% 5.02/5.32 ! [B: rat] :
% 5.02/5.32 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.02/5.32 = ( uminus_uminus_rat @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(2)
% 5.02/5.32 thf(fact_5445_mult__1s__ring__1_I2_J,axiom,
% 5.02/5.32 ! [B: code_integer] :
% 5.02/5.32 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(2)
% 5.02/5.32 thf(fact_5446_mult__1s__ring__1_I1_J,axiom,
% 5.02/5.32 ! [B: real] :
% 5.02/5.32 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.02/5.32 = ( uminus_uminus_real @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(1)
% 5.02/5.32 thf(fact_5447_mult__1s__ring__1_I1_J,axiom,
% 5.02/5.32 ! [B: int] :
% 5.02/5.32 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.02/5.32 = ( uminus_uminus_int @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(1)
% 5.02/5.32 thf(fact_5448_mult__1s__ring__1_I1_J,axiom,
% 5.02/5.32 ! [B: complex] :
% 5.02/5.32 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(1)
% 5.02/5.32 thf(fact_5449_mult__1s__ring__1_I1_J,axiom,
% 5.02/5.32 ! [B: rat] :
% 5.02/5.32 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.02/5.32 = ( uminus_uminus_rat @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(1)
% 5.02/5.32 thf(fact_5450_mult__1s__ring__1_I1_J,axiom,
% 5.02/5.32 ! [B: code_integer] :
% 5.02/5.32 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % mult_1s_ring_1(1)
% 5.02/5.32 thf(fact_5451_divide__eq__minus__1__iff,axiom,
% 5.02/5.32 ! [A: real,B: real] :
% 5.02/5.32 ( ( ( divide_divide_real @ A @ B )
% 5.02/5.32 = ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.32 = ( ( B != zero_zero_real )
% 5.02/5.32 & ( A
% 5.02/5.32 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_eq_minus_1_iff
% 5.02/5.32 thf(fact_5452_divide__eq__minus__1__iff,axiom,
% 5.02/5.32 ! [A: complex,B: complex] :
% 5.02/5.32 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.32 = ( ( B != zero_zero_complex )
% 5.02/5.32 & ( A
% 5.02/5.32 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_eq_minus_1_iff
% 5.02/5.32 thf(fact_5453_divide__eq__minus__1__iff,axiom,
% 5.02/5.32 ! [A: rat,B: rat] :
% 5.02/5.32 ( ( ( divide_divide_rat @ A @ B )
% 5.02/5.32 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.32 = ( ( B != zero_zero_rat )
% 5.02/5.32 & ( A
% 5.02/5.32 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_eq_minus_1_iff
% 5.02/5.32 thf(fact_5454_uminus__numeral__One,axiom,
% 5.02/5.32 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.02/5.32 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_numeral_One
% 5.02/5.32 thf(fact_5455_uminus__numeral__One,axiom,
% 5.02/5.32 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_numeral_One
% 5.02/5.32 thf(fact_5456_uminus__numeral__One,axiom,
% 5.02/5.32 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_numeral_One
% 5.02/5.32 thf(fact_5457_uminus__numeral__One,axiom,
% 5.02/5.32 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.02/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_numeral_One
% 5.02/5.32 thf(fact_5458_uminus__numeral__One,axiom,
% 5.02/5.32 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_numeral_One
% 5.02/5.32 thf(fact_5459_power__minus,axiom,
% 5.02/5.32 ! [A: real,N2: nat] :
% 5.02/5.32 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.02/5.32 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus
% 5.02/5.32 thf(fact_5460_power__minus,axiom,
% 5.02/5.32 ! [A: int,N2: nat] :
% 5.02/5.32 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.02/5.32 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus
% 5.02/5.32 thf(fact_5461_power__minus,axiom,
% 5.02/5.32 ! [A: complex,N2: nat] :
% 5.02/5.32 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.02/5.32 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus
% 5.02/5.32 thf(fact_5462_power__minus,axiom,
% 5.02/5.32 ! [A: rat,N2: nat] :
% 5.02/5.32 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.02/5.32 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus
% 5.02/5.32 thf(fact_5463_power__minus,axiom,
% 5.02/5.32 ! [A: code_integer,N2: nat] :
% 5.02/5.32 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.02/5.32 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus
% 5.02/5.32 thf(fact_5464_bset_I1_J,axiom,
% 5.02/5.32 ! [D4: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.02/5.32 ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ B4 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( P @ X5 )
% 5.02/5.32 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ B4 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( Q @ X5 )
% 5.02/5.32 => ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ( P @ X3 )
% 5.02/5.32 & ( Q @ X3 ) )
% 5.02/5.32 => ( ( P @ ( minus_minus_int @ X3 @ D4 ) )
% 5.02/5.32 & ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(1)
% 5.02/5.32 thf(fact_5465_bset_I2_J,axiom,
% 5.02/5.32 ! [D4: int,B4: set_int,P: int > $o,Q: int > $o] :
% 5.02/5.32 ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ B4 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( P @ X5 )
% 5.02/5.32 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ B4 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( Q @ X5 )
% 5.02/5.32 => ( Q @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ( P @ X3 )
% 5.02/5.32 | ( Q @ X3 ) )
% 5.02/5.32 => ( ( P @ ( minus_minus_int @ X3 @ D4 ) )
% 5.02/5.32 | ( Q @ ( minus_minus_int @ X3 @ D4 ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(2)
% 5.02/5.32 thf(fact_5466_aset_I1_J,axiom,
% 5.02/5.32 ! [D4: int,A3: set_int,P: int > $o,Q: int > $o] :
% 5.02/5.32 ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ A3 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( P @ X5 )
% 5.02/5.32 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ A3 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( Q @ X5 )
% 5.02/5.32 => ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ( P @ X3 )
% 5.02/5.32 & ( Q @ X3 ) )
% 5.02/5.32 => ( ( P @ ( plus_plus_int @ X3 @ D4 ) )
% 5.02/5.32 & ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(1)
% 5.02/5.32 thf(fact_5467_aset_I2_J,axiom,
% 5.02/5.32 ! [D4: int,A3: set_int,P: int > $o,Q: int > $o] :
% 5.02/5.32 ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ A3 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( P @ X5 )
% 5.02/5.32 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ A3 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( Q @ X5 )
% 5.02/5.32 => ( Q @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ( P @ X3 )
% 5.02/5.32 | ( Q @ X3 ) )
% 5.02/5.32 => ( ( P @ ( plus_plus_int @ X3 @ D4 ) )
% 5.02/5.32 | ( Q @ ( plus_plus_int @ X3 @ D4 ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(2)
% 5.02/5.32 thf(fact_5468_power__minus__Bit0,axiom,
% 5.02/5.32 ! [X2: real,K: num] :
% 5.02/5.32 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.02/5.32 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus_Bit0
% 5.02/5.32 thf(fact_5469_power__minus__Bit0,axiom,
% 5.02/5.32 ! [X2: int,K: num] :
% 5.02/5.32 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.02/5.32 = ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus_Bit0
% 5.02/5.32 thf(fact_5470_power__minus__Bit0,axiom,
% 5.02/5.32 ! [X2: complex,K: num] :
% 5.02/5.32 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.02/5.32 = ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus_Bit0
% 5.02/5.32 thf(fact_5471_power__minus__Bit0,axiom,
% 5.02/5.32 ! [X2: rat,K: num] :
% 5.02/5.32 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.02/5.32 = ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus_Bit0
% 5.02/5.32 thf(fact_5472_power__minus__Bit0,axiom,
% 5.02/5.32 ! [X2: code_integer,K: num] :
% 5.02/5.32 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.02/5.32 = ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus_Bit0
% 5.02/5.32 thf(fact_5473_real__0__less__add__iff,axiom,
% 5.02/5.32 ! [X2: real,Y: real] :
% 5.02/5.32 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.02/5.32 = ( ord_less_real @ ( uminus_uminus_real @ X2 ) @ Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_0_less_add_iff
% 5.02/5.32 thf(fact_5474_real__add__less__0__iff,axiom,
% 5.02/5.32 ! [X2: real,Y: real] :
% 5.02/5.32 ( ( ord_less_real @ ( plus_plus_real @ X2 @ Y ) @ zero_zero_real )
% 5.02/5.32 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_add_less_0_iff
% 5.02/5.32 thf(fact_5475_real__add__le__0__iff,axiom,
% 5.02/5.32 ! [X2: real,Y: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( plus_plus_real @ X2 @ Y ) @ zero_zero_real )
% 5.02/5.32 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_add_le_0_iff
% 5.02/5.32 thf(fact_5476_real__0__le__add__iff,axiom,
% 5.02/5.32 ! [X2: real,Y: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.02/5.32 = ( ord_less_eq_real @ ( uminus_uminus_real @ X2 ) @ Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_0_le_add_iff
% 5.02/5.32 thf(fact_5477_zmod__zminus1__eq__if,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.32 = zero_zero_int ) )
% 5.02/5.32 & ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 != zero_zero_int )
% 5.02/5.32 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.32 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zmod_zminus1_eq_if
% 5.02/5.32 thf(fact_5478_zmod__zminus2__eq__if,axiom,
% 5.02/5.32 ! [A: int,B: int] :
% 5.02/5.32 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.32 = zero_zero_int ) )
% 5.02/5.32 & ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 != zero_zero_int )
% 5.02/5.32 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.32 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zmod_zminus2_eq_if
% 5.02/5.32 thf(fact_5479_less__minus__divide__eq,axiom,
% 5.02/5.32 ! [A: real,B: real,C: real] :
% 5.02/5.32 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.02/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_divide_eq
% 5.02/5.32 thf(fact_5480_less__minus__divide__eq,axiom,
% 5.02/5.32 ! [A: rat,B: rat,C: rat] :
% 5.02/5.32 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.02/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_minus_divide_eq
% 5.02/5.32 thf(fact_5481_minus__divide__less__eq,axiom,
% 5.02/5.32 ! [B: real,C: real,A: real] :
% 5.02/5.32 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.02/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_less_eq
% 5.02/5.32 thf(fact_5482_minus__divide__less__eq,axiom,
% 5.02/5.32 ! [B: rat,C: rat,A: rat] :
% 5.02/5.32 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.02/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_less_eq
% 5.02/5.32 thf(fact_5483_neg__less__minus__divide__eq,axiom,
% 5.02/5.32 ! [C: real,A: real,B: real] :
% 5.02/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.02/5.32 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_less_minus_divide_eq
% 5.02/5.32 thf(fact_5484_neg__less__minus__divide__eq,axiom,
% 5.02/5.32 ! [C: rat,A: rat,B: rat] :
% 5.02/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.02/5.32 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_less_minus_divide_eq
% 5.02/5.32 thf(fact_5485_neg__minus__divide__less__eq,axiom,
% 5.02/5.32 ! [C: real,B: real,A: real] :
% 5.02/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.02/5.32 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_minus_divide_less_eq
% 5.02/5.32 thf(fact_5486_neg__minus__divide__less__eq,axiom,
% 5.02/5.32 ! [C: rat,B: rat,A: rat] :
% 5.02/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.02/5.32 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_minus_divide_less_eq
% 5.02/5.32 thf(fact_5487_pos__less__minus__divide__eq,axiom,
% 5.02/5.32 ! [C: real,A: real,B: real] :
% 5.02/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.02/5.32 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_less_minus_divide_eq
% 5.02/5.32 thf(fact_5488_pos__less__minus__divide__eq,axiom,
% 5.02/5.32 ! [C: rat,A: rat,B: rat] :
% 5.02/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.02/5.32 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_less_minus_divide_eq
% 5.02/5.32 thf(fact_5489_pos__minus__divide__less__eq,axiom,
% 5.02/5.32 ! [C: real,B: real,A: real] :
% 5.02/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.02/5.32 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_minus_divide_less_eq
% 5.02/5.32 thf(fact_5490_pos__minus__divide__less__eq,axiom,
% 5.02/5.32 ! [C: rat,B: rat,A: rat] :
% 5.02/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.02/5.32 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_minus_divide_less_eq
% 5.02/5.32 thf(fact_5491_divide__eq__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [B: real,C: real,W: num] :
% 5.02/5.32 ( ( ( divide_divide_real @ B @ C )
% 5.02/5.32 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.32 = ( ( ( C != zero_zero_real )
% 5.02/5.32 => ( B
% 5.02/5.32 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ( C = zero_zero_real )
% 5.02/5.32 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.32 = zero_zero_real ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_eq_eq_numeral(2)
% 5.02/5.32 thf(fact_5492_divide__eq__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [B: complex,C: complex,W: num] :
% 5.02/5.32 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.02/5.32 = ( ( ( C != zero_zero_complex )
% 5.02/5.32 => ( B
% 5.02/5.32 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ( C = zero_zero_complex )
% 5.02/5.32 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.32 = zero_zero_complex ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_eq_eq_numeral(2)
% 5.02/5.32 thf(fact_5493_divide__eq__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [B: rat,C: rat,W: num] :
% 5.02/5.32 ( ( ( divide_divide_rat @ B @ C )
% 5.02/5.32 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.02/5.32 = ( ( ( C != zero_zero_rat )
% 5.02/5.32 => ( B
% 5.02/5.32 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ( C = zero_zero_rat )
% 5.02/5.32 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.02/5.32 = zero_zero_rat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_eq_eq_numeral(2)
% 5.02/5.32 thf(fact_5494_eq__divide__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [W: num,B: real,C: real] :
% 5.02/5.32 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.32 = ( divide_divide_real @ B @ C ) )
% 5.02/5.32 = ( ( ( C != zero_zero_real )
% 5.02/5.32 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.02/5.32 = B ) )
% 5.02/5.32 & ( ( C = zero_zero_real )
% 5.02/5.32 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.32 = zero_zero_real ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_divide_eq_numeral(2)
% 5.02/5.32 thf(fact_5495_eq__divide__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [W: num,B: complex,C: complex] :
% 5.02/5.32 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.32 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.02/5.32 = ( ( ( C != zero_zero_complex )
% 5.02/5.32 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.02/5.32 = B ) )
% 5.02/5.32 & ( ( C = zero_zero_complex )
% 5.02/5.32 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.32 = zero_zero_complex ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_divide_eq_numeral(2)
% 5.02/5.32 thf(fact_5496_eq__divide__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [W: num,B: rat,C: rat] :
% 5.02/5.32 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.02/5.32 = ( divide_divide_rat @ B @ C ) )
% 5.02/5.32 = ( ( ( C != zero_zero_rat )
% 5.02/5.32 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.02/5.32 = B ) )
% 5.02/5.32 & ( ( C = zero_zero_rat )
% 5.02/5.32 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.02/5.32 = zero_zero_rat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % eq_divide_eq_numeral(2)
% 5.02/5.32 thf(fact_5497_subset__decode__imp__le,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 5.02/5.32 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % subset_decode_imp_le
% 5.02/5.32 thf(fact_5498_add__divide__eq__if__simps_I3_J,axiom,
% 5.02/5.32 ! [Z: real,A: real,B: real] :
% 5.02/5.32 ( ( ( Z = zero_zero_real )
% 5.02/5.32 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.02/5.32 = B ) )
% 5.02/5.32 & ( ( Z != zero_zero_real )
% 5.02/5.32 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.02/5.32 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(3)
% 5.02/5.32 thf(fact_5499_add__divide__eq__if__simps_I3_J,axiom,
% 5.02/5.32 ! [Z: complex,A: complex,B: complex] :
% 5.02/5.32 ( ( ( Z = zero_zero_complex )
% 5.02/5.32 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.02/5.32 = B ) )
% 5.02/5.32 & ( ( Z != zero_zero_complex )
% 5.02/5.32 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.02/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(3)
% 5.02/5.32 thf(fact_5500_add__divide__eq__if__simps_I3_J,axiom,
% 5.02/5.32 ! [Z: rat,A: rat,B: rat] :
% 5.02/5.32 ( ( ( Z = zero_zero_rat )
% 5.02/5.32 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.02/5.32 = B ) )
% 5.02/5.32 & ( ( Z != zero_zero_rat )
% 5.02/5.32 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.02/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(3)
% 5.02/5.32 thf(fact_5501_minus__divide__add__eq__iff,axiom,
% 5.02/5.32 ! [Z: real,X2: real,Y: real] :
% 5.02/5.32 ( ( Z != zero_zero_real )
% 5.02/5.32 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y )
% 5.02/5.32 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_add_eq_iff
% 5.02/5.32 thf(fact_5502_minus__divide__add__eq__iff,axiom,
% 5.02/5.32 ! [Z: complex,X2: complex,Y: complex] :
% 5.02/5.32 ( ( Z != zero_zero_complex )
% 5.02/5.32 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y )
% 5.02/5.32 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_add_eq_iff
% 5.02/5.32 thf(fact_5503_minus__divide__add__eq__iff,axiom,
% 5.02/5.32 ! [Z: rat,X2: rat,Y: rat] :
% 5.02/5.32 ( ( Z != zero_zero_rat )
% 5.02/5.32 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y )
% 5.02/5.32 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_add_eq_iff
% 5.02/5.32 thf(fact_5504_minus__divide__diff__eq__iff,axiom,
% 5.02/5.32 ! [Z: real,X2: real,Y: real] :
% 5.02/5.32 ( ( Z != zero_zero_real )
% 5.02/5.32 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X2 @ Z ) ) @ Y )
% 5.02/5.32 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_diff_eq_iff
% 5.02/5.32 thf(fact_5505_minus__divide__diff__eq__iff,axiom,
% 5.02/5.32 ! [Z: complex,X2: complex,Y: complex] :
% 5.02/5.32 ( ( Z != zero_zero_complex )
% 5.02/5.32 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X2 @ Z ) ) @ Y )
% 5.02/5.32 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_diff_eq_iff
% 5.02/5.32 thf(fact_5506_minus__divide__diff__eq__iff,axiom,
% 5.02/5.32 ! [Z: rat,X2: rat,Y: rat] :
% 5.02/5.32 ( ( Z != zero_zero_rat )
% 5.02/5.32 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X2 @ Z ) ) @ Y )
% 5.02/5.32 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X2 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_diff_eq_iff
% 5.02/5.32 thf(fact_5507_add__divide__eq__if__simps_I5_J,axiom,
% 5.02/5.32 ! [Z: real,A: real,B: real] :
% 5.02/5.32 ( ( ( Z = zero_zero_real )
% 5.02/5.32 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.02/5.32 = ( uminus_uminus_real @ B ) ) )
% 5.02/5.32 & ( ( Z != zero_zero_real )
% 5.02/5.32 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.02/5.32 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(5)
% 5.02/5.32 thf(fact_5508_add__divide__eq__if__simps_I5_J,axiom,
% 5.02/5.32 ! [Z: complex,A: complex,B: complex] :
% 5.02/5.32 ( ( ( Z = zero_zero_complex )
% 5.02/5.32 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.02/5.32 & ( ( Z != zero_zero_complex )
% 5.02/5.32 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.02/5.32 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(5)
% 5.02/5.32 thf(fact_5509_add__divide__eq__if__simps_I5_J,axiom,
% 5.02/5.32 ! [Z: rat,A: rat,B: rat] :
% 5.02/5.32 ( ( ( Z = zero_zero_rat )
% 5.02/5.32 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.02/5.32 = ( uminus_uminus_rat @ B ) ) )
% 5.02/5.32 & ( ( Z != zero_zero_rat )
% 5.02/5.32 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.02/5.32 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(5)
% 5.02/5.32 thf(fact_5510_add__divide__eq__if__simps_I6_J,axiom,
% 5.02/5.32 ! [Z: real,A: real,B: real] :
% 5.02/5.32 ( ( ( Z = zero_zero_real )
% 5.02/5.32 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.02/5.32 = ( uminus_uminus_real @ B ) ) )
% 5.02/5.32 & ( ( Z != zero_zero_real )
% 5.02/5.32 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.02/5.32 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(6)
% 5.02/5.32 thf(fact_5511_add__divide__eq__if__simps_I6_J,axiom,
% 5.02/5.32 ! [Z: complex,A: complex,B: complex] :
% 5.02/5.32 ( ( ( Z = zero_zero_complex )
% 5.02/5.32 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.02/5.32 & ( ( Z != zero_zero_complex )
% 5.02/5.32 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.02/5.32 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(6)
% 5.02/5.32 thf(fact_5512_add__divide__eq__if__simps_I6_J,axiom,
% 5.02/5.32 ! [Z: rat,A: rat,B: rat] :
% 5.02/5.32 ( ( ( Z = zero_zero_rat )
% 5.02/5.32 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.02/5.32 = ( uminus_uminus_rat @ B ) ) )
% 5.02/5.32 & ( ( Z != zero_zero_rat )
% 5.02/5.32 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.02/5.32 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % add_divide_eq_if_simps(6)
% 5.02/5.32 thf(fact_5513_even__minus,axiom,
% 5.02/5.32 ! [A: int] :
% 5.02/5.32 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.02/5.32 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % even_minus
% 5.02/5.32 thf(fact_5514_even__minus,axiom,
% 5.02/5.32 ! [A: code_integer] :
% 5.02/5.32 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.32 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % even_minus
% 5.02/5.32 thf(fact_5515_power2__eq__iff,axiom,
% 5.02/5.32 ! [X2: real,Y: real] :
% 5.02/5.32 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.32 = ( ( X2 = Y )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_iff
% 5.02/5.32 thf(fact_5516_power2__eq__iff,axiom,
% 5.02/5.32 ! [X2: int,Y: int] :
% 5.02/5.32 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.32 = ( ( X2 = Y )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_iff
% 5.02/5.32 thf(fact_5517_power2__eq__iff,axiom,
% 5.02/5.32 ! [X2: complex,Y: complex] :
% 5.02/5.32 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.32 = ( ( X2 = Y )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_iff
% 5.02/5.32 thf(fact_5518_power2__eq__iff,axiom,
% 5.02/5.32 ! [X2: rat,Y: rat] :
% 5.02/5.32 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.32 = ( ( X2 = Y )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_iff
% 5.02/5.32 thf(fact_5519_power2__eq__iff,axiom,
% 5.02/5.32 ! [X2: code_integer,Y: code_integer] :
% 5.02/5.32 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.32 = ( ( X2 = Y )
% 5.02/5.32 | ( X2
% 5.02/5.32 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_iff
% 5.02/5.32 thf(fact_5520_aset_I10_J,axiom,
% 5.02/5.32 ! [D: int,D4: int,A3: set_int,T2: int] :
% 5.02/5.32 ( ( dvd_dvd_int @ D @ D4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T2 ) )
% 5.02/5.32 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X3 @ D4 ) @ T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(10)
% 5.02/5.32 thf(fact_5521_aset_I9_J,axiom,
% 5.02/5.32 ! [D: int,D4: int,A3: set_int,T2: int] :
% 5.02/5.32 ( ( dvd_dvd_int @ D @ D4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T2 ) )
% 5.02/5.32 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X3 @ D4 ) @ T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(9)
% 5.02/5.32 thf(fact_5522_bset_I10_J,axiom,
% 5.02/5.32 ! [D: int,D4: int,B4: set_int,T2: int] :
% 5.02/5.32 ( ( dvd_dvd_int @ D @ D4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T2 ) )
% 5.02/5.32 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ D4 ) @ T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(10)
% 5.02/5.32 thf(fact_5523_bset_I9_J,axiom,
% 5.02/5.32 ! [D: int,D4: int,B4: set_int,T2: int] :
% 5.02/5.32 ( ( dvd_dvd_int @ D @ D4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X3 @ T2 ) )
% 5.02/5.32 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X3 @ D4 ) @ T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(9)
% 5.02/5.32 thf(fact_5524_verit__less__mono__div__int2,axiom,
% 5.02/5.32 ! [A3: int,B4: int,N2: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ A3 @ B4 )
% 5.02/5.32 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 5.02/5.32 => ( ord_less_eq_int @ ( divide_divide_int @ B4 @ N2 ) @ ( divide_divide_int @ A3 @ N2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % verit_less_mono_div_int2
% 5.02/5.32 thf(fact_5525_div__eq__minus1,axiom,
% 5.02/5.32 ! [B: int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.32 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % div_eq_minus1
% 5.02/5.32 thf(fact_5526_of__bool__odd__eq__mod__2,axiom,
% 5.02/5.32 ! [A: nat] :
% 5.02/5.32 ( ( zero_n2687167440665602831ol_nat
% 5.02/5.32 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.32 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_odd_eq_mod_2
% 5.02/5.32 thf(fact_5527_of__bool__odd__eq__mod__2,axiom,
% 5.02/5.32 ! [A: int] :
% 5.02/5.32 ( ( zero_n2684676970156552555ol_int
% 5.02/5.32 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.32 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_odd_eq_mod_2
% 5.02/5.32 thf(fact_5528_of__bool__odd__eq__mod__2,axiom,
% 5.02/5.32 ! [A: code_integer] :
% 5.02/5.32 ( ( zero_n356916108424825756nteger
% 5.02/5.32 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.32 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_bool_odd_eq_mod_2
% 5.02/5.32 thf(fact_5529_le__minus__divide__eq,axiom,
% 5.02/5.32 ! [A: real,B: real,C: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.02/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_divide_eq
% 5.02/5.32 thf(fact_5530_le__minus__divide__eq,axiom,
% 5.02/5.32 ! [A: rat,B: rat,C: rat] :
% 5.02/5.32 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.02/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_minus_divide_eq
% 5.02/5.32 thf(fact_5531_minus__divide__le__eq,axiom,
% 5.02/5.32 ! [B: real,C: real,A: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.02/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_le_eq
% 5.02/5.32 thf(fact_5532_minus__divide__le__eq,axiom,
% 5.02/5.32 ! [B: rat,C: rat,A: rat] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.02/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_divide_le_eq
% 5.02/5.32 thf(fact_5533_neg__le__minus__divide__eq,axiom,
% 5.02/5.32 ! [C: real,A: real,B: real] :
% 5.02/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.02/5.32 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_le_minus_divide_eq
% 5.02/5.32 thf(fact_5534_neg__le__minus__divide__eq,axiom,
% 5.02/5.32 ! [C: rat,A: rat,B: rat] :
% 5.02/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.02/5.32 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_le_minus_divide_eq
% 5.02/5.32 thf(fact_5535_neg__minus__divide__le__eq,axiom,
% 5.02/5.32 ! [C: real,B: real,A: real] :
% 5.02/5.32 ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.02/5.32 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_minus_divide_le_eq
% 5.02/5.32 thf(fact_5536_neg__minus__divide__le__eq,axiom,
% 5.02/5.32 ! [C: rat,B: rat,A: rat] :
% 5.02/5.32 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.02/5.32 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_minus_divide_le_eq
% 5.02/5.32 thf(fact_5537_pos__le__minus__divide__eq,axiom,
% 5.02/5.32 ! [C: real,A: real,B: real] :
% 5.02/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.02/5.32 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_le_minus_divide_eq
% 5.02/5.32 thf(fact_5538_pos__le__minus__divide__eq,axiom,
% 5.02/5.32 ! [C: rat,A: rat,B: rat] :
% 5.02/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.02/5.32 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_le_minus_divide_eq
% 5.02/5.32 thf(fact_5539_pos__minus__divide__le__eq,axiom,
% 5.02/5.32 ! [C: real,B: real,A: real] :
% 5.02/5.32 ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.02/5.32 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_minus_divide_le_eq
% 5.02/5.32 thf(fact_5540_pos__minus__divide__le__eq,axiom,
% 5.02/5.32 ! [C: rat,B: rat,A: rat] :
% 5.02/5.32 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.02/5.32 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % pos_minus_divide_le_eq
% 5.02/5.32 thf(fact_5541_divide__less__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [B: real,C: real,W: num] :
% 5.02/5.32 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_less_eq_numeral(2)
% 5.02/5.32 thf(fact_5542_divide__less__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [B: rat,C: rat,W: num] :
% 5.02/5.32 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.02/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_less_eq_numeral(2)
% 5.02/5.32 thf(fact_5543_less__divide__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [W: num,B: real,C: real] :
% 5.02/5.32 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.02/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_divide_eq_numeral(2)
% 5.02/5.32 thf(fact_5544_less__divide__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [W: num,B: rat,C: rat] :
% 5.02/5.32 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.02/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % less_divide_eq_numeral(2)
% 5.02/5.32 thf(fact_5545_periodic__finite__ex,axiom,
% 5.02/5.32 ! [D: int,P: int > $o] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D )
% 5.02/5.32 => ( ! [X5: int,K2: int] :
% 5.02/5.32 ( ( P @ X5 )
% 5.02/5.32 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.02/5.32 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.02/5.32 = ( ? [X: int] :
% 5.02/5.32 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.02/5.32 & ( P @ X ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % periodic_finite_ex
% 5.02/5.32 thf(fact_5546_bset_I3_J,axiom,
% 5.02/5.32 ! [D4: int,T2: int,B4: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ( member_int @ ( minus_minus_int @ T2 @ one_one_int ) @ B4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( X3 = T2 )
% 5.02/5.32 => ( ( minus_minus_int @ X3 @ D4 )
% 5.02/5.32 = T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(3)
% 5.02/5.32 thf(fact_5547_bset_I4_J,axiom,
% 5.02/5.32 ! [D4: int,T2: int,B4: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ( member_int @ T2 @ B4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( X3 != T2 )
% 5.02/5.32 => ( ( minus_minus_int @ X3 @ D4 )
% 5.02/5.32 != T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(4)
% 5.02/5.32 thf(fact_5548_bset_I5_J,axiom,
% 5.02/5.32 ! [D4: int,B4: set_int,T2: int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ord_less_int @ X3 @ T2 )
% 5.02/5.32 => ( ord_less_int @ ( minus_minus_int @ X3 @ D4 ) @ T2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(5)
% 5.02/5.32 thf(fact_5549_bset_I7_J,axiom,
% 5.02/5.32 ! [D4: int,T2: int,B4: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ( member_int @ T2 @ B4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ord_less_int @ T2 @ X3 )
% 5.02/5.32 => ( ord_less_int @ T2 @ ( minus_minus_int @ X3 @ D4 ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(7)
% 5.02/5.32 thf(fact_5550_aset_I3_J,axiom,
% 5.02/5.32 ! [D4: int,T2: int,A3: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ( member_int @ ( plus_plus_int @ T2 @ one_one_int ) @ A3 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( X3 = T2 )
% 5.02/5.32 => ( ( plus_plus_int @ X3 @ D4 )
% 5.02/5.32 = T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(3)
% 5.02/5.32 thf(fact_5551_aset_I4_J,axiom,
% 5.02/5.32 ! [D4: int,T2: int,A3: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ( member_int @ T2 @ A3 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( X3 != T2 )
% 5.02/5.32 => ( ( plus_plus_int @ X3 @ D4 )
% 5.02/5.32 != T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(4)
% 5.02/5.32 thf(fact_5552_aset_I5_J,axiom,
% 5.02/5.32 ! [D4: int,T2: int,A3: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ( member_int @ T2 @ A3 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ord_less_int @ X3 @ T2 )
% 5.02/5.32 => ( ord_less_int @ ( plus_plus_int @ X3 @ D4 ) @ T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(5)
% 5.02/5.32 thf(fact_5553_aset_I7_J,axiom,
% 5.02/5.32 ! [D4: int,A3: set_int,T2: int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ord_less_int @ T2 @ X3 )
% 5.02/5.32 => ( ord_less_int @ T2 @ ( plus_plus_int @ X3 @ D4 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(7)
% 5.02/5.32 thf(fact_5554_power2__eq__1__iff,axiom,
% 5.02/5.32 ! [A: real] :
% 5.02/5.32 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = one_one_real )
% 5.02/5.32 = ( ( A = one_one_real )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_1_iff
% 5.02/5.32 thf(fact_5555_power2__eq__1__iff,axiom,
% 5.02/5.32 ! [A: int] :
% 5.02/5.32 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = one_one_int )
% 5.02/5.32 = ( ( A = one_one_int )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_1_iff
% 5.02/5.32 thf(fact_5556_power2__eq__1__iff,axiom,
% 5.02/5.32 ! [A: complex] :
% 5.02/5.32 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = one_one_complex )
% 5.02/5.32 = ( ( A = one_one_complex )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_1_iff
% 5.02/5.32 thf(fact_5557_power2__eq__1__iff,axiom,
% 5.02/5.32 ! [A: rat] :
% 5.02/5.32 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = one_one_rat )
% 5.02/5.32 = ( ( A = one_one_rat )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_1_iff
% 5.02/5.32 thf(fact_5558_power2__eq__1__iff,axiom,
% 5.02/5.32 ! [A: code_integer] :
% 5.02/5.32 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = one_one_Code_integer )
% 5.02/5.32 = ( ( A = one_one_Code_integer )
% 5.02/5.32 | ( A
% 5.02/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % power2_eq_1_iff
% 5.02/5.32 thf(fact_5559_uminus__power__if,axiom,
% 5.02/5.32 ! [N2: nat,A: real] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.02/5.32 = ( power_power_real @ A @ N2 ) ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.02/5.32 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_power_if
% 5.02/5.32 thf(fact_5560_uminus__power__if,axiom,
% 5.02/5.32 ! [N2: nat,A: int] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.02/5.32 = ( power_power_int @ A @ N2 ) ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.02/5.32 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_power_if
% 5.02/5.32 thf(fact_5561_uminus__power__if,axiom,
% 5.02/5.32 ! [N2: nat,A: complex] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.02/5.32 = ( power_power_complex @ A @ N2 ) ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_power_if
% 5.02/5.32 thf(fact_5562_uminus__power__if,axiom,
% 5.02/5.32 ! [N2: nat,A: rat] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.02/5.32 = ( power_power_rat @ A @ N2 ) ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.02/5.32 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_power_if
% 5.02/5.32 thf(fact_5563_uminus__power__if,axiom,
% 5.02/5.32 ! [N2: nat,A: code_integer] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.02/5.32 = ( power_8256067586552552935nteger @ A @ N2 ) ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % uminus_power_if
% 5.02/5.32 thf(fact_5564_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.02/5.32 ! [K: nat,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.32 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.02/5.32 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_power_add_eq_neg_one_power_diff
% 5.02/5.32 thf(fact_5565_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.02/5.32 ! [K: nat,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.32 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.02/5.32 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_power_add_eq_neg_one_power_diff
% 5.02/5.32 thf(fact_5566_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.02/5.32 ! [K: nat,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.32 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.02/5.32 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_power_add_eq_neg_one_power_diff
% 5.02/5.32 thf(fact_5567_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.02/5.32 ! [K: nat,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.32 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.02/5.32 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_power_add_eq_neg_one_power_diff
% 5.02/5.32 thf(fact_5568_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.02/5.32 ! [K: nat,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.32 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.02/5.32 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_one_power_add_eq_neg_one_power_diff
% 5.02/5.32 thf(fact_5569_realpow__square__minus__le,axiom,
% 5.02/5.32 ! [U: real,X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % realpow_square_minus_le
% 5.02/5.32 thf(fact_5570_minus__mod__int__eq,axiom,
% 5.02/5.32 ! [L: int,K: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.02/5.32 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.02/5.32 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_mod_int_eq
% 5.02/5.32 thf(fact_5571_zmod__minus1,axiom,
% 5.02/5.32 ! [B: int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.32 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.02/5.32 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zmod_minus1
% 5.02/5.32 thf(fact_5572_zdiv__zminus1__eq__if,axiom,
% 5.02/5.32 ! [B: int,A: int] :
% 5.02/5.32 ( ( B != zero_zero_int )
% 5.02/5.32 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.32 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.02/5.32 & ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 != zero_zero_int )
% 5.02/5.32 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.32 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zdiv_zminus1_eq_if
% 5.02/5.32 thf(fact_5573_zdiv__zminus2__eq__if,axiom,
% 5.02/5.32 ! [B: int,A: int] :
% 5.02/5.32 ( ( B != zero_zero_int )
% 5.02/5.32 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.32 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.02/5.32 & ( ( ( modulo_modulo_int @ A @ B )
% 5.02/5.32 != zero_zero_int )
% 5.02/5.32 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.02/5.32 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zdiv_zminus2_eq_if
% 5.02/5.32 thf(fact_5574_zminus1__lemma,axiom,
% 5.02/5.32 ! [A: int,B: int,Q2: int,R2: int] :
% 5.02/5.32 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.02/5.32 => ( ( B != zero_zero_int )
% 5.02/5.32 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R2 = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R2 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R2 ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zminus1_lemma
% 5.02/5.32 thf(fact_5575_bits__induct,axiom,
% 5.02/5.32 ! [P: nat > $o,A: nat] :
% 5.02/5.32 ( ! [A4: nat] :
% 5.02/5.32 ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = A4 )
% 5.02/5.32 => ( P @ A4 ) )
% 5.02/5.32 => ( ! [A4: nat,B3: $o] :
% 5.02/5.32 ( ( P @ A4 )
% 5.02/5.32 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = A4 )
% 5.02/5.32 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.02/5.32 => ( P @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bits_induct
% 5.02/5.32 thf(fact_5576_bits__induct,axiom,
% 5.02/5.32 ! [P: int > $o,A: int] :
% 5.02/5.32 ( ! [A4: int] :
% 5.02/5.32 ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.32 = A4 )
% 5.02/5.32 => ( P @ A4 ) )
% 5.02/5.32 => ( ! [A4: int,B3: $o] :
% 5.02/5.32 ( ( P @ A4 )
% 5.02/5.32 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.32 = A4 )
% 5.02/5.32 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.02/5.32 => ( P @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bits_induct
% 5.02/5.32 thf(fact_5577_bits__induct,axiom,
% 5.02/5.32 ! [P: code_integer > $o,A: code_integer] :
% 5.02/5.32 ( ! [A4: code_integer] :
% 5.02/5.32 ( ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.32 = A4 )
% 5.02/5.32 => ( P @ A4 ) )
% 5.02/5.32 => ( ! [A4: code_integer,B3: $o] :
% 5.02/5.32 ( ( P @ A4 )
% 5.02/5.32 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.32 = A4 )
% 5.02/5.32 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.02/5.32 => ( P @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bits_induct
% 5.02/5.32 thf(fact_5578_divide__le__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [B: real,C: real,W: num] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_le_eq_numeral(2)
% 5.02/5.32 thf(fact_5579_divide__le__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [B: rat,C: rat,W: num] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.02/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divide_le_eq_numeral(2)
% 5.02/5.32 thf(fact_5580_le__divide__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [W: num,B: real,C: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.02/5.32 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.32 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.02/5.32 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_divide_eq_numeral(2)
% 5.02/5.32 thf(fact_5581_le__divide__eq__numeral_I2_J,axiom,
% 5.02/5.32 ! [W: num,B: rat,C: rat] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.02/5.32 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.02/5.32 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.02/5.32 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % le_divide_eq_numeral(2)
% 5.02/5.32 thf(fact_5582_bset_I6_J,axiom,
% 5.02/5.32 ! [D4: int,B4: set_int,T2: int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ord_less_eq_int @ X3 @ T2 )
% 5.02/5.32 => ( ord_less_eq_int @ ( minus_minus_int @ X3 @ D4 ) @ T2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(6)
% 5.02/5.32 thf(fact_5583_bset_I8_J,axiom,
% 5.02/5.32 ! [D4: int,T2: int,B4: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ( member_int @ ( minus_minus_int @ T2 @ one_one_int ) @ B4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ B4 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ord_less_eq_int @ T2 @ X3 )
% 5.02/5.32 => ( ord_less_eq_int @ T2 @ ( minus_minus_int @ X3 @ D4 ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % bset(8)
% 5.02/5.32 thf(fact_5584_aset_I6_J,axiom,
% 5.02/5.32 ! [D4: int,T2: int,A3: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ( member_int @ ( plus_plus_int @ T2 @ one_one_int ) @ A3 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ord_less_eq_int @ X3 @ T2 )
% 5.02/5.32 => ( ord_less_eq_int @ ( plus_plus_int @ X3 @ D4 ) @ T2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(6)
% 5.02/5.32 thf(fact_5585_aset_I8_J,axiom,
% 5.02/5.32 ! [D4: int,A3: set_int,T2: int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ! [X3: int] :
% 5.02/5.32 ( ! [Xa3: int] :
% 5.02/5.32 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb2: int] :
% 5.02/5.32 ( ( member_int @ Xb2 @ A3 )
% 5.02/5.32 => ( X3
% 5.02/5.32 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.02/5.32 => ( ( ord_less_eq_int @ T2 @ X3 )
% 5.02/5.32 => ( ord_less_eq_int @ T2 @ ( plus_plus_int @ X3 @ D4 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % aset(8)
% 5.02/5.32 thf(fact_5586_cpmi,axiom,
% 5.02/5.32 ! [D4: int,P: int > $o,P5: int > $o,B4: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ? [Z4: int] :
% 5.02/5.32 ! [X5: int] :
% 5.02/5.32 ( ( ord_less_int @ X5 @ Z4 )
% 5.02/5.32 => ( ( P @ X5 )
% 5.02/5.32 = ( P5 @ X5 ) ) )
% 5.02/5.32 => ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ B4 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( P @ X5 )
% 5.02/5.32 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ( ! [X5: int,K2: int] :
% 5.02/5.32 ( ( P5 @ X5 )
% 5.02/5.32 = ( P5 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.02/5.32 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.02/5.32 = ( ? [X: int] :
% 5.02/5.32 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 & ( P5 @ X ) )
% 5.02/5.32 | ? [X: int] :
% 5.02/5.32 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 & ? [Y6: int] :
% 5.02/5.32 ( ( member_int @ Y6 @ B4 )
% 5.02/5.32 & ( P @ ( plus_plus_int @ Y6 @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % cpmi
% 5.02/5.32 thf(fact_5587_cppi,axiom,
% 5.02/5.32 ! [D4: int,P: int > $o,P5: int > $o,A3: set_int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.02/5.32 => ( ? [Z4: int] :
% 5.02/5.32 ! [X5: int] :
% 5.02/5.32 ( ( ord_less_int @ Z4 @ X5 )
% 5.02/5.32 => ( ( P @ X5 )
% 5.02/5.32 = ( P5 @ X5 ) ) )
% 5.02/5.32 => ( ! [X5: int] :
% 5.02/5.32 ( ! [Xa: int] :
% 5.02/5.32 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 => ! [Xb: int] :
% 5.02/5.32 ( ( member_int @ Xb @ A3 )
% 5.02/5.32 => ( X5
% 5.02/5.32 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.02/5.32 => ( ( P @ X5 )
% 5.02/5.32 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.02/5.32 => ( ! [X5: int,K2: int] :
% 5.02/5.32 ( ( P5 @ X5 )
% 5.02/5.32 = ( P5 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.02/5.32 => ( ( ? [X4: int] : ( P @ X4 ) )
% 5.02/5.32 = ( ? [X: int] :
% 5.02/5.32 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 & ( P5 @ X ) )
% 5.02/5.32 | ? [X: int] :
% 5.02/5.32 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.02/5.32 & ? [Y6: int] :
% 5.02/5.32 ( ( member_int @ Y6 @ A3 )
% 5.02/5.32 & ( P @ ( minus_minus_int @ Y6 @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % cppi
% 5.02/5.32 thf(fact_5588_square__le__1,axiom,
% 5.02/5.32 ! [X2: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.32 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.32 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_le_1
% 5.02/5.32 thf(fact_5589_square__le__1,axiom,
% 5.02/5.32 ! [X2: code_integer] :
% 5.02/5.32 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 5.02/5.32 => ( ( ord_le3102999989581377725nteger @ X2 @ one_one_Code_integer )
% 5.02/5.32 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_le_1
% 5.02/5.32 thf(fact_5590_square__le__1,axiom,
% 5.02/5.32 ! [X2: rat] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X2 )
% 5.02/5.32 => ( ( ord_less_eq_rat @ X2 @ one_one_rat )
% 5.02/5.32 => ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_le_1
% 5.02/5.32 thf(fact_5591_square__le__1,axiom,
% 5.02/5.32 ! [X2: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 5.02/5.32 => ( ( ord_less_eq_int @ X2 @ one_one_int )
% 5.02/5.32 => ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % square_le_1
% 5.02/5.32 thf(fact_5592_minus__power__mult__self,axiom,
% 5.02/5.32 ! [A: real,N2: nat] :
% 5.02/5.32 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.02/5.32 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_power_mult_self
% 5.02/5.32 thf(fact_5593_minus__power__mult__self,axiom,
% 5.02/5.32 ! [A: int,N2: nat] :
% 5.02/5.32 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.02/5.32 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_power_mult_self
% 5.02/5.32 thf(fact_5594_minus__power__mult__self,axiom,
% 5.02/5.32 ! [A: complex,N2: nat] :
% 5.02/5.32 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) )
% 5.02/5.32 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_power_mult_self
% 5.02/5.32 thf(fact_5595_minus__power__mult__self,axiom,
% 5.02/5.32 ! [A: rat,N2: nat] :
% 5.02/5.32 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.02/5.32 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_power_mult_self
% 5.02/5.32 thf(fact_5596_minus__power__mult__self,axiom,
% 5.02/5.32 ! [A: code_integer,N2: nat] :
% 5.02/5.32 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.02/5.32 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_power_mult_self
% 5.02/5.32 thf(fact_5597_minus__one__power__iff,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.02/5.32 = one_one_real ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.02/5.32 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_one_power_iff
% 5.02/5.32 thf(fact_5598_minus__one__power__iff,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.02/5.32 = one_one_int ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_one_power_iff
% 5.02/5.32 thf(fact_5599_minus__one__power__iff,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.02/5.32 = one_one_complex ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_one_power_iff
% 5.02/5.32 thf(fact_5600_minus__one__power__iff,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.02/5.32 = one_one_rat ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.02/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_one_power_iff
% 5.02/5.32 thf(fact_5601_minus__one__power__iff,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.02/5.32 = one_one_Code_integer ) )
% 5.02/5.32 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.32 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_one_power_iff
% 5.02/5.32 thf(fact_5602_minus__1__div__exp__eq__int,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % minus_1_div_exp_eq_int
% 5.02/5.32 thf(fact_5603_div__pos__neg__trivial,axiom,
% 5.02/5.32 ! [K: int,L: int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ K )
% 5.02/5.32 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.02/5.32 => ( ( divide_divide_int @ K @ L )
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % div_pos_neg_trivial
% 5.02/5.32 thf(fact_5604_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.02/5.32 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_int_greater_eq_minus_exp
% 5.02/5.32 thf(fact_5605_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.02/5.32 ! [N2: nat,K: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.02/5.32 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_int_less_eq_self_iff
% 5.02/5.32 thf(fact_5606_signed__take__bit__int__greater__self__iff,axiom,
% 5.02/5.32 ! [K: int,N2: nat] :
% 5.02/5.32 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.02/5.32 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_int_greater_self_iff
% 5.02/5.32 thf(fact_5607_exp__mod__exp,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % exp_mod_exp
% 5.02/5.32 thf(fact_5608_exp__mod__exp,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % exp_mod_exp
% 5.02/5.32 thf(fact_5609_exp__mod__exp,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % exp_mod_exp
% 5.02/5.32 thf(fact_5610_power__minus1__odd,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.32 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus1_odd
% 5.02/5.32 thf(fact_5611_power__minus1__odd,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.32 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus1_odd
% 5.02/5.32 thf(fact_5612_power__minus1__odd,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus1_odd
% 5.02/5.32 thf(fact_5613_power__minus1__odd,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.32 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus1_odd
% 5.02/5.32 thf(fact_5614_power__minus1__odd,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.32
% 5.02/5.32 % power_minus1_odd
% 5.02/5.32 thf(fact_5615_int__bit__induct,axiom,
% 5.02/5.32 ! [P: int > $o,K: int] :
% 5.02/5.32 ( ( P @ zero_zero_int )
% 5.02/5.32 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.32 => ( ! [K2: int] :
% 5.02/5.32 ( ( P @ K2 )
% 5.02/5.32 => ( ( K2 != zero_zero_int )
% 5.02/5.32 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.32 => ( ! [K2: int] :
% 5.02/5.32 ( ( P @ K2 )
% 5.02/5.32 => ( ( K2
% 5.02/5.32 != ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.32 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.02/5.32 => ( P @ K ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % int_bit_induct
% 5.02/5.32 thf(fact_5616_signed__take__bit__int__eq__self__iff,axiom,
% 5.02/5.32 ! [N2: nat,K: int] :
% 5.02/5.32 ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.02/5.32 = K )
% 5.02/5.32 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.02/5.32 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_int_eq_self_iff
% 5.02/5.32 thf(fact_5617_signed__take__bit__int__eq__self,axiom,
% 5.02/5.32 ! [N2: nat,K: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.02/5.32 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.02/5.32 = K ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_int_eq_self
% 5.02/5.32 thf(fact_5618_exp__div__exp__eq,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_times_nat
% 5.02/5.32 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.32 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.02/5.32 != zero_zero_nat )
% 5.02/5.32 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.02/5.32 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % exp_div_exp_eq
% 5.02/5.32 thf(fact_5619_exp__div__exp__eq,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_times_int
% 5.02/5.32 @ ( zero_n2684676970156552555ol_int
% 5.02/5.32 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.02/5.32 != zero_zero_int )
% 5.02/5.32 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.02/5.32 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % exp_div_exp_eq
% 5.02/5.32 thf(fact_5620_exp__div__exp__eq,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_3573771949741848930nteger
% 5.02/5.32 @ ( zero_n356916108424825756nteger
% 5.02/5.32 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.02/5.32 != zero_z3403309356797280102nteger )
% 5.02/5.32 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.02/5.32 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % exp_div_exp_eq
% 5.02/5.32 thf(fact_5621_signed__take__bit__int__greater__eq,axiom,
% 5.02/5.32 ! [K: int,N2: nat] :
% 5.02/5.32 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.32 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_int_greater_eq
% 5.02/5.32 thf(fact_5622_set__decode__def,axiom,
% 5.02/5.32 ( nat_set_decode
% 5.02/5.32 = ( ^ [X: nat] :
% 5.02/5.32 ( collect_nat
% 5.02/5.32 @ ^ [N3: nat] :
% 5.02/5.32 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % set_decode_def
% 5.02/5.32 thf(fact_5623_Divides_Oadjust__div__eq,axiom,
% 5.02/5.32 ! [Q2: int,R2: int] :
% 5.02/5.32 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.02/5.32 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R2 != zero_zero_int ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % Divides.adjust_div_eq
% 5.02/5.32 thf(fact_5624_signed__take__bit__Suc__minus__bit1,axiom,
% 5.02/5.32 ! [N2: nat,K: num] :
% 5.02/5.32 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.02/5.32 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_Suc_minus_bit1
% 5.02/5.32 thf(fact_5625_divmod__step__def,axiom,
% 5.02/5.32 ( unique5026877609467782581ep_nat
% 5.02/5.32 = ( ^ [L2: num] :
% 5.02/5.32 ( produc2626176000494625587at_nat
% 5.02/5.32 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divmod_step_def
% 5.02/5.32 thf(fact_5626_divmod__step__def,axiom,
% 5.02/5.32 ( unique5024387138958732305ep_int
% 5.02/5.32 = ( ^ [L2: num] :
% 5.02/5.32 ( produc4245557441103728435nt_int
% 5.02/5.32 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divmod_step_def
% 5.02/5.32 thf(fact_5627_divmod__step__def,axiom,
% 5.02/5.32 ( unique4921790084139445826nteger
% 5.02/5.32 = ( ^ [L2: num] :
% 5.02/5.32 ( produc6916734918728496179nteger
% 5.02/5.32 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % divmod_step_def
% 5.02/5.32 thf(fact_5628_signed__take__bit__Suc__bit1,axiom,
% 5.02/5.32 ! [N2: nat,K: num] :
% 5.02/5.32 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.02/5.32 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % signed_take_bit_Suc_bit1
% 5.02/5.32 thf(fact_5629_take__bit__rec,axiom,
% 5.02/5.32 ( bit_se2923211474154528505it_int
% 5.02/5.32 = ( ^ [N3: nat,A5: int] : ( if_int @ ( N3 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_rec
% 5.02/5.32 thf(fact_5630_take__bit__rec,axiom,
% 5.02/5.32 ( bit_se2925701944663578781it_nat
% 5.02/5.32 = ( ^ [N3: nat,A5: nat] : ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_rec
% 5.02/5.32 thf(fact_5631_of__int__code__if,axiom,
% 5.02/5.32 ( ring_1_of_int_real
% 5.02/5.32 = ( ^ [K3: int] :
% 5.02/5.32 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.02/5.32 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.02/5.32 @ ( if_real
% 5.02/5.32 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.02/5.32 @ ( 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 ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_code_if
% 5.02/5.32 thf(fact_5632_of__int__code__if,axiom,
% 5.02/5.32 ( ring_1_of_int_int
% 5.02/5.32 = ( ^ [K3: int] :
% 5.02/5.32 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.02/5.32 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.02/5.32 @ ( if_int
% 5.02/5.32 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.02/5.32 @ ( 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 ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_code_if
% 5.02/5.32 thf(fact_5633_of__int__code__if,axiom,
% 5.02/5.32 ( ring_17405671764205052669omplex
% 5.02/5.32 = ( ^ [K3: int] :
% 5.02/5.32 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.02/5.32 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.02/5.32 @ ( if_complex
% 5.02/5.32 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.02/5.32 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_code_if
% 5.02/5.32 thf(fact_5634_of__int__code__if,axiom,
% 5.02/5.32 ( ring_1_of_int_rat
% 5.02/5.32 = ( ^ [K3: int] :
% 5.02/5.32 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 5.02/5.32 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 5.02/5.32 @ ( if_rat
% 5.02/5.32 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.02/5.32 @ ( 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 ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_code_if
% 5.02/5.32 thf(fact_5635_of__int__code__if,axiom,
% 5.02/5.32 ( ring_18347121197199848620nteger
% 5.02/5.32 = ( ^ [K3: int] :
% 5.02/5.32 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.02/5.32 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.02/5.32 @ ( if_Code_integer
% 5.02/5.32 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.02/5.32 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_code_if
% 5.02/5.32 thf(fact_5636_sqrt__sum__squares__half__less,axiom,
% 5.02/5.32 ! [X2: real,U: real,Y: real] :
% 5.02/5.32 ( ( ord_less_real @ X2 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.32 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.32 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.32 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % sqrt_sum_squares_half_less
% 5.02/5.32 thf(fact_5637_semiring__norm_I90_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( ( bit1 @ M )
% 5.02/5.32 = ( bit1 @ N2 ) )
% 5.02/5.32 = ( M = N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(90)
% 5.02/5.32 thf(fact_5638_of__int__eq__iff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ( ring_1_of_int_real @ W )
% 5.02/5.32 = ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( W = Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_iff
% 5.02/5.32 thf(fact_5639_of__int__eq__iff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ( ring_1_of_int_rat @ W )
% 5.02/5.32 = ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( W = Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_iff
% 5.02/5.32 thf(fact_5640_semiring__norm_I88_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( bit0 @ M )
% 5.02/5.32 != ( bit1 @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(88)
% 5.02/5.32 thf(fact_5641_semiring__norm_I89_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( bit1 @ M )
% 5.02/5.32 != ( bit0 @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(89)
% 5.02/5.32 thf(fact_5642_semiring__norm_I84_J,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( one
% 5.02/5.32 != ( bit1 @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(84)
% 5.02/5.32 thf(fact_5643_semiring__norm_I86_J,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ( ( bit1 @ M )
% 5.02/5.32 != one ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(86)
% 5.02/5.32 thf(fact_5644_take__bit__of__0,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 5.02/5.32 = zero_zero_int ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_0
% 5.02/5.32 thf(fact_5645_take__bit__of__0,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 5.02/5.32 = zero_zero_nat ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_0
% 5.02/5.32 thf(fact_5646_real__sqrt__one,axiom,
% 5.02/5.32 ( ( sqrt @ one_one_real )
% 5.02/5.32 = one_one_real ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_one
% 5.02/5.32 thf(fact_5647_real__sqrt__eq__1__iff,axiom,
% 5.02/5.32 ! [X2: real] :
% 5.02/5.32 ( ( ( sqrt @ X2 )
% 5.02/5.32 = one_one_real )
% 5.02/5.32 = ( X2 = one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_eq_1_iff
% 5.02/5.32 thf(fact_5648_concat__bit__of__zero__2,axiom,
% 5.02/5.32 ! [N2: nat,K: int] :
% 5.02/5.32 ( ( bit_concat_bit @ N2 @ K @ zero_zero_int )
% 5.02/5.32 = ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.02/5.32
% 5.02/5.32 % concat_bit_of_zero_2
% 5.02/5.32 thf(fact_5649_semiring__norm_I73_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(73)
% 5.02/5.32 thf(fact_5650_semiring__norm_I80_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( ord_less_num @ M @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(80)
% 5.02/5.32 thf(fact_5651_case__prod__conv,axiom,
% 5.02/5.32 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.02/5.32 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.02/5.32 = ( F @ A @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % case_prod_conv
% 5.02/5.32 thf(fact_5652_case__prod__conv,axiom,
% 5.02/5.32 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.02/5.32 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.02/5.32 = ( F @ A @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % case_prod_conv
% 5.02/5.32 thf(fact_5653_case__prod__conv,axiom,
% 5.02/5.32 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.02/5.32 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.02/5.32 = ( F @ A @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % case_prod_conv
% 5.02/5.32 thf(fact_5654_case__prod__conv,axiom,
% 5.02/5.32 ! [F: int > int > $o,A: int,B: int] :
% 5.02/5.32 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.02/5.32 = ( F @ A @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % case_prod_conv
% 5.02/5.32 thf(fact_5655_case__prod__conv,axiom,
% 5.02/5.32 ! [F: int > int > int,A: int,B: int] :
% 5.02/5.32 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.02/5.32 = ( F @ A @ B ) ) ).
% 5.02/5.32
% 5.02/5.32 % case_prod_conv
% 5.02/5.32 thf(fact_5656_of__int__eq__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.02/5.32 = zero_zero_complex )
% 5.02/5.32 = ( Z = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_0_iff
% 5.02/5.32 thf(fact_5657_of__int__eq__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ( ring_1_of_int_int @ Z )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 = ( Z = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_0_iff
% 5.02/5.32 thf(fact_5658_of__int__eq__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ( ring_1_of_int_real @ Z )
% 5.02/5.32 = zero_zero_real )
% 5.02/5.32 = ( Z = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_0_iff
% 5.02/5.32 thf(fact_5659_of__int__eq__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ( ring_1_of_int_rat @ Z )
% 5.02/5.32 = zero_zero_rat )
% 5.02/5.32 = ( Z = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_0_iff
% 5.02/5.32 thf(fact_5660_of__int__0__eq__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( zero_zero_complex
% 5.02/5.32 = ( ring_17405671764205052669omplex @ Z ) )
% 5.02/5.32 = ( Z = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_eq_iff
% 5.02/5.32 thf(fact_5661_of__int__0__eq__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( zero_zero_int
% 5.02/5.32 = ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( Z = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_eq_iff
% 5.02/5.32 thf(fact_5662_of__int__0__eq__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( zero_zero_real
% 5.02/5.32 = ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( Z = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_eq_iff
% 5.02/5.32 thf(fact_5663_of__int__0__eq__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( zero_zero_rat
% 5.02/5.32 = ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( Z = zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_eq_iff
% 5.02/5.32 thf(fact_5664_of__int__0,axiom,
% 5.02/5.32 ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 5.02/5.32 = zero_zero_complex ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0
% 5.02/5.32 thf(fact_5665_of__int__0,axiom,
% 5.02/5.32 ( ( ring_1_of_int_int @ zero_zero_int )
% 5.02/5.32 = zero_zero_int ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0
% 5.02/5.32 thf(fact_5666_of__int__0,axiom,
% 5.02/5.32 ( ( ring_1_of_int_real @ zero_zero_int )
% 5.02/5.32 = zero_zero_real ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0
% 5.02/5.32 thf(fact_5667_of__int__0,axiom,
% 5.02/5.32 ( ( ring_1_of_int_rat @ zero_zero_int )
% 5.02/5.32 = zero_zero_rat ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0
% 5.02/5.32 thf(fact_5668_take__bit__0,axiom,
% 5.02/5.32 ! [A: int] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.02/5.32 = zero_zero_int ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_0
% 5.02/5.32 thf(fact_5669_take__bit__0,axiom,
% 5.02/5.32 ! [A: nat] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.02/5.32 = zero_zero_nat ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_0
% 5.02/5.32 thf(fact_5670_take__bit__Suc__1,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 5.02/5.32 = one_one_int ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_Suc_1
% 5.02/5.32 thf(fact_5671_take__bit__Suc__1,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.02/5.32 = one_one_nat ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_Suc_1
% 5.02/5.32 thf(fact_5672_of__int__le__iff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_iff
% 5.02/5.32 thf(fact_5673_of__int__le__iff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_iff
% 5.02/5.32 thf(fact_5674_of__int__le__iff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_iff
% 5.02/5.32 thf(fact_5675_of__int__eq__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.02/5.32 = ( numera6690914467698888265omplex @ N2 ) )
% 5.02/5.32 = ( Z
% 5.02/5.32 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_numeral_iff
% 5.02/5.32 thf(fact_5676_of__int__eq__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ( ring_1_of_int_real @ Z )
% 5.02/5.32 = ( numeral_numeral_real @ N2 ) )
% 5.02/5.32 = ( Z
% 5.02/5.32 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_numeral_iff
% 5.02/5.32 thf(fact_5677_of__int__eq__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ( ring_1_of_int_rat @ Z )
% 5.02/5.32 = ( numeral_numeral_rat @ N2 ) )
% 5.02/5.32 = ( Z
% 5.02/5.32 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_numeral_iff
% 5.02/5.32 thf(fact_5678_of__int__eq__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ( ring_1_of_int_int @ Z )
% 5.02/5.32 = ( numeral_numeral_int @ N2 ) )
% 5.02/5.32 = ( Z
% 5.02/5.32 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_numeral_iff
% 5.02/5.32 thf(fact_5679_of__int__numeral,axiom,
% 5.02/5.32 ! [K: num] :
% 5.02/5.32 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.02/5.32 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral
% 5.02/5.32 thf(fact_5680_of__int__numeral,axiom,
% 5.02/5.32 ! [K: num] :
% 5.02/5.32 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.02/5.32 = ( numeral_numeral_real @ K ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral
% 5.02/5.32 thf(fact_5681_of__int__numeral,axiom,
% 5.02/5.32 ! [K: num] :
% 5.02/5.32 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.02/5.32 = ( numeral_numeral_rat @ K ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral
% 5.02/5.32 thf(fact_5682_of__int__numeral,axiom,
% 5.02/5.32 ! [K: num] :
% 5.02/5.32 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.02/5.32 = ( numeral_numeral_int @ K ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral
% 5.02/5.32 thf(fact_5683_take__bit__numeral__1,axiom,
% 5.02/5.32 ! [L: num] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 5.02/5.32 = one_one_int ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_numeral_1
% 5.02/5.32 thf(fact_5684_take__bit__numeral__1,axiom,
% 5.02/5.32 ! [L: num] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 5.02/5.32 = one_one_nat ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_numeral_1
% 5.02/5.32 thf(fact_5685_of__int__less__iff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( ord_less_int @ W @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_iff
% 5.02/5.32 thf(fact_5686_of__int__less__iff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( ord_less_int @ W @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_iff
% 5.02/5.32 thf(fact_5687_of__int__less__iff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( ord_less_int @ W @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_iff
% 5.02/5.32 thf(fact_5688_of__int__eq__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.02/5.32 = one_one_complex )
% 5.02/5.32 = ( Z = one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_1_iff
% 5.02/5.32 thf(fact_5689_of__int__eq__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ( ring_1_of_int_int @ Z )
% 5.02/5.32 = one_one_int )
% 5.02/5.32 = ( Z = one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_1_iff
% 5.02/5.32 thf(fact_5690_of__int__eq__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ( ring_1_of_int_real @ Z )
% 5.02/5.32 = one_one_real )
% 5.02/5.32 = ( Z = one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_1_iff
% 5.02/5.32 thf(fact_5691_of__int__eq__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ( ring_1_of_int_rat @ Z )
% 5.02/5.32 = one_one_rat )
% 5.02/5.32 = ( Z = one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_1_iff
% 5.02/5.32 thf(fact_5692_of__int__1,axiom,
% 5.02/5.32 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.02/5.32 = one_one_complex ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1
% 5.02/5.32 thf(fact_5693_of__int__1,axiom,
% 5.02/5.32 ( ( ring_1_of_int_int @ one_one_int )
% 5.02/5.32 = one_one_int ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1
% 5.02/5.32 thf(fact_5694_of__int__1,axiom,
% 5.02/5.32 ( ( ring_1_of_int_real @ one_one_int )
% 5.02/5.32 = one_one_real ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1
% 5.02/5.32 thf(fact_5695_of__int__1,axiom,
% 5.02/5.32 ( ( ring_1_of_int_rat @ one_one_int )
% 5.02/5.32 = one_one_rat ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1
% 5.02/5.32 thf(fact_5696_of__int__mult,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.02/5.32 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_mult
% 5.02/5.32 thf(fact_5697_of__int__mult,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.02/5.32 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_mult
% 5.02/5.32 thf(fact_5698_of__int__mult,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.02/5.32 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_mult
% 5.02/5.32 thf(fact_5699_of__int__add,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.02/5.32 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_add
% 5.02/5.32 thf(fact_5700_of__int__add,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.02/5.32 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_add
% 5.02/5.32 thf(fact_5701_of__int__add,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.02/5.32 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_add
% 5.02/5.32 thf(fact_5702_of__int__minus,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ Z ) )
% 5.02/5.32 = ( uminus_uminus_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_minus
% 5.02/5.32 thf(fact_5703_of__int__minus,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z ) )
% 5.02/5.32 = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_minus
% 5.02/5.32 thf(fact_5704_of__int__minus,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ Z ) )
% 5.02/5.32 = ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_minus
% 5.02/5.32 thf(fact_5705_of__int__minus,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z ) )
% 5.02/5.32 = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_minus
% 5.02/5.32 thf(fact_5706_of__int__minus,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z ) )
% 5.02/5.32 = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_minus
% 5.02/5.32 thf(fact_5707_of__int__diff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 5.02/5.32 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_diff
% 5.02/5.32 thf(fact_5708_of__int__diff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 5.02/5.32 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_diff
% 5.02/5.32 thf(fact_5709_of__int__diff,axiom,
% 5.02/5.32 ! [W: int,Z: int] :
% 5.02/5.32 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 5.02/5.32 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_diff
% 5.02/5.32 thf(fact_5710_real__sqrt__gt__1__iff,axiom,
% 5.02/5.32 ! [Y: real] :
% 5.02/5.32 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.02/5.32 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_gt_1_iff
% 5.02/5.32 thf(fact_5711_real__sqrt__lt__1__iff,axiom,
% 5.02/5.32 ! [X2: real] :
% 5.02/5.32 ( ( ord_less_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.02/5.32 = ( ord_less_real @ X2 @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_lt_1_iff
% 5.02/5.32 thf(fact_5712_real__sqrt__ge__1__iff,axiom,
% 5.02/5.32 ! [Y: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.02/5.32 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_ge_1_iff
% 5.02/5.32 thf(fact_5713_real__sqrt__le__1__iff,axiom,
% 5.02/5.32 ! [X2: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ one_one_real )
% 5.02/5.32 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_le_1_iff
% 5.02/5.32 thf(fact_5714_semiring__norm_I9_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.32 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(9)
% 5.02/5.32 thf(fact_5715_semiring__norm_I7_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(7)
% 5.02/5.32 thf(fact_5716_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_rat @ X2 )
% 5.02/5.32 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.02/5.32 = ( X2
% 5.02/5.32 = ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5717_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_int @ X2 )
% 5.02/5.32 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.02/5.32 = ( X2
% 5.02/5.32 = ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5718_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_real @ X2 )
% 5.02/5.32 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.02/5.32 = ( X2
% 5.02/5.32 = ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5719_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ( ring_17405671764205052669omplex @ X2 )
% 5.02/5.32 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.02/5.32 = ( X2
% 5.02/5.32 = ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5720_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.02/5.32 = ( ring_1_of_int_rat @ X2 ) )
% 5.02/5.32 = ( ( power_power_int @ B @ W )
% 5.02/5.32 = X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5721_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.02/5.32 = ( ring_1_of_int_int @ X2 ) )
% 5.02/5.32 = ( ( power_power_int @ B @ W )
% 5.02/5.32 = X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5722_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.02/5.32 = ( ring_1_of_int_real @ X2 ) )
% 5.02/5.32 = ( ( power_power_int @ B @ W )
% 5.02/5.32 = X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5723_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.02/5.32 = ( ring_17405671764205052669omplex @ X2 ) )
% 5.02/5.32 = ( ( power_power_int @ B @ W )
% 5.02/5.32 = X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5724_of__int__power,axiom,
% 5.02/5.32 ! [Z: int,N2: nat] :
% 5.02/5.32 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N2 ) )
% 5.02/5.32 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power
% 5.02/5.32 thf(fact_5725_of__int__power,axiom,
% 5.02/5.32 ! [Z: int,N2: nat] :
% 5.02/5.32 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N2 ) )
% 5.02/5.32 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power
% 5.02/5.32 thf(fact_5726_of__int__power,axiom,
% 5.02/5.32 ! [Z: int,N2: nat] :
% 5.02/5.32 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N2 ) )
% 5.02/5.32 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power
% 5.02/5.32 thf(fact_5727_of__int__power,axiom,
% 5.02/5.32 ! [Z: int,N2: nat] :
% 5.02/5.32 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N2 ) )
% 5.02/5.32 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power
% 5.02/5.32 thf(fact_5728_semiring__norm_I15_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.32 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(15)
% 5.02/5.32 thf(fact_5729_semiring__norm_I14_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N2 ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(14)
% 5.02/5.32 thf(fact_5730_semiring__norm_I81_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.32 = ( ord_less_num @ M @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(81)
% 5.02/5.32 thf(fact_5731_semiring__norm_I72_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(72)
% 5.02/5.32 thf(fact_5732_semiring__norm_I77_J,axiom,
% 5.02/5.32 ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(77)
% 5.02/5.32 thf(fact_5733_semiring__norm_I70_J,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(70)
% 5.02/5.32 thf(fact_5734_of__int__of__bool,axiom,
% 5.02/5.32 ! [P: $o] :
% 5.02/5.32 ( ( ring_1_of_int_real @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.02/5.32 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_of_bool
% 5.02/5.32 thf(fact_5735_of__int__of__bool,axiom,
% 5.02/5.32 ! [P: $o] :
% 5.02/5.32 ( ( ring_1_of_int_rat @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.02/5.32 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_of_bool
% 5.02/5.32 thf(fact_5736_of__int__of__bool,axiom,
% 5.02/5.32 ! [P: $o] :
% 5.02/5.32 ( ( ring_1_of_int_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.02/5.32 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_of_bool
% 5.02/5.32 thf(fact_5737_of__int__of__bool,axiom,
% 5.02/5.32 ! [P: $o] :
% 5.02/5.32 ( ( ring_18347121197199848620nteger @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.02/5.32 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_of_bool
% 5.02/5.32 thf(fact_5738_take__bit__of__1__eq__0__iff,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.02/5.32 = zero_zero_int )
% 5.02/5.32 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_1_eq_0_iff
% 5.02/5.32 thf(fact_5739_take__bit__of__1__eq__0__iff,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.02/5.32 = zero_zero_nat )
% 5.02/5.32 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_1_eq_0_iff
% 5.02/5.32 thf(fact_5740_real__sqrt__four,axiom,
% 5.02/5.32 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.32 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_four
% 5.02/5.32 thf(fact_5741_zdiv__numeral__Bit1,axiom,
% 5.02/5.32 ! [V: num,W: num] :
% 5.02/5.32 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.02/5.32 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % zdiv_numeral_Bit1
% 5.02/5.32 thf(fact_5742_semiring__norm_I3_J,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 5.02/5.32 = ( bit1 @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(3)
% 5.02/5.32 thf(fact_5743_semiring__norm_I4_J,axiom,
% 5.02/5.32 ! [N2: num] :
% 5.02/5.32 ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(4)
% 5.02/5.32 thf(fact_5744_semiring__norm_I5_J,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.02/5.32 = ( bit1 @ M ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(5)
% 5.02/5.32 thf(fact_5745_semiring__norm_I8_J,axiom,
% 5.02/5.32 ! [M: num] :
% 5.02/5.32 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.02/5.32 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(8)
% 5.02/5.32 thf(fact_5746_semiring__norm_I10_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ one ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(10)
% 5.02/5.32 thf(fact_5747_take__bit__of__Suc__0,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.02/5.32 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_Suc_0
% 5.02/5.32 thf(fact_5748_semiring__norm_I16_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(16)
% 5.02/5.32 thf(fact_5749_semiring__norm_I79_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(79)
% 5.02/5.32 thf(fact_5750_semiring__norm_I74_J,axiom,
% 5.02/5.32 ! [M: num,N2: num] :
% 5.02/5.32 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.32 = ( ord_less_num @ M @ N2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % semiring_norm(74)
% 5.02/5.32 thf(fact_5751_of__int__le__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_0_iff
% 5.02/5.32 thf(fact_5752_of__int__le__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_0_iff
% 5.02/5.32 thf(fact_5753_of__int__le__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_0_iff
% 5.02/5.32 thf(fact_5754_of__int__0__le__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_le_iff
% 5.02/5.32 thf(fact_5755_of__int__0__le__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_le_iff
% 5.02/5.32 thf(fact_5756_of__int__0__le__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_le_iff
% 5.02/5.32 thf(fact_5757_of__int__less__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.02/5.32 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_0_iff
% 5.02/5.32 thf(fact_5758_of__int__less__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.02/5.32 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_0_iff
% 5.02/5.32 thf(fact_5759_of__int__less__0__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.02/5.32 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_0_iff
% 5.02/5.32 thf(fact_5760_of__int__0__less__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_less_iff
% 5.02/5.32 thf(fact_5761_of__int__0__less__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_less_iff
% 5.02/5.32 thf(fact_5762_of__int__0__less__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_0_less_iff
% 5.02/5.32 thf(fact_5763_of__int__numeral__le__iff,axiom,
% 5.02/5.32 ! [N2: num,Z: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral_le_iff
% 5.02/5.32 thf(fact_5764_of__int__numeral__le__iff,axiom,
% 5.02/5.32 ! [N2: num,Z: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral_le_iff
% 5.02/5.32 thf(fact_5765_of__int__numeral__le__iff,axiom,
% 5.02/5.32 ! [N2: num,Z: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral_le_iff
% 5.02/5.32 thf(fact_5766_of__int__le__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_numeral_iff
% 5.02/5.32 thf(fact_5767_of__int__le__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_numeral_iff
% 5.02/5.32 thf(fact_5768_of__int__le__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_numeral_iff
% 5.02/5.32 thf(fact_5769_of__int__numeral__less__iff,axiom,
% 5.02/5.32 ! [N2: num,Z: int] :
% 5.02/5.32 ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral_less_iff
% 5.02/5.32 thf(fact_5770_of__int__numeral__less__iff,axiom,
% 5.02/5.32 ! [N2: num,Z: int] :
% 5.02/5.32 ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral_less_iff
% 5.02/5.32 thf(fact_5771_of__int__numeral__less__iff,axiom,
% 5.02/5.32 ! [N2: num,Z: int] :
% 5.02/5.32 ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_numeral_less_iff
% 5.02/5.32 thf(fact_5772_of__int__less__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_numeral_iff
% 5.02/5.32 thf(fact_5773_of__int__less__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_numeral_iff
% 5.02/5.32 thf(fact_5774_of__int__less__numeral__iff,axiom,
% 5.02/5.32 ! [Z: int,N2: num] :
% 5.02/5.32 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_numeral_iff
% 5.02/5.32 thf(fact_5775_of__int__1__le__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1_le_iff
% 5.02/5.32 thf(fact_5776_of__int__1__le__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1_le_iff
% 5.02/5.32 thf(fact_5777_of__int__1__le__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1_le_iff
% 5.02/5.32 thf(fact_5778_of__int__le__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_1_iff
% 5.02/5.32 thf(fact_5779_of__int__le__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_1_iff
% 5.02/5.32 thf(fact_5780_of__int__le__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.02/5.32 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_1_iff
% 5.02/5.32 thf(fact_5781_of__int__1__less__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.02/5.32 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1_less_iff
% 5.02/5.32 thf(fact_5782_of__int__1__less__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.02/5.32 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1_less_iff
% 5.02/5.32 thf(fact_5783_of__int__1__less__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.02/5.32 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_1_less_iff
% 5.02/5.32 thf(fact_5784_of__int__less__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.02/5.32 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_1_iff
% 5.02/5.32 thf(fact_5785_of__int__less__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.02/5.32 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_1_iff
% 5.02/5.32 thf(fact_5786_of__int__less__1__iff,axiom,
% 5.02/5.32 ! [Z: int] :
% 5.02/5.32 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.02/5.32 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_1_iff
% 5.02/5.32 thf(fact_5787_take__bit__of__1,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 5.02/5.32 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_1
% 5.02/5.32 thf(fact_5788_take__bit__of__1,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.02/5.32 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_1
% 5.02/5.32 thf(fact_5789_take__bit__of__1,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.02/5.32 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_1
% 5.02/5.32 thf(fact_5790_of__int__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.02/5.32 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5791_of__int__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.02/5.32 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5792_of__int__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.02/5.32 = ( ord_less_eq_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5793_of__int__le__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5794_of__int__le__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5795_of__int__le__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5796_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.02/5.32 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5797_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_real @ Y )
% 5.02/5.32 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5798_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_rat @ Y )
% 5.02/5.32 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5799_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_int @ Y )
% 5.02/5.32 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5800_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N2 )
% 5.02/5.32 = ( ring_17405671764205052669omplex @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5801_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N2 )
% 5.02/5.32 = ( ring_1_of_int_real @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5802_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N2 )
% 5.02/5.32 = ( ring_1_of_int_rat @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5803_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 )
% 5.02/5.32 = ( ring_1_of_int_int @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5804_of__int__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ord_less_real @ ( ring_1_of_int_real @ X2 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.02/5.32 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5805_of__int__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X2 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.02/5.32 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5806_of__int__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: int,B: int,W: nat] :
% 5.02/5.32 ( ( ord_less_int @ ( ring_1_of_int_int @ X2 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.02/5.32 = ( ord_less_int @ X2 @ ( power_power_int @ B @ W ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5807_of__int__less__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X2 ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5808_of__int__less__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5809_of__int__less__of__int__power__cancel__iff,axiom,
% 5.02/5.32 ! [B: int,W: nat,X2: int] :
% 5.02/5.32 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X2 ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_of_int_power_cancel_iff
% 5.02/5.32 thf(fact_5810_even__take__bit__eq,axiom,
% 5.02/5.32 ! [N2: nat,A: code_integer] :
% 5.02/5.32 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 5.02/5.32 = ( ( N2 = zero_zero_nat )
% 5.02/5.32 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % even_take_bit_eq
% 5.02/5.32 thf(fact_5811_even__take__bit__eq,axiom,
% 5.02/5.32 ! [N2: nat,A: int] :
% 5.02/5.32 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.02/5.32 = ( ( N2 = zero_zero_nat )
% 5.02/5.32 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % even_take_bit_eq
% 5.02/5.32 thf(fact_5812_even__take__bit__eq,axiom,
% 5.02/5.32 ! [N2: nat,A: nat] :
% 5.02/5.32 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 5.02/5.32 = ( ( N2 = zero_zero_nat )
% 5.02/5.32 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % even_take_bit_eq
% 5.02/5.32 thf(fact_5813_Suc__div__eq__add3__div__numeral,axiom,
% 5.02/5.32 ! [M: nat,V: num] :
% 5.02/5.32 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.02/5.32 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % Suc_div_eq_add3_div_numeral
% 5.02/5.32 thf(fact_5814_div__Suc__eq__div__add3,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.02/5.32 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % div_Suc_eq_div_add3
% 5.02/5.32 thf(fact_5815_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.02/5.32 ! [M: nat,V: num] :
% 5.02/5.32 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.02/5.32 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % Suc_mod_eq_add3_mod_numeral
% 5.02/5.32 thf(fact_5816_mod__Suc__eq__mod__add3,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.02/5.32 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % mod_Suc_eq_mod_add3
% 5.02/5.32 thf(fact_5817_take__bit__Suc__0,axiom,
% 5.02/5.32 ! [A: int] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.02/5.32 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_Suc_0
% 5.02/5.32 thf(fact_5818_take__bit__Suc__0,axiom,
% 5.02/5.32 ! [A: nat] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.02/5.32 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_Suc_0
% 5.02/5.32 thf(fact_5819_real__sqrt__pow2__iff,axiom,
% 5.02/5.32 ! [X2: real] :
% 5.02/5.32 ( ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = X2 )
% 5.02/5.32 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_pow2_iff
% 5.02/5.32 thf(fact_5820_real__sqrt__pow2,axiom,
% 5.02/5.32 ! [X2: real] :
% 5.02/5.32 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.32 => ( ( power_power_real @ ( sqrt @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = X2 ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_pow2
% 5.02/5.32 thf(fact_5821_of__int__le__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5822_of__int__le__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5823_of__int__le__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5824_numeral__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5825_numeral__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5826_numeral__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5827_of__int__less__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5828_of__int__less__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5829_of__int__less__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5830_numeral__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5831_numeral__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5832_numeral__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % numeral_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5833_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.02/5.32 ! [X2: real,Y: real,Xa2: real,Ya: real] :
% 5.02/5.32 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % real_sqrt_sum_squares_mult_squared_eq
% 5.02/5.32 thf(fact_5834_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_real @ Y )
% 5.02/5.32 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5835_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_int @ Y )
% 5.02/5.32 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5836_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.02/5.32 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5837_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_1_of_int_rat @ Y )
% 5.02/5.32 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5838_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ( ring_18347121197199848620nteger @ Y )
% 5.02/5.32 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( Y
% 5.02/5.32 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_eq_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5839_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N2 )
% 5.02/5.32 = ( ring_1_of_int_real @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5840_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 )
% 5.02/5.32 = ( ring_1_of_int_int @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5841_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X2 ) ) @ N2 )
% 5.02/5.32 = ( ring_17405671764205052669omplex @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5842_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N2 )
% 5.02/5.32 = ( ring_1_of_int_rat @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5843_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.32 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N2 )
% 5.02/5.32 = ( ring_18347121197199848620nteger @ Y ) )
% 5.02/5.32 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 )
% 5.02/5.32 = Y ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_eq_of_int_cancel_iff
% 5.02/5.32 thf(fact_5844_take__bit__of__exp,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_exp
% 5.02/5.32 thf(fact_5845_take__bit__of__exp,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_exp
% 5.02/5.32 thf(fact_5846_take__bit__of__exp,axiom,
% 5.02/5.32 ! [M: nat,N2: nat] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.32 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_exp
% 5.02/5.32 thf(fact_5847_take__bit__of__2,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_2
% 5.02/5.32 thf(fact_5848_take__bit__of__2,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_2
% 5.02/5.32 thf(fact_5849_take__bit__of__2,axiom,
% 5.02/5.32 ! [N2: nat] :
% 5.02/5.32 ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.32 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_of_2
% 5.02/5.32 thf(fact_5850_zmod__numeral__Bit1,axiom,
% 5.02/5.32 ! [V: num,W: num] :
% 5.02/5.32 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.02/5.32 = ( 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 ) ) ).
% 5.02/5.32
% 5.02/5.32 % zmod_numeral_Bit1
% 5.02/5.32 thf(fact_5851_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5852_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5853_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5854_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_le_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5855_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5856_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5857_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5858_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.02/5.32 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_le_of_int_cancel_iff
% 5.02/5.32 thf(fact_5859_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5860_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5861_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5862_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.02/5.32 ! [A: int,X2: num,N2: nat] :
% 5.02/5.32 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N2 ) )
% 5.02/5.32 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % of_int_less_neg_numeral_power_cancel_iff
% 5.02/5.32 thf(fact_5863_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X2 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5864_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5865_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X2 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5866_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.02/5.32 ! [X2: num,N2: nat,A: int] :
% 5.02/5.32 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X2 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.02/5.32 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X2 ) ) @ N2 ) @ A ) ) ).
% 5.02/5.32
% 5.02/5.32 % neg_numeral_power_less_of_int_cancel_iff
% 5.02/5.32 thf(fact_5867_take__bit__minus,axiom,
% 5.02/5.32 ! [N2: nat,K: int] :
% 5.02/5.32 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 5.02/5.32 = ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.02/5.32
% 5.02/5.32 % take_bit_minus
% 5.02/5.32 thf(fact_5868_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 5.02/5.32 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.02/5.32 = ( produc4947309494688390418_int_o
% 5.02/5.32 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.32 @ Prod ) ) ).
% 5.02/5.32
% 5.02/5.32 % prod.case_distrib
% 5.02/5.32 thf(fact_5869_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: $o > int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.02/5.32 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.02/5.32 = ( produc8211389475949308722nt_int
% 5.02/5.32 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.32 @ Prod ) ) ).
% 5.02/5.32
% 5.02/5.32 % prod.case_distrib
% 5.02/5.32 thf(fact_5870_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 5.02/5.32 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.02/5.32 = ( produc4947309494688390418_int_o
% 5.02/5.32 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.32 @ Prod ) ) ).
% 5.02/5.32
% 5.02/5.32 % prod.case_distrib
% 5.02/5.32 thf(fact_5871_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 5.02/5.32 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.02/5.32 = ( produc8211389475949308722nt_int
% 5.02/5.32 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.32 @ Prod ) ) ).
% 5.02/5.32
% 5.02/5.32 % prod.case_distrib
% 5.02/5.32 thf(fact_5872_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.02/5.32 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.02/5.32 = ( produc4947309494688390418_int_o
% 5.02/5.32 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.32 @ Prod ) ) ).
% 5.02/5.32
% 5.02/5.32 % prod.case_distrib
% 5.02/5.32 thf(fact_5873_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.02/5.32 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.02/5.32 = ( produc8211389475949308722nt_int
% 5.02/5.32 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.32 @ Prod ) ) ).
% 5.02/5.32
% 5.02/5.32 % prod.case_distrib
% 5.02/5.32 thf(fact_5874_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: $o > product_prod_int_int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.02/5.32 ( ( H2 @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.02/5.32 = ( produc4245557441103728435nt_int
% 5.02/5.32 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.32 @ Prod ) ) ).
% 5.02/5.32
% 5.02/5.32 % prod.case_distrib
% 5.02/5.32 thf(fact_5875_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 5.02/5.32 ( ( H2 @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.02/5.32 = ( produc4245557441103728435nt_int
% 5.02/5.32 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.32 @ Prod ) ) ).
% 5.02/5.32
% 5.02/5.32 % prod.case_distrib
% 5.02/5.32 thf(fact_5876_prod_Ocase__distrib,axiom,
% 5.02/5.32 ! [H2: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.02/5.33 ( ( H2 @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.02/5.33 = ( produc4245557441103728435nt_int
% 5.02/5.33 @ ^ [X15: int,X24: int] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.33 @ Prod ) ) ).
% 5.02/5.33
% 5.02/5.33 % prod.case_distrib
% 5.02/5.33 thf(fact_5877_prod_Ocase__distrib,axiom,
% 5.02/5.33 ! [H2: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 5.02/5.33 ( ( H2 @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 5.02/5.33 = ( produc8739625826339149834_nat_o
% 5.02/5.33 @ ^ [X15: nat,X24: nat] : ( H2 @ ( F @ X15 @ X24 ) )
% 5.02/5.33 @ Prod ) ) ).
% 5.02/5.33
% 5.02/5.33 % prod.case_distrib
% 5.02/5.33 thf(fact_5878_take__bit__of__int,axiom,
% 5.02/5.33 ! [N2: nat,K: int] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 5.02/5.33 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_of_int
% 5.02/5.33 thf(fact_5879_take__bit__add,axiom,
% 5.02/5.33 ! [N2: nat,A: int,B: int] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_add
% 5.02/5.33 thf(fact_5880_take__bit__add,axiom,
% 5.02/5.33 ! [N2: nat,A: nat,B: nat] :
% 5.02/5.33 ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 5.02/5.33 = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_add
% 5.02/5.33 thf(fact_5881_take__bit__tightened,axiom,
% 5.02/5.33 ! [N2: nat,A: int,B: int,M: nat] :
% 5.02/5.33 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.02/5.33 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_tightened
% 5.02/5.33 thf(fact_5882_take__bit__tightened,axiom,
% 5.02/5.33 ! [N2: nat,A: nat,B: nat,M: nat] :
% 5.02/5.33 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.02/5.33 = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 5.02/5.33 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.02/5.33 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_tightened
% 5.02/5.33 thf(fact_5883_take__bit__tightened__less__eq__nat,axiom,
% 5.02/5.33 ! [M: nat,N2: nat,Q2: nat] :
% 5.02/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.33 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_tightened_less_eq_nat
% 5.02/5.33 thf(fact_5884_take__bit__nat__less__eq__self,axiom,
% 5.02/5.33 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_nat_less_eq_self
% 5.02/5.33 thf(fact_5885_mult__of__int__commute,axiom,
% 5.02/5.33 ! [X2: int,Y: real] :
% 5.02/5.33 ( ( times_times_real @ ( ring_1_of_int_real @ X2 ) @ Y )
% 5.02/5.33 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mult_of_int_commute
% 5.02/5.33 thf(fact_5886_mult__of__int__commute,axiom,
% 5.02/5.33 ! [X2: int,Y: rat] :
% 5.02/5.33 ( ( times_times_rat @ ( ring_1_of_int_rat @ X2 ) @ Y )
% 5.02/5.33 = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mult_of_int_commute
% 5.02/5.33 thf(fact_5887_mult__of__int__commute,axiom,
% 5.02/5.33 ! [X2: int,Y: int] :
% 5.02/5.33 ( ( times_times_int @ ( ring_1_of_int_int @ X2 ) @ Y )
% 5.02/5.33 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mult_of_int_commute
% 5.02/5.33 thf(fact_5888_real__sqrt__mult,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( sqrt @ ( times_times_real @ X2 @ Y ) )
% 5.02/5.33 = ( times_times_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_mult
% 5.02/5.33 thf(fact_5889_take__bit__mult,axiom,
% 5.02/5.33 ! [N2: nat,K: int,L: int] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_mult
% 5.02/5.33 thf(fact_5890_verit__eq__simplify_I14_J,axiom,
% 5.02/5.33 ! [X22: num,X32: num] :
% 5.02/5.33 ( ( bit0 @ X22 )
% 5.02/5.33 != ( bit1 @ X32 ) ) ).
% 5.02/5.33
% 5.02/5.33 % verit_eq_simplify(14)
% 5.02/5.33 thf(fact_5891_verit__eq__simplify_I12_J,axiom,
% 5.02/5.33 ! [X32: num] :
% 5.02/5.33 ( one
% 5.02/5.33 != ( bit1 @ X32 ) ) ).
% 5.02/5.33
% 5.02/5.33 % verit_eq_simplify(12)
% 5.02/5.33 thf(fact_5892_take__bit__diff,axiom,
% 5.02/5.33 ! [N2: nat,K: int,L: int] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_diff
% 5.02/5.33 thf(fact_5893_of__int__max,axiom,
% 5.02/5.33 ! [X2: int,Y: int] :
% 5.02/5.33 ( ( ring_1_of_int_real @ ( ord_max_int @ X2 @ Y ) )
% 5.02/5.33 = ( ord_max_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_max
% 5.02/5.33 thf(fact_5894_of__int__max,axiom,
% 5.02/5.33 ! [X2: int,Y: int] :
% 5.02/5.33 ( ( ring_1_of_int_rat @ ( ord_max_int @ X2 @ Y ) )
% 5.02/5.33 = ( ord_max_rat @ ( ring_1_of_int_rat @ X2 ) @ ( ring_1_of_int_rat @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_max
% 5.02/5.33 thf(fact_5895_of__int__max,axiom,
% 5.02/5.33 ! [X2: int,Y: int] :
% 5.02/5.33 ( ( ring_1_of_int_int @ ( ord_max_int @ X2 @ Y ) )
% 5.02/5.33 = ( ord_max_int @ ( ring_1_of_int_int @ X2 ) @ ( ring_1_of_int_int @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_max
% 5.02/5.33 thf(fact_5896_old_Oprod_Ocase,axiom,
% 5.02/5.33 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 5.02/5.33 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.02/5.33 = ( F @ X1 @ X22 ) ) ).
% 5.02/5.33
% 5.02/5.33 % old.prod.case
% 5.02/5.33 thf(fact_5897_old_Oprod_Ocase,axiom,
% 5.02/5.33 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 5.02/5.33 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.02/5.33 = ( F @ X1 @ X22 ) ) ).
% 5.02/5.33
% 5.02/5.33 % old.prod.case
% 5.02/5.33 thf(fact_5898_old_Oprod_Ocase,axiom,
% 5.02/5.33 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 5.02/5.33 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.02/5.33 = ( F @ X1 @ X22 ) ) ).
% 5.02/5.33
% 5.02/5.33 % old.prod.case
% 5.02/5.33 thf(fact_5899_old_Oprod_Ocase,axiom,
% 5.02/5.33 ! [F: int > int > $o,X1: int,X22: int] :
% 5.02/5.33 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.02/5.33 = ( F @ X1 @ X22 ) ) ).
% 5.02/5.33
% 5.02/5.33 % old.prod.case
% 5.02/5.33 thf(fact_5900_old_Oprod_Ocase,axiom,
% 5.02/5.33 ! [F: int > int > int,X1: int,X22: int] :
% 5.02/5.33 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.02/5.33 = ( F @ X1 @ X22 ) ) ).
% 5.02/5.33
% 5.02/5.33 % old.prod.case
% 5.02/5.33 thf(fact_5901_concat__bit__eq__iff,axiom,
% 5.02/5.33 ! [N2: nat,K: int,L: int,R2: int,S2: int] :
% 5.02/5.33 ( ( ( bit_concat_bit @ N2 @ K @ L )
% 5.02/5.33 = ( bit_concat_bit @ N2 @ R2 @ S2 ) )
% 5.02/5.33 = ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ N2 @ R2 ) )
% 5.02/5.33 & ( L = S2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % concat_bit_eq_iff
% 5.02/5.33 thf(fact_5902_concat__bit__take__bit__eq,axiom,
% 5.02/5.33 ! [N2: nat,B: int] :
% 5.02/5.33 ( ( bit_concat_bit @ N2 @ ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.02/5.33 = ( bit_concat_bit @ N2 @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % concat_bit_take_bit_eq
% 5.02/5.33 thf(fact_5903_case__prodE2,axiom,
% 5.02/5.33 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.02/5.33 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.02/5.33 => ~ ! [X5: nat,Y3: nat] :
% 5.02/5.33 ( ( Z
% 5.02/5.33 = ( product_Pair_nat_nat @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( Q @ ( P @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE2
% 5.02/5.33 thf(fact_5904_case__prodE2,axiom,
% 5.02/5.33 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.02/5.33 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.02/5.33 => ~ ! [X5: nat,Y3: nat] :
% 5.02/5.33 ( ( Z
% 5.02/5.33 = ( product_Pair_nat_nat @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( Q @ ( P @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE2
% 5.02/5.33 thf(fact_5905_case__prodE2,axiom,
% 5.02/5.33 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.02/5.33 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.02/5.33 => ~ ! [X5: int,Y3: int] :
% 5.02/5.33 ( ( Z
% 5.02/5.33 = ( product_Pair_int_int @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( Q @ ( P @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE2
% 5.02/5.33 thf(fact_5906_case__prodE2,axiom,
% 5.02/5.33 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.02/5.33 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.02/5.33 => ~ ! [X5: int,Y3: int] :
% 5.02/5.33 ( ( Z
% 5.02/5.33 = ( product_Pair_int_int @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( Q @ ( P @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE2
% 5.02/5.33 thf(fact_5907_case__prodE2,axiom,
% 5.02/5.33 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.02/5.33 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.02/5.33 => ~ ! [X5: int,Y3: int] :
% 5.02/5.33 ( ( Z
% 5.02/5.33 = ( product_Pair_int_int @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( Q @ ( P @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE2
% 5.02/5.33 thf(fact_5908_case__prod__eta,axiom,
% 5.02/5.33 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.02/5.33 ( ( produc27273713700761075at_nat
% 5.02/5.33 @ ^ [X: nat,Y6: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y6 ) ) )
% 5.02/5.33 = F ) ).
% 5.02/5.33
% 5.02/5.33 % case_prod_eta
% 5.02/5.33 thf(fact_5909_case__prod__eta,axiom,
% 5.02/5.33 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.02/5.33 ( ( produc8739625826339149834_nat_o
% 5.02/5.33 @ ^ [X: nat,Y6: nat] : ( F @ ( product_Pair_nat_nat @ X @ Y6 ) ) )
% 5.02/5.33 = F ) ).
% 5.02/5.33
% 5.02/5.33 % case_prod_eta
% 5.02/5.33 thf(fact_5910_case__prod__eta,axiom,
% 5.02/5.33 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.02/5.33 ( ( produc4245557441103728435nt_int
% 5.02/5.33 @ ^ [X: int,Y6: int] : ( F @ ( product_Pair_int_int @ X @ Y6 ) ) )
% 5.02/5.33 = F ) ).
% 5.02/5.33
% 5.02/5.33 % case_prod_eta
% 5.02/5.33 thf(fact_5911_case__prod__eta,axiom,
% 5.02/5.33 ! [F: product_prod_int_int > $o] :
% 5.02/5.33 ( ( produc4947309494688390418_int_o
% 5.02/5.33 @ ^ [X: int,Y6: int] : ( F @ ( product_Pair_int_int @ X @ Y6 ) ) )
% 5.02/5.33 = F ) ).
% 5.02/5.33
% 5.02/5.33 % case_prod_eta
% 5.02/5.33 thf(fact_5912_case__prod__eta,axiom,
% 5.02/5.33 ! [F: product_prod_int_int > int] :
% 5.02/5.33 ( ( produc8211389475949308722nt_int
% 5.02/5.33 @ ^ [X: int,Y6: int] : ( F @ ( product_Pair_int_int @ X @ Y6 ) ) )
% 5.02/5.33 = F ) ).
% 5.02/5.33
% 5.02/5.33 % case_prod_eta
% 5.02/5.33 thf(fact_5913_cond__case__prod__eta,axiom,
% 5.02/5.33 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.02/5.33 ( ! [X5: nat,Y3: nat] :
% 5.02/5.33 ( ( F @ X5 @ Y3 )
% 5.02/5.33 = ( G @ ( product_Pair_nat_nat @ X5 @ Y3 ) ) )
% 5.02/5.33 => ( ( produc27273713700761075at_nat @ F )
% 5.02/5.33 = G ) ) ).
% 5.02/5.33
% 5.02/5.33 % cond_case_prod_eta
% 5.02/5.33 thf(fact_5914_cond__case__prod__eta,axiom,
% 5.02/5.33 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.02/5.33 ( ! [X5: nat,Y3: nat] :
% 5.02/5.33 ( ( F @ X5 @ Y3 )
% 5.02/5.33 = ( G @ ( product_Pair_nat_nat @ X5 @ Y3 ) ) )
% 5.02/5.33 => ( ( produc8739625826339149834_nat_o @ F )
% 5.02/5.33 = G ) ) ).
% 5.02/5.33
% 5.02/5.33 % cond_case_prod_eta
% 5.02/5.33 thf(fact_5915_cond__case__prod__eta,axiom,
% 5.02/5.33 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.02/5.33 ( ! [X5: int,Y3: int] :
% 5.02/5.33 ( ( F @ X5 @ Y3 )
% 5.02/5.33 = ( G @ ( product_Pair_int_int @ X5 @ Y3 ) ) )
% 5.02/5.33 => ( ( produc4245557441103728435nt_int @ F )
% 5.02/5.33 = G ) ) ).
% 5.02/5.33
% 5.02/5.33 % cond_case_prod_eta
% 5.02/5.33 thf(fact_5916_cond__case__prod__eta,axiom,
% 5.02/5.33 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.02/5.33 ( ! [X5: int,Y3: int] :
% 5.02/5.33 ( ( F @ X5 @ Y3 )
% 5.02/5.33 = ( G @ ( product_Pair_int_int @ X5 @ Y3 ) ) )
% 5.02/5.33 => ( ( produc4947309494688390418_int_o @ F )
% 5.02/5.33 = G ) ) ).
% 5.02/5.33
% 5.02/5.33 % cond_case_prod_eta
% 5.02/5.33 thf(fact_5917_cond__case__prod__eta,axiom,
% 5.02/5.33 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.02/5.33 ( ! [X5: int,Y3: int] :
% 5.02/5.33 ( ( F @ X5 @ Y3 )
% 5.02/5.33 = ( G @ ( product_Pair_int_int @ X5 @ Y3 ) ) )
% 5.02/5.33 => ( ( produc8211389475949308722nt_int @ F )
% 5.02/5.33 = G ) ) ).
% 5.02/5.33
% 5.02/5.33 % cond_case_prod_eta
% 5.02/5.33 thf(fact_5918_real__sqrt__ge__one,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.02/5.33 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_ge_one
% 5.02/5.33 thf(fact_5919_take__bit__tightened__less__eq__int,axiom,
% 5.02/5.33 ! [M: nat,N2: nat,K: int] :
% 5.02/5.33 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.33 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_tightened_less_eq_int
% 5.02/5.33 thf(fact_5920_take__bit__nonnegative,axiom,
% 5.02/5.33 ! [N2: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_nonnegative
% 5.02/5.33 thf(fact_5921_take__bit__int__less__eq__self__iff,axiom,
% 5.02/5.33 ! [N2: nat,K: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.02/5.33 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_less_eq_self_iff
% 5.02/5.33 thf(fact_5922_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.02/5.33 ! [N2: nat,A: int,B: int] :
% 5.02/5.33 ( ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 5.02/5.33 = ( bit_ri631733984087533419it_int @ N2 @ B ) )
% 5.02/5.33 = ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % signed_take_bit_eq_iff_take_bit_eq
% 5.02/5.33 thf(fact_5923_not__take__bit__negative,axiom,
% 5.02/5.33 ! [N2: nat,K: int] :
% 5.02/5.33 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 5.02/5.33
% 5.02/5.33 % not_take_bit_negative
% 5.02/5.33 thf(fact_5924_take__bit__int__greater__self__iff,axiom,
% 5.02/5.33 ! [K: int,N2: nat] :
% 5.02/5.33 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.02/5.33 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_greater_self_iff
% 5.02/5.33 thf(fact_5925_signed__take__bit__take__bit,axiom,
% 5.02/5.33 ! [M: nat,N2: nat,A: int] :
% 5.02/5.33 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.02/5.33 = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % signed_take_bit_take_bit
% 5.02/5.33 thf(fact_5926_num_Oexhaust,axiom,
% 5.02/5.33 ! [Y: num] :
% 5.02/5.33 ( ( Y != one )
% 5.02/5.33 => ( ! [X23: num] :
% 5.02/5.33 ( Y
% 5.02/5.33 != ( bit0 @ X23 ) )
% 5.02/5.33 => ~ ! [X33: num] :
% 5.02/5.33 ( Y
% 5.02/5.33 != ( bit1 @ X33 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % num.exhaust
% 5.02/5.33 thf(fact_5927_xor__num_Ocases,axiom,
% 5.02/5.33 ! [X2: product_prod_num_num] :
% 5.02/5.33 ( ( X2
% 5.02/5.33 != ( product_Pair_num_num @ one @ one ) )
% 5.02/5.33 => ( ! [N: num] :
% 5.02/5.33 ( X2
% 5.02/5.33 != ( product_Pair_num_num @ one @ ( bit0 @ N ) ) )
% 5.02/5.33 => ( ! [N: num] :
% 5.02/5.33 ( X2
% 5.02/5.33 != ( product_Pair_num_num @ one @ ( bit1 @ N ) ) )
% 5.02/5.33 => ( ! [M3: num] :
% 5.02/5.33 ( X2
% 5.02/5.33 != ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) )
% 5.02/5.33 => ( ! [M3: num,N: num] :
% 5.02/5.33 ( X2
% 5.02/5.33 != ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N ) ) )
% 5.02/5.33 => ( ! [M3: num,N: num] :
% 5.02/5.33 ( X2
% 5.02/5.33 != ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N ) ) )
% 5.02/5.33 => ( ! [M3: num] :
% 5.02/5.33 ( X2
% 5.02/5.33 != ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) )
% 5.02/5.33 => ( ! [M3: num,N: num] :
% 5.02/5.33 ( X2
% 5.02/5.33 != ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N ) ) )
% 5.02/5.33 => ~ ! [M3: num,N: num] :
% 5.02/5.33 ( X2
% 5.02/5.33 != ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % xor_num.cases
% 5.02/5.33 thf(fact_5928_take__bit__unset__bit__eq,axiom,
% 5.02/5.33 ! [N2: nat,M: nat,A: int] :
% 5.02/5.33 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.02/5.33 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_unset_bit_eq
% 5.02/5.33 thf(fact_5929_take__bit__unset__bit__eq,axiom,
% 5.02/5.33 ! [N2: nat,M: nat,A: nat] :
% 5.02/5.33 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.02/5.33 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.02/5.33 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_unset_bit_eq
% 5.02/5.33 thf(fact_5930_take__bit__set__bit__eq,axiom,
% 5.02/5.33 ! [N2: nat,M: nat,A: int] :
% 5.02/5.33 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.02/5.33 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_set_bit_eq
% 5.02/5.33 thf(fact_5931_take__bit__set__bit__eq,axiom,
% 5.02/5.33 ! [N2: nat,M: nat,A: nat] :
% 5.02/5.33 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.02/5.33 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.02/5.33 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_set_bit_eq
% 5.02/5.33 thf(fact_5932_take__bit__flip__bit__eq,axiom,
% 5.02/5.33 ! [N2: nat,M: nat,A: int] :
% 5.02/5.33 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.02/5.33 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_flip_bit_eq
% 5.02/5.33 thf(fact_5933_take__bit__flip__bit__eq,axiom,
% 5.02/5.33 ! [N2: nat,M: nat,A: nat] :
% 5.02/5.33 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.02/5.33 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.02/5.33 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_flip_bit_eq
% 5.02/5.33 thf(fact_5934_sqrt__add__le__add__sqrt,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.33 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X2 @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X2 ) @ ( sqrt @ Y ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % sqrt_add_le_add_sqrt
% 5.02/5.33 thf(fact_5935_take__bit__signed__take__bit,axiom,
% 5.02/5.33 ! [M: nat,N2: nat,A: int] :
% 5.02/5.33 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 5.02/5.33 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_signed_take_bit
% 5.02/5.33 thf(fact_5936_of__int__neg__numeral,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_neg_numeral
% 5.02/5.33 thf(fact_5937_of__int__neg__numeral,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_neg_numeral
% 5.02/5.33 thf(fact_5938_of__int__neg__numeral,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_neg_numeral
% 5.02/5.33 thf(fact_5939_of__int__neg__numeral,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_neg_numeral
% 5.02/5.33 thf(fact_5940_of__int__neg__numeral,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_neg_numeral
% 5.02/5.33 thf(fact_5941_le__real__sqrt__sumsq,axiom,
% 5.02/5.33 ! [X2: real,Y: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X2 @ X2 ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % le_real_sqrt_sumsq
% 5.02/5.33 thf(fact_5942_numeral__Bit1,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_Bit1
% 5.02/5.33 thf(fact_5943_numeral__Bit1,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_Bit1
% 5.02/5.33 thf(fact_5944_numeral__Bit1,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_Bit1
% 5.02/5.33 thf(fact_5945_numeral__Bit1,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_Bit1
% 5.02/5.33 thf(fact_5946_numeral__Bit1,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_Bit1
% 5.02/5.33 thf(fact_5947_take__bit__decr__eq,axiom,
% 5.02/5.33 ! [N2: nat,K: int] :
% 5.02/5.33 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.02/5.33 != zero_zero_int )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ one_one_int ) )
% 5.02/5.33 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ one_one_int ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_decr_eq
% 5.02/5.33 thf(fact_5948_eval__nat__numeral_I3_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % eval_nat_numeral(3)
% 5.02/5.33 thf(fact_5949_cong__exp__iff__simps_I10_J,axiom,
% 5.02/5.33 ! [M: num,Q2: num,N2: num] :
% 5.02/5.33 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(10)
% 5.02/5.33 thf(fact_5950_cong__exp__iff__simps_I10_J,axiom,
% 5.02/5.33 ! [M: num,Q2: num,N2: num] :
% 5.02/5.33 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(10)
% 5.02/5.33 thf(fact_5951_cong__exp__iff__simps_I12_J,axiom,
% 5.02/5.33 ! [M: num,Q2: num,N2: num] :
% 5.02/5.33 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(12)
% 5.02/5.33 thf(fact_5952_cong__exp__iff__simps_I12_J,axiom,
% 5.02/5.33 ! [M: num,Q2: num,N2: num] :
% 5.02/5.33 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(12)
% 5.02/5.33 thf(fact_5953_cong__exp__iff__simps_I13_J,axiom,
% 5.02/5.33 ! [M: num,Q2: num,N2: num] :
% 5.02/5.33 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.02/5.33 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.02/5.33 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(13)
% 5.02/5.33 thf(fact_5954_cong__exp__iff__simps_I13_J,axiom,
% 5.02/5.33 ! [M: num,Q2: num,N2: num] :
% 5.02/5.33 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.02/5.33 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.02/5.33 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(13)
% 5.02/5.33 thf(fact_5955_power__minus__Bit1,axiom,
% 5.02/5.33 ! [X2: real,K: num] :
% 5.02/5.33 ( ( power_power_real @ ( uminus_uminus_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_minus_Bit1
% 5.02/5.33 thf(fact_5956_power__minus__Bit1,axiom,
% 5.02/5.33 ! [X2: int,K: num] :
% 5.02/5.33 ( ( power_power_int @ ( uminus_uminus_int @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_minus_Bit1
% 5.02/5.33 thf(fact_5957_power__minus__Bit1,axiom,
% 5.02/5.33 ! [X2: complex,K: num] :
% 5.02/5.33 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_minus_Bit1
% 5.02/5.33 thf(fact_5958_power__minus__Bit1,axiom,
% 5.02/5.33 ! [X2: rat,K: num] :
% 5.02/5.33 ( ( power_power_rat @ ( uminus_uminus_rat @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_minus_Bit1
% 5.02/5.33 thf(fact_5959_power__minus__Bit1,axiom,
% 5.02/5.33 ! [X2: code_integer,K: num] :
% 5.02/5.33 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_minus_Bit1
% 5.02/5.33 thf(fact_5960_real__of__int__div4,axiom,
% 5.02/5.33 ! [N2: int,X2: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X2 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_of_int_div4
% 5.02/5.33 thf(fact_5961_take__bit__Suc__bit1,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc_bit1
% 5.02/5.33 thf(fact_5962_take__bit__Suc__bit1,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc_bit1
% 5.02/5.33 thf(fact_5963_real__of__int__div,axiom,
% 5.02/5.33 ! [D: int,N2: int] :
% 5.02/5.33 ( ( dvd_dvd_int @ D @ N2 )
% 5.02/5.33 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ D ) )
% 5.02/5.33 = ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_of_int_div
% 5.02/5.33 thf(fact_5964_numeral__code_I3_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_code(3)
% 5.02/5.33 thf(fact_5965_numeral__code_I3_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_code(3)
% 5.02/5.33 thf(fact_5966_numeral__code_I3_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_code(3)
% 5.02/5.33 thf(fact_5967_numeral__code_I3_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_code(3)
% 5.02/5.33 thf(fact_5968_numeral__code_I3_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_code(3)
% 5.02/5.33 thf(fact_5969_power__numeral__odd,axiom,
% 5.02/5.33 ! [Z: complex,W: num] :
% 5.02/5.33 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.02/5.33 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_numeral_odd
% 5.02/5.33 thf(fact_5970_power__numeral__odd,axiom,
% 5.02/5.33 ! [Z: real,W: num] :
% 5.02/5.33 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.02/5.33 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_numeral_odd
% 5.02/5.33 thf(fact_5971_power__numeral__odd,axiom,
% 5.02/5.33 ! [Z: rat,W: num] :
% 5.02/5.33 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.02/5.33 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_numeral_odd
% 5.02/5.33 thf(fact_5972_power__numeral__odd,axiom,
% 5.02/5.33 ! [Z: nat,W: num] :
% 5.02/5.33 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.02/5.33 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_numeral_odd
% 5.02/5.33 thf(fact_5973_power__numeral__odd,axiom,
% 5.02/5.33 ! [Z: int,W: num] :
% 5.02/5.33 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.02/5.33 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_numeral_odd
% 5.02/5.33 thf(fact_5974_sqrt2__less__2,axiom,
% 5.02/5.33 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.02/5.33
% 5.02/5.33 % sqrt2_less_2
% 5.02/5.33 thf(fact_5975_of__int__nonneg,axiom,
% 5.02/5.33 ! [Z: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.33 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_nonneg
% 5.02/5.33 thf(fact_5976_of__int__nonneg,axiom,
% 5.02/5.33 ! [Z: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.33 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_nonneg
% 5.02/5.33 thf(fact_5977_of__int__nonneg,axiom,
% 5.02/5.33 ! [Z: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.33 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_nonneg
% 5.02/5.33 thf(fact_5978_of__int__pos,axiom,
% 5.02/5.33 ! [Z: int] :
% 5.02/5.33 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.02/5.33 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_pos
% 5.02/5.33 thf(fact_5979_of__int__pos,axiom,
% 5.02/5.33 ! [Z: int] :
% 5.02/5.33 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.02/5.33 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_pos
% 5.02/5.33 thf(fact_5980_of__int__pos,axiom,
% 5.02/5.33 ! [Z: int] :
% 5.02/5.33 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.02/5.33 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_pos
% 5.02/5.33 thf(fact_5981_numeral__Bit1__div__2,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.33 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_Bit1_div_2
% 5.02/5.33 thf(fact_5982_numeral__Bit1__div__2,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.33 = ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_Bit1_div_2
% 5.02/5.33 thf(fact_5983_odd__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % odd_numeral
% 5.02/5.33 thf(fact_5984_odd__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % odd_numeral
% 5.02/5.33 thf(fact_5985_odd__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % odd_numeral
% 5.02/5.33 thf(fact_5986_cong__exp__iff__simps_I3_J,axiom,
% 5.02/5.33 ! [N2: num,Q2: num] :
% 5.02/5.33 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 != zero_zero_nat ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(3)
% 5.02/5.33 thf(fact_5987_cong__exp__iff__simps_I3_J,axiom,
% 5.02/5.33 ! [N2: num,Q2: num] :
% 5.02/5.33 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 != zero_zero_int ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(3)
% 5.02/5.33 thf(fact_5988_power3__eq__cube,axiom,
% 5.02/5.33 ! [A: complex] :
% 5.02/5.33 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.02/5.33 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % power3_eq_cube
% 5.02/5.33 thf(fact_5989_power3__eq__cube,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.02/5.33 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % power3_eq_cube
% 5.02/5.33 thf(fact_5990_power3__eq__cube,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.02/5.33 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % power3_eq_cube
% 5.02/5.33 thf(fact_5991_power3__eq__cube,axiom,
% 5.02/5.33 ! [A: nat] :
% 5.02/5.33 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.02/5.33 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % power3_eq_cube
% 5.02/5.33 thf(fact_5992_power3__eq__cube,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.02/5.33 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % power3_eq_cube
% 5.02/5.33 thf(fact_5993_numeral__3__eq__3,axiom,
% 5.02/5.33 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.02/5.33 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_3_eq_3
% 5.02/5.33 thf(fact_5994_int__le__real__less,axiom,
% 5.02/5.33 ( ord_less_eq_int
% 5.02/5.33 = ( ^ [N3: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N3 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % int_le_real_less
% 5.02/5.33 thf(fact_5995_Suc3__eq__add__3,axiom,
% 5.02/5.33 ! [N2: nat] :
% 5.02/5.33 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 5.02/5.33 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % Suc3_eq_add_3
% 5.02/5.33 thf(fact_5996_int__less__real__le,axiom,
% 5.02/5.33 ( ord_less_int
% 5.02/5.33 = ( ^ [N3: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N3 ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % int_less_real_le
% 5.02/5.33 thf(fact_5997_real__of__int__div__aux,axiom,
% 5.02/5.33 ! [X2: int,D: int] :
% 5.02/5.33 ( ( divide_divide_real @ ( ring_1_of_int_real @ X2 ) @ ( ring_1_of_int_real @ D ) )
% 5.02/5.33 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X2 @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X2 @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_of_int_div_aux
% 5.02/5.33 thf(fact_5998_take__bit__Suc__bit0,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.02/5.33 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc_bit0
% 5.02/5.33 thf(fact_5999_take__bit__Suc__bit0,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.02/5.33 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc_bit0
% 5.02/5.33 thf(fact_6000_take__bit__eq__mod,axiom,
% 5.02/5.33 ( bit_se2923211474154528505it_int
% 5.02/5.33 = ( ^ [N3: nat,A5: int] : ( modulo_modulo_int @ A5 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_eq_mod
% 5.02/5.33 thf(fact_6001_take__bit__eq__mod,axiom,
% 5.02/5.33 ( bit_se2925701944663578781it_nat
% 5.02/5.33 = ( ^ [N3: nat,A5: nat] : ( modulo_modulo_nat @ A5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_eq_mod
% 5.02/5.33 thf(fact_6002_take__bit__nat__eq__self__iff,axiom,
% 5.02/5.33 ! [N2: nat,M: nat] :
% 5.02/5.33 ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.02/5.33 = M )
% 5.02/5.33 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_nat_eq_self_iff
% 5.02/5.33 thf(fact_6003_take__bit__nat__less__exp,axiom,
% 5.02/5.33 ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_nat_less_exp
% 5.02/5.33 thf(fact_6004_take__bit__nat__eq__self,axiom,
% 5.02/5.33 ! [M: nat,N2: nat] :
% 5.02/5.33 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.02/5.33 = M ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_nat_eq_self
% 5.02/5.33 thf(fact_6005_real__less__rsqrt,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.02/5.33 => ( ord_less_real @ X2 @ ( sqrt @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_less_rsqrt
% 5.02/5.33 thf(fact_6006_real__le__rsqrt,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.02/5.33 => ( ord_less_eq_real @ X2 @ ( sqrt @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_le_rsqrt
% 5.02/5.33 thf(fact_6007_sqrt__le__D,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y )
% 5.02/5.33 => ( ord_less_eq_real @ X2 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % sqrt_le_D
% 5.02/5.33 thf(fact_6008_num_Osize_I6_J,axiom,
% 5.02/5.33 ! [X32: num] :
% 5.02/5.33 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.02/5.33 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % num.size(6)
% 5.02/5.33 thf(fact_6009_num_Osize__gen_I3_J,axiom,
% 5.02/5.33 ! [X32: num] :
% 5.02/5.33 ( ( size_num @ ( bit1 @ X32 ) )
% 5.02/5.33 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % num.size_gen(3)
% 5.02/5.33 thf(fact_6010_take__bit__nat__def,axiom,
% 5.02/5.33 ( bit_se2925701944663578781it_nat
% 5.02/5.33 = ( ^ [N3: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_nat_def
% 5.02/5.33 thf(fact_6011_take__bit__Suc__minus__bit0,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.02/5.33 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc_minus_bit0
% 5.02/5.33 thf(fact_6012_take__bit__int__less__exp,axiom,
% 5.02/5.33 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_less_exp
% 5.02/5.33 thf(fact_6013_take__bit__int__def,axiom,
% 5.02/5.33 ( bit_se2923211474154528505it_int
% 5.02/5.33 = ( ^ [N3: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_def
% 5.02/5.33 thf(fact_6014_cong__exp__iff__simps_I7_J,axiom,
% 5.02/5.33 ! [Q2: num,N2: num] :
% 5.02/5.33 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.02/5.33 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.02/5.33 = zero_zero_nat ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(7)
% 5.02/5.33 thf(fact_6015_cong__exp__iff__simps_I7_J,axiom,
% 5.02/5.33 ! [Q2: num,N2: num] :
% 5.02/5.33 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.02/5.33 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q2 ) )
% 5.02/5.33 = zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(7)
% 5.02/5.33 thf(fact_6016_cong__exp__iff__simps_I11_J,axiom,
% 5.02/5.33 ! [M: num,Q2: num] :
% 5.02/5.33 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.02/5.33 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.02/5.33 = zero_zero_nat ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(11)
% 5.02/5.33 thf(fact_6017_cong__exp__iff__simps_I11_J,axiom,
% 5.02/5.33 ! [M: num,Q2: num] :
% 5.02/5.33 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.02/5.33 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.02/5.33 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.02/5.33 = zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % cong_exp_iff_simps(11)
% 5.02/5.33 thf(fact_6018_Suc__div__eq__add3__div,axiom,
% 5.02/5.33 ! [M: nat,N2: nat] :
% 5.02/5.33 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.02/5.33 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % Suc_div_eq_add3_div
% 5.02/5.33 thf(fact_6019_real__of__int__div2,axiom,
% 5.02/5.33 ! [N2: int,X2: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_of_int_div2
% 5.02/5.33 thf(fact_6020_real__of__int__div3,axiom,
% 5.02/5.33 ! [N2: int,X2: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X2 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X2 ) ) ) @ one_one_real ) ).
% 5.02/5.33
% 5.02/5.33 % real_of_int_div3
% 5.02/5.33 thf(fact_6021_Suc__mod__eq__add3__mod,axiom,
% 5.02/5.33 ! [M: nat,N2: nat] :
% 5.02/5.33 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.02/5.33 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % Suc_mod_eq_add3_mod
% 5.02/5.33 thf(fact_6022_take__bit__eq__0__iff,axiom,
% 5.02/5.33 ! [N2: nat,A: code_integer] :
% 5.02/5.33 ( ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.02/5.33 = zero_z3403309356797280102nteger )
% 5.02/5.33 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_eq_0_iff
% 5.02/5.33 thf(fact_6023_take__bit__eq__0__iff,axiom,
% 5.02/5.33 ! [N2: nat,A: int] :
% 5.02/5.33 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.02/5.33 = zero_zero_int )
% 5.02/5.33 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_eq_0_iff
% 5.02/5.33 thf(fact_6024_take__bit__eq__0__iff,axiom,
% 5.02/5.33 ! [N2: nat,A: nat] :
% 5.02/5.33 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.02/5.33 = zero_zero_nat )
% 5.02/5.33 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_eq_0_iff
% 5.02/5.33 thf(fact_6025_take__bit__nat__less__self__iff,axiom,
% 5.02/5.33 ! [N2: nat,M: nat] :
% 5.02/5.33 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 5.02/5.33 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_nat_less_self_iff
% 5.02/5.33 thf(fact_6026_real__sqrt__unique,axiom,
% 5.02/5.33 ! [Y: real,X2: real] :
% 5.02/5.33 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.33 = X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.33 => ( ( sqrt @ X2 )
% 5.02/5.33 = Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_unique
% 5.02/5.33 thf(fact_6027_real__le__lsqrt,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.33 => ( ( ord_less_eq_real @ X2 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.33 => ( ord_less_eq_real @ ( sqrt @ X2 ) @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_le_lsqrt
% 5.02/5.33 thf(fact_6028_lemma__real__divide__sqrt__less,axiom,
% 5.02/5.33 ! [U: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ U )
% 5.02/5.33 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.02/5.33
% 5.02/5.33 % lemma_real_divide_sqrt_less
% 5.02/5.33 thf(fact_6029_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.33 = Y )
% 5.02/5.33 => ( X2 = zero_zero_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_sum_squares_eq_cancel2
% 5.02/5.33 thf(fact_6030_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.33 = X2 )
% 5.02/5.33 => ( Y = zero_zero_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_sum_squares_eq_cancel
% 5.02/5.33 thf(fact_6031_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.02/5.33 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_sum_squares_triangle_ineq
% 5.02/5.33 thf(fact_6032_real__sqrt__sum__squares__ge2,axiom,
% 5.02/5.33 ! [Y: real,X2: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_sum_squares_ge2
% 5.02/5.33 thf(fact_6033_real__sqrt__sum__squares__ge1,axiom,
% 5.02/5.33 ! [X2: real,Y: real] : ( ord_less_eq_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_sum_squares_ge1
% 5.02/5.33 thf(fact_6034_even__of__int__iff,axiom,
% 5.02/5.33 ! [K: int] :
% 5.02/5.33 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.02/5.33 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % even_of_int_iff
% 5.02/5.33 thf(fact_6035_even__of__int__iff,axiom,
% 5.02/5.33 ! [K: int] :
% 5.02/5.33 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.02/5.33 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % even_of_int_iff
% 5.02/5.33 thf(fact_6036_take__bit__int__less__self__iff,axiom,
% 5.02/5.33 ! [N2: nat,K: int] :
% 5.02/5.33 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.02/5.33 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_less_self_iff
% 5.02/5.33 thf(fact_6037_take__bit__int__greater__eq__self__iff,axiom,
% 5.02/5.33 ! [K: int,N2: nat] :
% 5.02/5.33 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.02/5.33 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_greater_eq_self_iff
% 5.02/5.33 thf(fact_6038_real__less__lsqrt,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.33 => ( ( ord_less_real @ X2 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.33 => ( ord_less_real @ ( sqrt @ X2 ) @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_less_lsqrt
% 5.02/5.33 thf(fact_6039_sqrt__sum__squares__le__sum,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.33 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X2 @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % sqrt_sum_squares_le_sum
% 5.02/5.33 thf(fact_6040_sqrt__even__pow2,axiom,
% 5.02/5.33 ! [N2: nat] :
% 5.02/5.33 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.33 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.33 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % sqrt_even_pow2
% 5.02/5.33 thf(fact_6041_take__bit__int__eq__self,axiom,
% 5.02/5.33 ! [K: int,N2: nat] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.33 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.02/5.33 = K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_eq_self
% 5.02/5.33 thf(fact_6042_take__bit__int__eq__self__iff,axiom,
% 5.02/5.33 ! [N2: nat,K: int] :
% 5.02/5.33 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.02/5.33 = K )
% 5.02/5.33 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.33 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_eq_self_iff
% 5.02/5.33 thf(fact_6043_take__bit__incr__eq,axiom,
% 5.02/5.33 ! [N2: nat,K: int] :
% 5.02/5.33 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.02/5.33 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.02/5.33 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_incr_eq
% 5.02/5.33 thf(fact_6044_take__bit__Suc__minus__1__eq,axiom,
% 5.02/5.33 ! [N2: nat] :
% 5.02/5.33 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.33 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc_minus_1_eq
% 5.02/5.33 thf(fact_6045_take__bit__Suc__minus__1__eq,axiom,
% 5.02/5.33 ! [N2: nat] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc_minus_1_eq
% 5.02/5.33 thf(fact_6046_take__bit__numeral__minus__1__eq,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.33 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_numeral_minus_1_eq
% 5.02/5.33 thf(fact_6047_take__bit__numeral__minus__1__eq,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_numeral_minus_1_eq
% 5.02/5.33 thf(fact_6048_take__bit__Suc,axiom,
% 5.02/5.33 ! [N2: nat,A: int] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.02/5.33 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc
% 5.02/5.33 thf(fact_6049_take__bit__Suc,axiom,
% 5.02/5.33 ! [N2: nat,A: nat] :
% 5.02/5.33 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 5.02/5.33 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc
% 5.02/5.33 thf(fact_6050_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.02/5.33 ! [X2: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_sum_squares_mult_ge_zero
% 5.02/5.33 thf(fact_6051_real__sqrt__power__even,axiom,
% 5.02/5.33 ! [N2: nat,X2: real] :
% 5.02/5.33 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( power_power_real @ ( sqrt @ X2 ) @ N2 )
% 5.02/5.33 = ( power_power_real @ X2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_power_even
% 5.02/5.33 thf(fact_6052_arith__geo__mean__sqrt,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.33 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X2 @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % arith_geo_mean_sqrt
% 5.02/5.33 thf(fact_6053_take__bit__int__less__eq,axiom,
% 5.02/5.33 ! [N2: nat,K: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.02/5.33 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.33 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_less_eq
% 5.02/5.33 thf(fact_6054_take__bit__int__greater__eq,axiom,
% 5.02/5.33 ! [K: int,N2: nat] :
% 5.02/5.33 ( ( ord_less_int @ K @ zero_zero_int )
% 5.02/5.33 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_int_greater_eq
% 5.02/5.33 thf(fact_6055_take__bit__minus__small__eq,axiom,
% 5.02/5.33 ! [K: int,N2: nat] :
% 5.02/5.33 ( ( ord_less_int @ zero_zero_int @ K )
% 5.02/5.33 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 5.02/5.33 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_minus_small_eq
% 5.02/5.33 thf(fact_6056_signed__take__bit__eq__take__bit__shift,axiom,
% 5.02/5.33 ( bit_ri631733984087533419it_int
% 5.02/5.33 = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % signed_take_bit_eq_take_bit_shift
% 5.02/5.33 thf(fact_6057_stable__imp__take__bit__eq,axiom,
% 5.02/5.33 ! [A: code_integer,N2: nat] :
% 5.02/5.33 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.33 = A )
% 5.02/5.33 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.02/5.33 = zero_z3403309356797280102nteger ) )
% 5.02/5.33 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.02/5.33 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % stable_imp_take_bit_eq
% 5.02/5.33 thf(fact_6058_stable__imp__take__bit__eq,axiom,
% 5.02/5.33 ! [A: int,N2: nat] :
% 5.02/5.33 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.33 = A )
% 5.02/5.33 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.02/5.33 = zero_zero_int ) )
% 5.02/5.33 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.02/5.33 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % stable_imp_take_bit_eq
% 5.02/5.33 thf(fact_6059_stable__imp__take__bit__eq,axiom,
% 5.02/5.33 ! [A: nat,N2: nat] :
% 5.02/5.33 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.33 = A )
% 5.02/5.33 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.02/5.33 = zero_zero_nat ) )
% 5.02/5.33 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.02/5.33 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % stable_imp_take_bit_eq
% 5.02/5.33 thf(fact_6060_divmod__step__nat__def,axiom,
% 5.02/5.33 ( unique5026877609467782581ep_nat
% 5.02/5.33 = ( ^ [L2: num] :
% 5.02/5.33 ( produc2626176000494625587at_nat
% 5.02/5.33 @ ^ [Q4: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_step_nat_def
% 5.02/5.33 thf(fact_6061_divmod__step__int__def,axiom,
% 5.02/5.33 ( unique5024387138958732305ep_int
% 5.02/5.33 = ( ^ [L2: num] :
% 5.02/5.33 ( produc4245557441103728435nt_int
% 5.02/5.33 @ ^ [Q4: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_step_int_def
% 5.02/5.33 thf(fact_6062_odd__mod__4__div__2,axiom,
% 5.02/5.33 ! [N2: nat] :
% 5.02/5.33 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.02/5.33 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % odd_mod_4_div_2
% 5.02/5.33 thf(fact_6063_arsinh__real__aux,axiom,
% 5.02/5.33 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % arsinh_real_aux
% 5.02/5.33 thf(fact_6064_mod__exhaust__less__4,axiom,
% 5.02/5.33 ! [M: nat] :
% 5.02/5.33 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = zero_zero_nat )
% 5.02/5.33 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = one_one_nat )
% 5.02/5.33 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.33 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mod_exhaust_less_4
% 5.02/5.33 thf(fact_6065_floor__exists1,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ? [X5: int] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X5 ) @ X2 )
% 5.02/5.33 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.02/5.33 & ! [Y5: int] :
% 5.02/5.33 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y5 ) @ X2 )
% 5.02/5.33 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.02/5.33 => ( Y5 = X5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % floor_exists1
% 5.02/5.33 thf(fact_6066_floor__exists1,axiom,
% 5.02/5.33 ! [X2: rat] :
% 5.02/5.33 ? [X5: int] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X5 ) @ X2 )
% 5.02/5.33 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.02/5.33 & ! [Y5: int] :
% 5.02/5.33 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X2 )
% 5.02/5.33 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 5.02/5.33 => ( Y5 = X5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % floor_exists1
% 5.02/5.33 thf(fact_6067_floor__exists,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ? [Z3: int] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X2 )
% 5.02/5.33 & ( ord_less_real @ X2 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % floor_exists
% 5.02/5.33 thf(fact_6068_floor__exists,axiom,
% 5.02/5.33 ! [X2: rat] :
% 5.02/5.33 ? [Z3: int] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 )
% 5.02/5.33 & ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % floor_exists
% 5.02/5.33 thf(fact_6069_divmod__algorithm__code_I6_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.33 = ( produc4245557441103728435nt_int
% 5.02/5.33 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.02/5.33 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(6)
% 5.02/5.33 thf(fact_6070_divmod__algorithm__code_I6_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.33 = ( produc2626176000494625587at_nat
% 5.02/5.33 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.02/5.33 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(6)
% 5.02/5.33 thf(fact_6071_signed__take__bit__numeral__minus__bit1,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.02/5.33 = ( 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 ) ) ).
% 5.02/5.33
% 5.02/5.33 % signed_take_bit_numeral_minus_bit1
% 5.02/5.33 thf(fact_6072_dbl__dec__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(4)
% 5.02/5.33 thf(fact_6073_dbl__dec__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(4)
% 5.02/5.33 thf(fact_6074_dbl__dec__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(4)
% 5.02/5.33 thf(fact_6075_dbl__dec__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.33 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(4)
% 5.02/5.33 thf(fact_6076_dbl__dec__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(4)
% 5.02/5.33 thf(fact_6077_case__prodI2,axiom,
% 5.02/5.33 ! [P2: produc6271795597528267376eger_o,C: code_integer > $o > $o] :
% 5.02/5.33 ( ! [A4: code_integer,B3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ A4 @ B3 ) )
% 5.02/5.33 => ( C @ A4 @ B3 ) )
% 5.02/5.33 => ( produc7828578312038201481er_o_o @ C @ P2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI2
% 5.02/5.33 thf(fact_6078_case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_num_num,C: num > num > $o] :
% 5.02/5.33 ( ! [A4: num,B3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ A4 @ B3 ) )
% 5.02/5.33 => ( C @ A4 @ B3 ) )
% 5.02/5.33 => ( produc5703948589228662326_num_o @ C @ P2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI2
% 5.02/5.33 thf(fact_6079_case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_nat_num,C: nat > num > $o] :
% 5.02/5.33 ( ! [A4: nat,B3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_num @ A4 @ B3 ) )
% 5.02/5.33 => ( C @ A4 @ B3 ) )
% 5.02/5.33 => ( produc4927758841916487424_num_o @ C @ P2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI2
% 5.02/5.33 thf(fact_6080_case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_nat_nat,C: nat > nat > $o] :
% 5.02/5.33 ( ! [A4: nat,B3: nat] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_nat @ A4 @ B3 ) )
% 5.02/5.33 => ( C @ A4 @ B3 ) )
% 5.02/5.33 => ( produc6081775807080527818_nat_o @ C @ P2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI2
% 5.02/5.33 thf(fact_6081_case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_int_int,C: int > int > $o] :
% 5.02/5.33 ( ! [A4: int,B3: int] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_int_int @ A4 @ B3 ) )
% 5.02/5.33 => ( C @ A4 @ B3 ) )
% 5.02/5.33 => ( produc4947309494688390418_int_o @ C @ P2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI2
% 5.02/5.33 thf(fact_6082_case__prodI,axiom,
% 5.02/5.33 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.02/5.33 ( ( F @ A @ B )
% 5.02/5.33 => ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI
% 5.02/5.33 thf(fact_6083_case__prodI,axiom,
% 5.02/5.33 ! [F: num > num > $o,A: num,B: num] :
% 5.02/5.33 ( ( F @ A @ B )
% 5.02/5.33 => ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI
% 5.02/5.33 thf(fact_6084_case__prodI,axiom,
% 5.02/5.33 ! [F: nat > num > $o,A: nat,B: num] :
% 5.02/5.33 ( ( F @ A @ B )
% 5.02/5.33 => ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI
% 5.02/5.33 thf(fact_6085_case__prodI,axiom,
% 5.02/5.33 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.02/5.33 ( ( F @ A @ B )
% 5.02/5.33 => ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI
% 5.02/5.33 thf(fact_6086_case__prodI,axiom,
% 5.02/5.33 ! [F: int > int > $o,A: int,B: int] :
% 5.02/5.33 ( ( F @ A @ B )
% 5.02/5.33 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI
% 5.02/5.33 thf(fact_6087_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: produc6271795597528267376eger_o,Z: complex,C: code_integer > $o > set_complex] :
% 5.02/5.33 ( ! [A4: code_integer,B3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ A4 @ B3 ) )
% 5.02/5.33 => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6088_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: produc6271795597528267376eger_o,Z: real,C: code_integer > $o > set_real] :
% 5.02/5.33 ( ! [A4: code_integer,B3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ A4 @ B3 ) )
% 5.02/5.33 => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6089_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: produc6271795597528267376eger_o,Z: nat,C: code_integer > $o > set_nat] :
% 5.02/5.33 ( ! [A4: code_integer,B3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ A4 @ B3 ) )
% 5.02/5.33 => ( member_nat @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6090_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: produc6271795597528267376eger_o,Z: int,C: code_integer > $o > set_int] :
% 5.02/5.33 ( ! [A4: code_integer,B3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ A4 @ B3 ) )
% 5.02/5.33 => ( member_int @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6091_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_num_num,Z: complex,C: num > num > set_complex] :
% 5.02/5.33 ( ! [A4: num,B3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ A4 @ B3 ) )
% 5.02/5.33 => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6092_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_num_num,Z: real,C: num > num > set_real] :
% 5.02/5.33 ( ! [A4: num,B3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ A4 @ B3 ) )
% 5.02/5.33 => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6093_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_num_num,Z: nat,C: num > num > set_nat] :
% 5.02/5.33 ( ! [A4: num,B3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ A4 @ B3 ) )
% 5.02/5.33 => ( member_nat @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6094_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_num_num,Z: int,C: num > num > set_int] :
% 5.02/5.33 ( ! [A4: num,B3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ A4 @ B3 ) )
% 5.02/5.33 => ( member_int @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6095_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_nat_num,Z: complex,C: nat > num > set_complex] :
% 5.02/5.33 ( ! [A4: nat,B3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_num @ A4 @ B3 ) )
% 5.02/5.33 => ( member_complex @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6096_mem__case__prodI2,axiom,
% 5.02/5.33 ! [P2: product_prod_nat_num,Z: real,C: nat > num > set_real] :
% 5.02/5.33 ( ! [A4: nat,B3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_num @ A4 @ B3 ) )
% 5.02/5.33 => ( member_real @ Z @ ( C @ A4 @ B3 ) ) )
% 5.02/5.33 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI2
% 5.02/5.33 thf(fact_6097_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: complex,C: code_integer > $o > set_complex,A: code_integer,B: $o] :
% 5.02/5.33 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6098_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: real,C: code_integer > $o > set_real,A: code_integer,B: $o] :
% 5.02/5.33 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_real @ Z @ ( produc242741666403216561t_real @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6099_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: nat,C: code_integer > $o > set_nat,A: code_integer,B: $o] :
% 5.02/5.33 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6100_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: int,C: code_integer > $o > set_int,A: code_integer,B: $o] :
% 5.02/5.33 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ ( produc6677183202524767010eger_o @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6101_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: complex,C: num > num > set_complex,A: num,B: num] :
% 5.02/5.33 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6102_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: real,C: num > num > set_real,A: num,B: num] :
% 5.02/5.33 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6103_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: nat,C: num > num > set_nat,A: num,B: num] :
% 5.02/5.33 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6104_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: int,C: num > num > set_int,A: num,B: num] :
% 5.02/5.33 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ ( product_Pair_num_num @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6105_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: complex,C: nat > num > set_complex,A: nat,B: num] :
% 5.02/5.33 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6106_mem__case__prodI,axiom,
% 5.02/5.33 ! [Z: real,C: nat > num > set_real,A: nat,B: num] :
% 5.02/5.33 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.02/5.33 => ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ ( product_Pair_nat_num @ A @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodI
% 5.02/5.33 thf(fact_6107_case__prodI2_H,axiom,
% 5.02/5.33 ! [P2: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X2: product_prod_nat_nat] :
% 5.02/5.33 ( ! [A4: nat,B3: nat] :
% 5.02/5.33 ( ( ( product_Pair_nat_nat @ A4 @ B3 )
% 5.02/5.33 = P2 )
% 5.02/5.33 => ( C @ A4 @ B3 @ X2 ) )
% 5.02/5.33 => ( produc8739625826339149834_nat_o @ C @ P2 @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodI2'
% 5.02/5.33 thf(fact_6108_dbl__dec__simps_I3_J,axiom,
% 5.02/5.33 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.02/5.33 = one_one_complex ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(3)
% 5.02/5.33 thf(fact_6109_dbl__dec__simps_I3_J,axiom,
% 5.02/5.33 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.02/5.33 = one_one_real ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(3)
% 5.02/5.33 thf(fact_6110_dbl__dec__simps_I3_J,axiom,
% 5.02/5.33 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.02/5.33 = one_one_rat ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(3)
% 5.02/5.33 thf(fact_6111_dbl__dec__simps_I3_J,axiom,
% 5.02/5.33 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.02/5.33 = one_one_int ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(3)
% 5.02/5.33 thf(fact_6112_pred__numeral__simps_I1_J,axiom,
% 5.02/5.33 ( ( pred_numeral @ one )
% 5.02/5.33 = zero_zero_nat ) ).
% 5.02/5.33
% 5.02/5.33 % pred_numeral_simps(1)
% 5.02/5.33 thf(fact_6113_Suc__eq__numeral,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( ( suc @ N2 )
% 5.02/5.33 = ( numeral_numeral_nat @ K ) )
% 5.02/5.33 = ( N2
% 5.02/5.33 = ( pred_numeral @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % Suc_eq_numeral
% 5.02/5.33 thf(fact_6114_eq__numeral__Suc,axiom,
% 5.02/5.33 ! [K: num,N2: nat] :
% 5.02/5.33 ( ( ( numeral_numeral_nat @ K )
% 5.02/5.33 = ( suc @ N2 ) )
% 5.02/5.33 = ( ( pred_numeral @ K )
% 5.02/5.33 = N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % eq_numeral_Suc
% 5.02/5.33 thf(fact_6115_less__Suc__numeral,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.02/5.33 = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % less_Suc_numeral
% 5.02/5.33 thf(fact_6116_less__numeral__Suc,axiom,
% 5.02/5.33 ! [K: num,N2: nat] :
% 5.02/5.33 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.02/5.33 = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % less_numeral_Suc
% 5.02/5.33 thf(fact_6117_pred__numeral__simps_I3_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_numeral_simps(3)
% 5.02/5.33 thf(fact_6118_le__Suc__numeral,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.02/5.33 = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % le_Suc_numeral
% 5.02/5.33 thf(fact_6119_le__numeral__Suc,axiom,
% 5.02/5.33 ! [K: num,N2: nat] :
% 5.02/5.33 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.02/5.33 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % le_numeral_Suc
% 5.02/5.33 thf(fact_6120_diff__Suc__numeral,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.02/5.33 = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_Suc_numeral
% 5.02/5.33 thf(fact_6121_diff__numeral__Suc,axiom,
% 5.02/5.33 ! [K: num,N2: nat] :
% 5.02/5.33 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.02/5.33 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_Suc
% 5.02/5.33 thf(fact_6122_max__Suc__numeral,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.02/5.33 = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % max_Suc_numeral
% 5.02/5.33 thf(fact_6123_max__numeral__Suc,axiom,
% 5.02/5.33 ! [K: num,N2: nat] :
% 5.02/5.33 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.02/5.33 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % max_numeral_Suc
% 5.02/5.33 thf(fact_6124_dbl__dec__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.02/5.33 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(2)
% 5.02/5.33 thf(fact_6125_dbl__dec__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.02/5.33 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(2)
% 5.02/5.33 thf(fact_6126_dbl__dec__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(2)
% 5.02/5.33 thf(fact_6127_dbl__dec__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.02/5.33 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(2)
% 5.02/5.33 thf(fact_6128_dbl__dec__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(2)
% 5.02/5.33 thf(fact_6129_numeral__div__minus__numeral,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_div_minus_numeral
% 5.02/5.33 thf(fact_6130_minus__numeral__div__numeral,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % minus_numeral_div_numeral
% 5.02/5.33 thf(fact_6131_dvd__numeral__simp,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.02/5.33 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N2 @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_numeral_simp
% 5.02/5.33 thf(fact_6132_dvd__numeral__simp,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.33 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N2 @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_numeral_simp
% 5.02/5.33 thf(fact_6133_dvd__numeral__simp,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.33 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N2 @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_numeral_simp
% 5.02/5.33 thf(fact_6134_divmod__algorithm__code_I2_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( unique5052692396658037445od_int @ M @ one )
% 5.02/5.33 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(2)
% 5.02/5.33 thf(fact_6135_divmod__algorithm__code_I2_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.02/5.33 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(2)
% 5.02/5.33 thf(fact_6136_divmod__algorithm__code_I3_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 5.02/5.33 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(3)
% 5.02/5.33 thf(fact_6137_divmod__algorithm__code_I3_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 5.02/5.33 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(3)
% 5.02/5.33 thf(fact_6138_divmod__algorithm__code_I4_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(4)
% 5.02/5.33 thf(fact_6139_divmod__algorithm__code_I4_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(4)
% 5.02/5.33 thf(fact_6140_one__div__minus__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % one_div_minus_numeral
% 5.02/5.33 thf(fact_6141_minus__one__div__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % minus_one_div_numeral
% 5.02/5.33 thf(fact_6142_signed__take__bit__numeral__bit0,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.02/5.33 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % signed_take_bit_numeral_bit0
% 5.02/5.33 thf(fact_6143_divmod__algorithm__code_I5_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.33 = ( produc4245557441103728435nt_int
% 5.02/5.33 @ ^ [Q4: int,R5: int] : ( product_Pair_int_int @ Q4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.02/5.33 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(5)
% 5.02/5.33 thf(fact_6144_divmod__algorithm__code_I5_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.33 = ( produc2626176000494625587at_nat
% 5.02/5.33 @ ^ [Q4: nat,R5: nat] : ( product_Pair_nat_nat @ Q4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.02/5.33 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(5)
% 5.02/5.33 thf(fact_6145_signed__take__bit__numeral__minus__bit0,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.02/5.33 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % signed_take_bit_numeral_minus_bit0
% 5.02/5.33 thf(fact_6146_divmod__algorithm__code_I7_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.02/5.33 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.02/5.33 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(7)
% 5.02/5.33 thf(fact_6147_divmod__algorithm__code_I7_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.02/5.33 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.02/5.33 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(7)
% 5.02/5.33 thf(fact_6148_divmod__algorithm__code_I7_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.02/5.33 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.02/5.33 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.02/5.33 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(7)
% 5.02/5.33 thf(fact_6149_divmod__algorithm__code_I8_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( ( ord_less_num @ M @ N2 )
% 5.02/5.33 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.02/5.33 & ( ~ ( ord_less_num @ M @ N2 )
% 5.02/5.33 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(8)
% 5.02/5.33 thf(fact_6150_divmod__algorithm__code_I8_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( ( ord_less_num @ M @ N2 )
% 5.02/5.33 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.02/5.33 & ( ~ ( ord_less_num @ M @ N2 )
% 5.02/5.33 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(8)
% 5.02/5.33 thf(fact_6151_divmod__algorithm__code_I8_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( ( ord_less_num @ M @ N2 )
% 5.02/5.33 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.02/5.33 & ( ~ ( ord_less_num @ M @ N2 )
% 5.02/5.33 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_algorithm_code(8)
% 5.02/5.33 thf(fact_6152_signed__take__bit__numeral__bit1,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % signed_take_bit_numeral_bit1
% 5.02/5.33 thf(fact_6153_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: complex,C: code_integer > $o > set_complex,P2: produc6271795597528267376eger_o] :
% 5.02/5.33 ( ( member_complex @ Z @ ( produc1043322548047392435omplex @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: code_integer,Y3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_complex @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6154_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: real,C: code_integer > $o > set_real,P2: produc6271795597528267376eger_o] :
% 5.02/5.33 ( ( member_real @ Z @ ( produc242741666403216561t_real @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: code_integer,Y3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_real @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6155_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: nat,C: code_integer > $o > set_nat,P2: produc6271795597528267376eger_o] :
% 5.02/5.33 ( ( member_nat @ Z @ ( produc5431169771168744661et_nat @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: code_integer,Y3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_nat @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6156_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: int,C: code_integer > $o > set_int,P2: produc6271795597528267376eger_o] :
% 5.02/5.33 ( ( member_int @ Z @ ( produc1253318751659547953et_int @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: code_integer,Y3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_int @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6157_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: complex,C: num > num > set_complex,P2: product_prod_num_num] :
% 5.02/5.33 ( ( member_complex @ Z @ ( produc2866383454006189126omplex @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: num,Y3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_complex @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6158_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: real,C: num > num > set_real,P2: product_prod_num_num] :
% 5.02/5.33 ( ( member_real @ Z @ ( produc8296048397933160132t_real @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: num,Y3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_real @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6159_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: nat,C: num > num > set_nat,P2: product_prod_num_num] :
% 5.02/5.33 ( ( member_nat @ Z @ ( produc1361121860356118632et_nat @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: num,Y3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_nat @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6160_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: int,C: num > num > set_int,P2: product_prod_num_num] :
% 5.02/5.33 ( ( member_int @ Z @ ( produc6406642877701697732et_int @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: num,Y3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_int @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6161_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: complex,C: nat > num > set_complex,P2: product_prod_nat_num] :
% 5.02/5.33 ( ( member_complex @ Z @ ( produc6231982587499038204omplex @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: nat,Y3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_num @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_complex @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6162_mem__case__prodE,axiom,
% 5.02/5.33 ! [Z: real,C: nat > num > set_real,P2: product_prod_nat_num] :
% 5.02/5.33 ( ( member_real @ Z @ ( produc1435849484188172666t_real @ C @ P2 ) )
% 5.02/5.33 => ~ ! [X5: nat,Y3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_num @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( member_real @ Z @ ( C @ X5 @ Y3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % mem_case_prodE
% 5.02/5.33 thf(fact_6163_case__prodE,axiom,
% 5.02/5.33 ! [C: code_integer > $o > $o,P2: produc6271795597528267376eger_o] :
% 5.02/5.33 ( ( produc7828578312038201481er_o_o @ C @ P2 )
% 5.02/5.33 => ~ ! [X5: code_integer,Y3: $o] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( produc6677183202524767010eger_o @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( C @ X5 @ Y3 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE
% 5.02/5.33 thf(fact_6164_case__prodE,axiom,
% 5.02/5.33 ! [C: num > num > $o,P2: product_prod_num_num] :
% 5.02/5.33 ( ( produc5703948589228662326_num_o @ C @ P2 )
% 5.02/5.33 => ~ ! [X5: num,Y3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_num_num @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( C @ X5 @ Y3 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE
% 5.02/5.33 thf(fact_6165_case__prodE,axiom,
% 5.02/5.33 ! [C: nat > num > $o,P2: product_prod_nat_num] :
% 5.02/5.33 ( ( produc4927758841916487424_num_o @ C @ P2 )
% 5.02/5.33 => ~ ! [X5: nat,Y3: num] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_num @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( C @ X5 @ Y3 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE
% 5.02/5.33 thf(fact_6166_case__prodE,axiom,
% 5.02/5.33 ! [C: nat > nat > $o,P2: product_prod_nat_nat] :
% 5.02/5.33 ( ( produc6081775807080527818_nat_o @ C @ P2 )
% 5.02/5.33 => ~ ! [X5: nat,Y3: nat] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_nat @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( C @ X5 @ Y3 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE
% 5.02/5.33 thf(fact_6167_case__prodE,axiom,
% 5.02/5.33 ! [C: int > int > $o,P2: product_prod_int_int] :
% 5.02/5.33 ( ( produc4947309494688390418_int_o @ C @ P2 )
% 5.02/5.33 => ~ ! [X5: int,Y3: int] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_int_int @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( C @ X5 @ Y3 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE
% 5.02/5.33 thf(fact_6168_case__prodD,axiom,
% 5.02/5.33 ! [F: code_integer > $o > $o,A: code_integer,B: $o] :
% 5.02/5.33 ( ( produc7828578312038201481er_o_o @ F @ ( produc6677183202524767010eger_o @ A @ B ) )
% 5.02/5.33 => ( F @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodD
% 5.02/5.33 thf(fact_6169_case__prodD,axiom,
% 5.02/5.33 ! [F: num > num > $o,A: num,B: num] :
% 5.02/5.33 ( ( produc5703948589228662326_num_o @ F @ ( product_Pair_num_num @ A @ B ) )
% 5.02/5.33 => ( F @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodD
% 5.02/5.33 thf(fact_6170_case__prodD,axiom,
% 5.02/5.33 ! [F: nat > num > $o,A: nat,B: num] :
% 5.02/5.33 ( ( produc4927758841916487424_num_o @ F @ ( product_Pair_nat_num @ A @ B ) )
% 5.02/5.33 => ( F @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodD
% 5.02/5.33 thf(fact_6171_case__prodD,axiom,
% 5.02/5.33 ! [F: nat > nat > $o,A: nat,B: nat] :
% 5.02/5.33 ( ( produc6081775807080527818_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.02/5.33 => ( F @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodD
% 5.02/5.33 thf(fact_6172_case__prodD,axiom,
% 5.02/5.33 ! [F: int > int > $o,A: int,B: int] :
% 5.02/5.33 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.02/5.33 => ( F @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodD
% 5.02/5.33 thf(fact_6173_case__prodE_H,axiom,
% 5.02/5.33 ! [C: nat > nat > product_prod_nat_nat > $o,P2: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.02/5.33 ( ( produc8739625826339149834_nat_o @ C @ P2 @ Z )
% 5.02/5.33 => ~ ! [X5: nat,Y3: nat] :
% 5.02/5.33 ( ( P2
% 5.02/5.33 = ( product_Pair_nat_nat @ X5 @ Y3 ) )
% 5.02/5.33 => ~ ( C @ X5 @ Y3 @ Z ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodE'
% 5.02/5.33 thf(fact_6174_case__prodD_H,axiom,
% 5.02/5.33 ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.02/5.33 ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.02/5.33 => ( R @ A @ B @ C ) ) ).
% 5.02/5.33
% 5.02/5.33 % case_prodD'
% 5.02/5.33 thf(fact_6175_numeral__eq__Suc,axiom,
% 5.02/5.33 ( numeral_numeral_nat
% 5.02/5.33 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_eq_Suc
% 5.02/5.33 thf(fact_6176_pred__numeral__def,axiom,
% 5.02/5.33 ( pred_numeral
% 5.02/5.33 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_numeral_def
% 5.02/5.33 thf(fact_6177_divmod__int__def,axiom,
% 5.02/5.33 ( unique5052692396658037445od_int
% 5.02/5.33 = ( ^ [M6: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_int_def
% 5.02/5.33 thf(fact_6178_Divides_Oadjust__div__def,axiom,
% 5.02/5.33 ( adjust_div
% 5.02/5.33 = ( produc8211389475949308722nt_int
% 5.02/5.33 @ ^ [Q4: int,R5: int] : ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % Divides.adjust_div_def
% 5.02/5.33 thf(fact_6179_divmod__def,axiom,
% 5.02/5.33 ( unique5052692396658037445od_int
% 5.02/5.33 = ( ^ [M6: num,N3: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N3 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N3 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_def
% 5.02/5.33 thf(fact_6180_divmod__def,axiom,
% 5.02/5.33 ( unique5055182867167087721od_nat
% 5.02/5.33 = ( ^ [M6: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_def
% 5.02/5.33 thf(fact_6181_divmod_H__nat__def,axiom,
% 5.02/5.33 ( unique5055182867167087721od_nat
% 5.02/5.33 = ( ^ [M6: num,N3: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N3 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N3 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod'_nat_def
% 5.02/5.33 thf(fact_6182_dbl__dec__def,axiom,
% 5.02/5.33 ( neg_nu6511756317524482435omplex
% 5.02/5.33 = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_def
% 5.02/5.33 thf(fact_6183_dbl__dec__def,axiom,
% 5.02/5.33 ( neg_nu6075765906172075777c_real
% 5.02/5.33 = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_def
% 5.02/5.33 thf(fact_6184_dbl__dec__def,axiom,
% 5.02/5.33 ( neg_nu3179335615603231917ec_rat
% 5.02/5.33 = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_def
% 5.02/5.33 thf(fact_6185_dbl__dec__def,axiom,
% 5.02/5.33 ( neg_nu3811975205180677377ec_int
% 5.02/5.33 = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_def
% 5.02/5.33 thf(fact_6186_take__bit__numeral__bit0,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.02/5.33 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_numeral_bit0
% 5.02/5.33 thf(fact_6187_take__bit__numeral__bit0,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.02/5.33 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_numeral_bit0
% 5.02/5.33 thf(fact_6188_take__bit__numeral__minus__bit0,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.02/5.33 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_numeral_minus_bit0
% 5.02/5.33 thf(fact_6189_exists__least__lemma,axiom,
% 5.02/5.33 ! [P: nat > $o] :
% 5.02/5.33 ( ~ ( P @ zero_zero_nat )
% 5.02/5.33 => ( ? [X_1: nat] : ( P @ X_1 )
% 5.02/5.33 => ? [N: nat] :
% 5.02/5.33 ( ~ ( P @ N )
% 5.02/5.33 & ( P @ ( suc @ N ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % exists_least_lemma
% 5.02/5.33 thf(fact_6190_ex__le__of__int,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ? [Z3: int] : ( ord_less_eq_real @ X2 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % ex_le_of_int
% 5.02/5.33 thf(fact_6191_ex__le__of__int,axiom,
% 5.02/5.33 ! [X2: rat] :
% 5.02/5.33 ? [Z3: int] : ( ord_less_eq_rat @ X2 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % ex_le_of_int
% 5.02/5.33 thf(fact_6192_ex__of__int__less,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ? [Z3: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z3 ) @ X2 ) ).
% 5.02/5.33
% 5.02/5.33 % ex_of_int_less
% 5.02/5.33 thf(fact_6193_ex__of__int__less,axiom,
% 5.02/5.33 ! [X2: rat] :
% 5.02/5.33 ? [Z3: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z3 ) @ X2 ) ).
% 5.02/5.33
% 5.02/5.33 % ex_of_int_less
% 5.02/5.33 thf(fact_6194_ex__less__of__int,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ? [Z3: int] : ( ord_less_real @ X2 @ ( ring_1_of_int_real @ Z3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % ex_less_of_int
% 5.02/5.33 thf(fact_6195_ex__less__of__int,axiom,
% 5.02/5.33 ! [X2: rat] :
% 5.02/5.33 ? [Z3: int] : ( ord_less_rat @ X2 @ ( ring_1_of_int_rat @ Z3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % ex_less_of_int
% 5.02/5.33 thf(fact_6196_eq__diff__eq_H,axiom,
% 5.02/5.33 ! [X2: real,Y: real,Z: real] :
% 5.02/5.33 ( ( X2
% 5.02/5.33 = ( minus_minus_real @ Y @ Z ) )
% 5.02/5.33 = ( Y
% 5.02/5.33 = ( plus_plus_real @ X2 @ Z ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % eq_diff_eq'
% 5.02/5.33 thf(fact_6197_divmod__divmod__step,axiom,
% 5.02/5.33 ( unique5055182867167087721od_nat
% 5.02/5.33 = ( ^ [M6: num,N3: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N3 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N3 @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_divmod_step
% 5.02/5.33 thf(fact_6198_divmod__divmod__step,axiom,
% 5.02/5.33 ( unique5052692396658037445od_int
% 5.02/5.33 = ( ^ [M6: num,N3: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N3 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N3 @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_divmod_step
% 5.02/5.33 thf(fact_6199_divmod__divmod__step,axiom,
% 5.02/5.33 ( unique3479559517661332726nteger
% 5.02/5.33 = ( ^ [M6: num,N3: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N3 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N3 @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N3 ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_divmod_step
% 5.02/5.33 thf(fact_6200_take__bit__numeral__bit1,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_numeral_bit1
% 5.02/5.33 thf(fact_6201_take__bit__numeral__bit1,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.02/5.33 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_numeral_bit1
% 5.02/5.33 thf(fact_6202_arcosh__1,axiom,
% 5.02/5.33 ( ( arcosh_real @ one_one_real )
% 5.02/5.33 = zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % arcosh_1
% 5.02/5.33 thf(fact_6203_take__bit__numeral__minus__bit1,axiom,
% 5.02/5.33 ! [L: num,K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.02/5.33 = ( 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 ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_numeral_minus_bit1
% 5.02/5.33 thf(fact_6204_divmod__nat__if,axiom,
% 5.02/5.33 ( divmod_nat
% 5.02/5.33 = ( ^ [M6: nat,N3: nat] :
% 5.02/5.33 ( if_Pro6206227464963214023at_nat
% 5.02/5.33 @ ( ( N3 = zero_zero_nat )
% 5.02/5.33 | ( ord_less_nat @ M6 @ N3 ) )
% 5.02/5.33 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.02/5.33 @ ( produc2626176000494625587at_nat
% 5.02/5.33 @ ^ [Q4: nat] : ( product_Pair_nat_nat @ ( suc @ Q4 ) )
% 5.02/5.33 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N3 ) @ N3 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_nat_if
% 5.02/5.33 thf(fact_6205_round__unique,axiom,
% 5.02/5.33 ! [X2: real,Y: int] :
% 5.02/5.33 ( ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 5.02/5.33 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.02/5.33 => ( ( archim8280529875227126926d_real @ X2 )
% 5.02/5.33 = Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_unique
% 5.02/5.33 thf(fact_6206_round__unique,axiom,
% 5.02/5.33 ! [X2: rat,Y: int] :
% 5.02/5.33 ( ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 5.02/5.33 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.33 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.02/5.33 = Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_unique
% 5.02/5.33 thf(fact_6207_arsinh__0,axiom,
% 5.02/5.33 ( ( arsinh_real @ zero_zero_real )
% 5.02/5.33 = zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % arsinh_0
% 5.02/5.33 thf(fact_6208_artanh__0,axiom,
% 5.02/5.33 ( ( artanh_real @ zero_zero_real )
% 5.02/5.33 = zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % artanh_0
% 5.02/5.33 thf(fact_6209_split__part,axiom,
% 5.02/5.33 ! [P: $o,Q: int > int > $o] :
% 5.02/5.33 ( ( produc4947309494688390418_int_o
% 5.02/5.33 @ ^ [A5: int,B5: int] :
% 5.02/5.33 ( P
% 5.02/5.33 & ( Q @ A5 @ B5 ) ) )
% 5.02/5.33 = ( ^ [Ab: product_prod_int_int] :
% 5.02/5.33 ( P
% 5.02/5.33 & ( produc4947309494688390418_int_o @ Q @ Ab ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % split_part
% 5.02/5.33 thf(fact_6210_round__0,axiom,
% 5.02/5.33 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 5.02/5.33 = zero_zero_int ) ).
% 5.02/5.33
% 5.02/5.33 % round_0
% 5.02/5.33 thf(fact_6211_round__0,axiom,
% 5.02/5.33 ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 5.02/5.33 = zero_zero_int ) ).
% 5.02/5.33
% 5.02/5.33 % round_0
% 5.02/5.33 thf(fact_6212_round__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.33 = ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_numeral
% 5.02/5.33 thf(fact_6213_round__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.02/5.33 = ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_numeral
% 5.02/5.33 thf(fact_6214_round__1,axiom,
% 5.02/5.33 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.02/5.33 = one_one_int ) ).
% 5.02/5.33
% 5.02/5.33 % round_1
% 5.02/5.33 thf(fact_6215_round__1,axiom,
% 5.02/5.33 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.02/5.33 = one_one_int ) ).
% 5.02/5.33
% 5.02/5.33 % round_1
% 5.02/5.33 thf(fact_6216_pred__numeral__inc,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( pred_numeral @ ( inc @ K ) )
% 5.02/5.33 = ( numeral_numeral_nat @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_numeral_inc
% 5.02/5.33 thf(fact_6217_add__neg__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(5)
% 5.02/5.33 thf(fact_6218_add__neg__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(5)
% 5.02/5.33 thf(fact_6219_add__neg__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(5)
% 5.02/5.33 thf(fact_6220_add__neg__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.33 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(5)
% 5.02/5.33 thf(fact_6221_add__neg__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(5)
% 5.02/5.33 thf(fact_6222_add__neg__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(6)
% 5.02/5.33 thf(fact_6223_add__neg__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(6)
% 5.02/5.33 thf(fact_6224_add__neg__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(6)
% 5.02/5.33 thf(fact_6225_add__neg__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.33 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(6)
% 5.02/5.33 thf(fact_6226_add__neg__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_neg_numeral_special(6)
% 5.02/5.33 thf(fact_6227_diff__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.33 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(6)
% 5.02/5.33 thf(fact_6228_diff__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(6)
% 5.02/5.33 thf(fact_6229_diff__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.33 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(6)
% 5.02/5.33 thf(fact_6230_diff__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.33 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(6)
% 5.02/5.33 thf(fact_6231_diff__numeral__special_I6_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.33 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(6)
% 5.02/5.33 thf(fact_6232_diff__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(5)
% 5.02/5.33 thf(fact_6233_diff__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(5)
% 5.02/5.33 thf(fact_6234_diff__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(5)
% 5.02/5.33 thf(fact_6235_diff__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 5.02/5.33 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(5)
% 5.02/5.33 thf(fact_6236_diff__numeral__special_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % diff_numeral_special(5)
% 5.02/5.33 thf(fact_6237_round__neg__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_neg_numeral
% 5.02/5.33 thf(fact_6238_round__neg__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_neg_numeral
% 5.02/5.33 thf(fact_6239_prod_Odisc__eq__case,axiom,
% 5.02/5.33 ! [Prod: product_prod_int_int] :
% 5.02/5.33 ( produc4947309494688390418_int_o
% 5.02/5.33 @ ^ [Uu3: int,Uv3: int] : $true
% 5.02/5.33 @ Prod ) ).
% 5.02/5.33
% 5.02/5.33 % prod.disc_eq_case
% 5.02/5.33 thf(fact_6240_Collect__case__prod__mono,axiom,
% 5.02/5.33 ! [A3: int > int > $o,B4: int > int > $o] :
% 5.02/5.33 ( ( ord_le6741204236512500942_int_o @ A3 @ B4 )
% 5.02/5.33 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A3 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B4 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % Collect_case_prod_mono
% 5.02/5.33 thf(fact_6241_num__induct,axiom,
% 5.02/5.33 ! [P: num > $o,X2: num] :
% 5.02/5.33 ( ( P @ one )
% 5.02/5.33 => ( ! [X5: num] :
% 5.02/5.33 ( ( P @ X5 )
% 5.02/5.33 => ( P @ ( inc @ X5 ) ) )
% 5.02/5.33 => ( P @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % num_induct
% 5.02/5.33 thf(fact_6242_add__inc,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( plus_plus_num @ X2 @ ( inc @ Y ) )
% 5.02/5.33 = ( inc @ ( plus_plus_num @ X2 @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_inc
% 5.02/5.33 thf(fact_6243_inc_Osimps_I1_J,axiom,
% 5.02/5.33 ( ( inc @ one )
% 5.02/5.33 = ( bit0 @ one ) ) ).
% 5.02/5.33
% 5.02/5.33 % inc.simps(1)
% 5.02/5.33 thf(fact_6244_inc_Osimps_I2_J,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( inc @ ( bit0 @ X2 ) )
% 5.02/5.33 = ( bit1 @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % inc.simps(2)
% 5.02/5.33 thf(fact_6245_inc_Osimps_I3_J,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( inc @ ( bit1 @ X2 ) )
% 5.02/5.33 = ( bit0 @ ( inc @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % inc.simps(3)
% 5.02/5.33 thf(fact_6246_add__One,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( plus_plus_num @ X2 @ one )
% 5.02/5.33 = ( inc @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % add_One
% 5.02/5.33 thf(fact_6247_round__mono,axiom,
% 5.02/5.33 ! [X2: rat,Y: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ X2 @ Y )
% 5.02/5.33 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X2 ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_mono
% 5.02/5.33 thf(fact_6248_mult__inc,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( times_times_num @ X2 @ ( inc @ Y ) )
% 5.02/5.33 = ( plus_plus_num @ ( times_times_num @ X2 @ Y ) @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % mult_inc
% 5.02/5.33 thf(fact_6249_numeral__inc,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( numera6690914467698888265omplex @ ( inc @ X2 ) )
% 5.02/5.33 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X2 ) @ one_one_complex ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_inc
% 5.02/5.33 thf(fact_6250_numeral__inc,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( numeral_numeral_real @ ( inc @ X2 ) )
% 5.02/5.33 = ( plus_plus_real @ ( numeral_numeral_real @ X2 ) @ one_one_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_inc
% 5.02/5.33 thf(fact_6251_numeral__inc,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( numeral_numeral_rat @ ( inc @ X2 ) )
% 5.02/5.33 = ( plus_plus_rat @ ( numeral_numeral_rat @ X2 ) @ one_one_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_inc
% 5.02/5.33 thf(fact_6252_numeral__inc,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( numeral_numeral_nat @ ( inc @ X2 ) )
% 5.02/5.33 = ( plus_plus_nat @ ( numeral_numeral_nat @ X2 ) @ one_one_nat ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_inc
% 5.02/5.33 thf(fact_6253_numeral__inc,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( numeral_numeral_int @ ( inc @ X2 ) )
% 5.02/5.33 = ( plus_plus_int @ ( numeral_numeral_int @ X2 ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_inc
% 5.02/5.33 thf(fact_6254_divmod__nat__def,axiom,
% 5.02/5.33 ( divmod_nat
% 5.02/5.33 = ( ^ [M6: nat,N3: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N3 ) @ ( modulo_modulo_nat @ M6 @ N3 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_nat_def
% 5.02/5.33 thf(fact_6255_of__int__round__le,axiom,
% 5.02/5.33 ! [X2: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ ( plus_plus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_round_le
% 5.02/5.33 thf(fact_6256_of__int__round__le,axiom,
% 5.02/5.33 ! [X2: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ ( plus_plus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_round_le
% 5.02/5.33 thf(fact_6257_of__int__round__ge,axiom,
% 5.02/5.33 ! [X2: real] : ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_round_ge
% 5.02/5.33 thf(fact_6258_of__int__round__ge,axiom,
% 5.02/5.33 ! [X2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_round_ge
% 5.02/5.33 thf(fact_6259_of__int__round__gt,axiom,
% 5.02/5.33 ! [X2: real] : ( ord_less_real @ ( minus_minus_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_round_gt
% 5.02/5.33 thf(fact_6260_of__int__round__gt,axiom,
% 5.02/5.33 ! [X2: rat] : ( ord_less_rat @ ( minus_minus_rat @ X2 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_round_gt
% 5.02/5.33 thf(fact_6261_take__bit__Suc__minus__bit1,axiom,
% 5.02/5.33 ! [N2: nat,K: num] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.02/5.33 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_Suc_minus_bit1
% 5.02/5.33 thf(fact_6262_artanh__def,axiom,
% 5.02/5.33 ( artanh_real
% 5.02/5.33 = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % artanh_def
% 5.02/5.33 thf(fact_6263_dbl__inc__simps_I3_J,axiom,
% 5.02/5.33 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.02/5.33 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(3)
% 5.02/5.33 thf(fact_6264_dbl__inc__simps_I3_J,axiom,
% 5.02/5.33 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.02/5.33 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(3)
% 5.02/5.33 thf(fact_6265_dbl__inc__simps_I3_J,axiom,
% 5.02/5.33 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.02/5.33 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(3)
% 5.02/5.33 thf(fact_6266_dbl__inc__simps_I3_J,axiom,
% 5.02/5.33 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.02/5.33 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(3)
% 5.02/5.33 thf(fact_6267_or__int__unfold,axiom,
% 5.02/5.33 ( bit_se1409905431419307370or_int
% 5.02/5.33 = ( ^ [K3: int,L2: int] :
% 5.02/5.33 ( if_int
% 5.02/5.33 @ ( ( K3
% 5.02/5.33 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 | ( L2
% 5.02/5.33 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.02/5.33 @ ( uminus_uminus_int @ one_one_int )
% 5.02/5.33 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_int_unfold
% 5.02/5.33 thf(fact_6268_ln__one__minus__pos__lower__bound,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.33 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_one_minus_pos_lower_bound
% 5.02/5.33 thf(fact_6269_divmod__BitM__2__eq,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.02/5.33 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % divmod_BitM_2_eq
% 5.02/5.33 thf(fact_6270_or_Oright__idem,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ B )
% 5.02/5.33 = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.right_idem
% 5.02/5.33 thf(fact_6271_or_Oright__idem,axiom,
% 5.02/5.33 ! [A: nat,B: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ B )
% 5.02/5.33 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.right_idem
% 5.02/5.33 thf(fact_6272_or_Oleft__idem,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.02/5.33 = ( bit_se1409905431419307370or_int @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.left_idem
% 5.02/5.33 thf(fact_6273_or_Oleft__idem,axiom,
% 5.02/5.33 ! [A: nat,B: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.02/5.33 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.left_idem
% 5.02/5.33 thf(fact_6274_or_Oidem,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ A @ A )
% 5.02/5.33 = A ) ).
% 5.02/5.33
% 5.02/5.33 % or.idem
% 5.02/5.33 thf(fact_6275_or_Oidem,axiom,
% 5.02/5.33 ! [A: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ A @ A )
% 5.02/5.33 = A ) ).
% 5.02/5.33
% 5.02/5.33 % or.idem
% 5.02/5.33 thf(fact_6276_or_Oleft__neutral,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ zero_zero_int @ A )
% 5.02/5.33 = A ) ).
% 5.02/5.33
% 5.02/5.33 % or.left_neutral
% 5.02/5.33 thf(fact_6277_or_Oleft__neutral,axiom,
% 5.02/5.33 ! [A: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ zero_zero_nat @ A )
% 5.02/5.33 = A ) ).
% 5.02/5.33
% 5.02/5.33 % or.left_neutral
% 5.02/5.33 thf(fact_6278_or_Oright__neutral,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ A @ zero_zero_int )
% 5.02/5.33 = A ) ).
% 5.02/5.33
% 5.02/5.33 % or.right_neutral
% 5.02/5.33 thf(fact_6279_or_Oright__neutral,axiom,
% 5.02/5.33 ! [A: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ A @ zero_zero_nat )
% 5.02/5.33 = A ) ).
% 5.02/5.33
% 5.02/5.33 % or.right_neutral
% 5.02/5.33 thf(fact_6280_take__bit__or,axiom,
% 5.02/5.33 ! [N2: nat,A: int,B: int] :
% 5.02/5.33 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.02/5.33 = ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_or
% 5.02/5.33 thf(fact_6281_take__bit__or,axiom,
% 5.02/5.33 ! [N2: nat,A: nat,B: nat] :
% 5.02/5.33 ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.02/5.33 = ( bit_se1412395901928357646or_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % take_bit_or
% 5.02/5.33 thf(fact_6282_bit_Odisj__one__right,axiom,
% 5.02/5.33 ! [X2: code_integer] :
% 5.02/5.33 ( ( bit_se1080825931792720795nteger @ X2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.33
% 5.02/5.33 % bit.disj_one_right
% 5.02/5.33 thf(fact_6283_bit_Odisj__one__right,axiom,
% 5.02/5.33 ! [X2: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ X2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % bit.disj_one_right
% 5.02/5.33 thf(fact_6284_bit_Odisj__one__left,axiom,
% 5.02/5.33 ! [X2: code_integer] :
% 5.02/5.33 ( ( bit_se1080825931792720795nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X2 )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.33
% 5.02/5.33 % bit.disj_one_left
% 5.02/5.33 thf(fact_6285_bit_Odisj__one__left,axiom,
% 5.02/5.33 ! [X2: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ one_one_int ) @ X2 )
% 5.02/5.33 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % bit.disj_one_left
% 5.02/5.33 thf(fact_6286_ln__one,axiom,
% 5.02/5.33 ( ( ln_ln_real @ one_one_real )
% 5.02/5.33 = zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % ln_one
% 5.02/5.33 thf(fact_6287_or__nonnegative__int__iff,axiom,
% 5.02/5.33 ! [K: int,L: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.02/5.33 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.33 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_nonnegative_int_iff
% 5.02/5.33 thf(fact_6288_or__negative__int__iff,axiom,
% 5.02/5.33 ! [K: int,L: int] :
% 5.02/5.33 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.02/5.33 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.02/5.33 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_negative_int_iff
% 5.02/5.33 thf(fact_6289_dbl__inc__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.02/5.33 = one_one_complex ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(2)
% 5.02/5.33 thf(fact_6290_dbl__inc__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.02/5.33 = one_one_real ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(2)
% 5.02/5.33 thf(fact_6291_dbl__inc__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.02/5.33 = one_one_rat ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(2)
% 5.02/5.33 thf(fact_6292_dbl__inc__simps_I2_J,axiom,
% 5.02/5.33 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.02/5.33 = one_one_int ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(2)
% 5.02/5.33 thf(fact_6293_dbl__inc__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.33 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(4)
% 5.02/5.33 thf(fact_6294_dbl__inc__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(4)
% 5.02/5.33 thf(fact_6295_dbl__inc__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(4)
% 5.02/5.33 thf(fact_6296_dbl__inc__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.33 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(4)
% 5.02/5.33 thf(fact_6297_dbl__inc__simps_I4_J,axiom,
% 5.02/5.33 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(4)
% 5.02/5.33 thf(fact_6298_dbl__inc__simps_I5_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.02/5.33 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(5)
% 5.02/5.33 thf(fact_6299_dbl__inc__simps_I5_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.02/5.33 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(5)
% 5.02/5.33 thf(fact_6300_dbl__inc__simps_I5_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.02/5.33 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(5)
% 5.02/5.33 thf(fact_6301_dbl__inc__simps_I5_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.02/5.33 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(5)
% 5.02/5.33 thf(fact_6302_dbl__dec__simps_I5_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.02/5.33 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(5)
% 5.02/5.33 thf(fact_6303_dbl__dec__simps_I5_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.02/5.33 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(5)
% 5.02/5.33 thf(fact_6304_dbl__dec__simps_I5_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.02/5.33 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(5)
% 5.02/5.33 thf(fact_6305_dbl__dec__simps_I5_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.02/5.33 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(5)
% 5.02/5.33 thf(fact_6306_or__numerals_I2_J,axiom,
% 5.02/5.33 ! [Y: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.02/5.33 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(2)
% 5.02/5.33 thf(fact_6307_or__numerals_I2_J,axiom,
% 5.02/5.33 ! [Y: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(2)
% 5.02/5.33 thf(fact_6308_or__numerals_I8_J,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ one_one_int )
% 5.02/5.33 = ( numeral_numeral_int @ ( bit1 @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(8)
% 5.02/5.33 thf(fact_6309_or__numerals_I8_J,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ one_one_nat )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(8)
% 5.02/5.33 thf(fact_6310_ln__less__zero__iff,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.02/5.33 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_less_zero_iff
% 5.02/5.33 thf(fact_6311_ln__gt__zero__iff,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.02/5.33 = ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_gt_zero_iff
% 5.02/5.33 thf(fact_6312_ln__eq__zero__iff,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ( ln_ln_real @ X2 )
% 5.02/5.33 = zero_zero_real )
% 5.02/5.33 = ( X2 = one_one_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_eq_zero_iff
% 5.02/5.33 thf(fact_6313_pred__numeral__simps_I2_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_numeral_simps(2)
% 5.02/5.33 thf(fact_6314_dbl__dec__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(1)
% 5.02/5.33 thf(fact_6315_dbl__dec__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(1)
% 5.02/5.33 thf(fact_6316_dbl__dec__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(1)
% 5.02/5.33 thf(fact_6317_dbl__dec__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(1)
% 5.02/5.33 thf(fact_6318_dbl__dec__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_dec_simps(1)
% 5.02/5.33 thf(fact_6319_dbl__inc__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(1)
% 5.02/5.33 thf(fact_6320_dbl__inc__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(1)
% 5.02/5.33 thf(fact_6321_dbl__inc__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.02/5.33 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(1)
% 5.02/5.33 thf(fact_6322_dbl__inc__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.02/5.33 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(1)
% 5.02/5.33 thf(fact_6323_dbl__inc__simps_I1_J,axiom,
% 5.02/5.33 ! [K: num] :
% 5.02/5.33 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_simps(1)
% 5.02/5.33 thf(fact_6324_or__numerals_I3_J,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.02/5.33 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(3)
% 5.02/5.33 thf(fact_6325_or__numerals_I3_J,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.33 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(3)
% 5.02/5.33 thf(fact_6326_or__numerals_I5_J,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ one_one_int )
% 5.02/5.33 = ( numeral_numeral_int @ ( bit1 @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(5)
% 5.02/5.33 thf(fact_6327_or__numerals_I5_J,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ one_one_nat )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(5)
% 5.02/5.33 thf(fact_6328_or__numerals_I1_J,axiom,
% 5.02/5.33 ! [Y: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.02/5.33 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(1)
% 5.02/5.33 thf(fact_6329_or__numerals_I1_J,axiom,
% 5.02/5.33 ! [Y: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(1)
% 5.02/5.33 thf(fact_6330_ln__le__zero__iff,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ zero_zero_real )
% 5.02/5.33 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_le_zero_iff
% 5.02/5.33 thf(fact_6331_ln__ge__zero__iff,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.02/5.33 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_ge_zero_iff
% 5.02/5.33 thf(fact_6332_or__minus__numerals_I2_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_minus_numerals(2)
% 5.02/5.33 thf(fact_6333_or__minus__numerals_I6_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_minus_numerals(6)
% 5.02/5.33 thf(fact_6334_or__numerals_I7_J,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.02/5.33 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(7)
% 5.02/5.33 thf(fact_6335_or__numerals_I7_J,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.33 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(7)
% 5.02/5.33 thf(fact_6336_or__numerals_I6_J,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.02/5.33 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(6)
% 5.02/5.33 thf(fact_6337_or__numerals_I6_J,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.33 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(6)
% 5.02/5.33 thf(fact_6338_or__numerals_I4_J,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.02/5.33 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(4)
% 5.02/5.33 thf(fact_6339_or__numerals_I4_J,axiom,
% 5.02/5.33 ! [X2: num,Y: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.33 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_numerals(4)
% 5.02/5.33 thf(fact_6340_or_Oleft__commute,axiom,
% 5.02/5.33 ! [B: int,A: int,C: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ B @ ( bit_se1409905431419307370or_int @ A @ C ) )
% 5.02/5.33 = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.left_commute
% 5.02/5.33 thf(fact_6341_or_Oleft__commute,axiom,
% 5.02/5.33 ! [B: nat,A: nat,C: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ B @ ( bit_se1412395901928357646or_nat @ A @ C ) )
% 5.02/5.33 = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.left_commute
% 5.02/5.33 thf(fact_6342_or_Ocommute,axiom,
% 5.02/5.33 ( bit_se1409905431419307370or_int
% 5.02/5.33 = ( ^ [A5: int,B5: int] : ( bit_se1409905431419307370or_int @ B5 @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.commute
% 5.02/5.33 thf(fact_6343_or_Ocommute,axiom,
% 5.02/5.33 ( bit_se1412395901928357646or_nat
% 5.02/5.33 = ( ^ [A5: nat,B5: nat] : ( bit_se1412395901928357646or_nat @ B5 @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.commute
% 5.02/5.33 thf(fact_6344_or_Oassoc,axiom,
% 5.02/5.33 ! [A: int,B: int,C: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ C )
% 5.02/5.33 = ( bit_se1409905431419307370or_int @ A @ ( bit_se1409905431419307370or_int @ B @ C ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.assoc
% 5.02/5.33 thf(fact_6345_or_Oassoc,axiom,
% 5.02/5.33 ! [A: nat,B: nat,C: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ C )
% 5.02/5.33 = ( bit_se1412395901928357646or_nat @ A @ ( bit_se1412395901928357646or_nat @ B @ C ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or.assoc
% 5.02/5.33 thf(fact_6346_of__int__or__eq,axiom,
% 5.02/5.33 ! [K: int,L: int] :
% 5.02/5.33 ( ( ring_1_of_int_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.02/5.33 = ( bit_se1409905431419307370or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_or_eq
% 5.02/5.33 thf(fact_6347_or__eq__0__iff,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( ( bit_se1409905431419307370or_int @ A @ B )
% 5.02/5.33 = zero_zero_int )
% 5.02/5.33 = ( ( A = zero_zero_int )
% 5.02/5.33 & ( B = zero_zero_int ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_eq_0_iff
% 5.02/5.33 thf(fact_6348_or__eq__0__iff,axiom,
% 5.02/5.33 ! [A: nat,B: nat] :
% 5.02/5.33 ( ( ( bit_se1412395901928357646or_nat @ A @ B )
% 5.02/5.33 = zero_zero_nat )
% 5.02/5.33 = ( ( A = zero_zero_nat )
% 5.02/5.33 & ( B = zero_zero_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_eq_0_iff
% 5.02/5.33 thf(fact_6349_bit_Odisj__zero__right,axiom,
% 5.02/5.33 ! [X2: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ X2 @ zero_zero_int )
% 5.02/5.33 = X2 ) ).
% 5.02/5.33
% 5.02/5.33 % bit.disj_zero_right
% 5.02/5.33 thf(fact_6350_semiring__norm_I26_J,axiom,
% 5.02/5.33 ( ( bitM @ one )
% 5.02/5.33 = one ) ).
% 5.02/5.33
% 5.02/5.33 % semiring_norm(26)
% 5.02/5.33 thf(fact_6351_or__greater__eq,axiom,
% 5.02/5.33 ! [L: int,K: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.02/5.33 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_greater_eq
% 5.02/5.33 thf(fact_6352_OR__lower,axiom,
% 5.02/5.33 ! [X2: int,Y: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.33 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % OR_lower
% 5.02/5.33 thf(fact_6353_semiring__norm_I28_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bitM @ ( bit1 @ N2 ) )
% 5.02/5.33 = ( bit1 @ ( bit0 @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % semiring_norm(28)
% 5.02/5.33 thf(fact_6354_semiring__norm_I27_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bitM @ ( bit0 @ N2 ) )
% 5.02/5.33 = ( bit1 @ ( bitM @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % semiring_norm(27)
% 5.02/5.33 thf(fact_6355_inc__BitM__eq,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( inc @ ( bitM @ N2 ) )
% 5.02/5.33 = ( bit0 @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % inc_BitM_eq
% 5.02/5.33 thf(fact_6356_BitM__inc__eq,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bitM @ ( inc @ N2 ) )
% 5.02/5.33 = ( bit1 @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % BitM_inc_eq
% 5.02/5.33 thf(fact_6357_ln__gt__zero,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.33 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_gt_zero
% 5.02/5.33 thf(fact_6358_ln__less__zero,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.33 => ( ord_less_real @ ( ln_ln_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_less_zero
% 5.02/5.33 thf(fact_6359_ln__gt__zero__imp__gt__one,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.02/5.33 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_gt_zero_imp_gt_one
% 5.02/5.33 thf(fact_6360_ln__ge__zero,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.02/5.33 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_ge_zero
% 5.02/5.33 thf(fact_6361_eval__nat__numeral_I2_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.02/5.33 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % eval_nat_numeral(2)
% 5.02/5.33 thf(fact_6362_ln__ge__zero__imp__ge__one,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X2 ) )
% 5.02/5.33 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_ge_zero_imp_ge_one
% 5.02/5.33 thf(fact_6363_BitM__plus__one,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 5.02/5.33 = ( bit0 @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % BitM_plus_one
% 5.02/5.33 thf(fact_6364_one__plus__BitM,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 5.02/5.33 = ( bit0 @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % one_plus_BitM
% 5.02/5.33 thf(fact_6365_even__or__iff,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1080825931792720795nteger @ A @ B ) )
% 5.02/5.33 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % even_or_iff
% 5.02/5.33 thf(fact_6366_even__or__iff,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ A @ B ) )
% 5.02/5.33 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % even_or_iff
% 5.02/5.33 thf(fact_6367_even__or__iff,axiom,
% 5.02/5.33 ! [A: nat,B: nat] :
% 5.02/5.33 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ A @ B ) )
% 5.02/5.33 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.33 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % even_or_iff
% 5.02/5.33 thf(fact_6368_ln__add__one__self__le__self,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_add_one_self_le_self
% 5.02/5.33 thf(fact_6369_ln__mult,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.02/5.33 => ( ( ln_ln_real @ ( times_times_real @ X2 @ Y ) )
% 5.02/5.33 = ( plus_plus_real @ ( ln_ln_real @ X2 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_mult
% 5.02/5.33 thf(fact_6370_ln__eq__minus__one,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ( ln_ln_real @ X2 )
% 5.02/5.33 = ( minus_minus_real @ X2 @ one_one_real ) )
% 5.02/5.33 => ( X2 = one_one_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_eq_minus_one
% 5.02/5.33 thf(fact_6371_dbl__inc__def,axiom,
% 5.02/5.33 ( neg_nu8557863876264182079omplex
% 5.02/5.33 = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_def
% 5.02/5.33 thf(fact_6372_dbl__inc__def,axiom,
% 5.02/5.33 ( neg_nu8295874005876285629c_real
% 5.02/5.33 = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_def
% 5.02/5.33 thf(fact_6373_dbl__inc__def,axiom,
% 5.02/5.33 ( neg_nu5219082963157363817nc_rat
% 5.02/5.33 = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_def
% 5.02/5.33 thf(fact_6374_dbl__inc__def,axiom,
% 5.02/5.33 ( neg_nu5851722552734809277nc_int
% 5.02/5.33 = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % dbl_inc_def
% 5.02/5.33 thf(fact_6375_ln__2__less__1,axiom,
% 5.02/5.33 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.02/5.33
% 5.02/5.33 % ln_2_less_1
% 5.02/5.33 thf(fact_6376_numeral__BitM,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numera6690914467698888265omplex @ ( bitM @ N2 ) )
% 5.02/5.33 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N2 ) ) @ one_one_complex ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_BitM
% 5.02/5.33 thf(fact_6377_numeral__BitM,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_real @ ( bitM @ N2 ) )
% 5.02/5.33 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N2 ) ) @ one_one_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_BitM
% 5.02/5.33 thf(fact_6378_numeral__BitM,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_rat @ ( bitM @ N2 ) )
% 5.02/5.33 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N2 ) ) @ one_one_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_BitM
% 5.02/5.33 thf(fact_6379_numeral__BitM,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( numeral_numeral_int @ ( bitM @ N2 ) )
% 5.02/5.33 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ one_one_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % numeral_BitM
% 5.02/5.33 thf(fact_6380_odd__numeral__BitM,axiom,
% 5.02/5.33 ! [W: num] :
% 5.02/5.33 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % odd_numeral_BitM
% 5.02/5.33 thf(fact_6381_odd__numeral__BitM,axiom,
% 5.02/5.33 ! [W: num] :
% 5.02/5.33 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % odd_numeral_BitM
% 5.02/5.33 thf(fact_6382_odd__numeral__BitM,axiom,
% 5.02/5.33 ! [W: num] :
% 5.02/5.33 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % odd_numeral_BitM
% 5.02/5.33 thf(fact_6383_ln__le__minus__one,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_le_minus_one
% 5.02/5.33 thf(fact_6384_ln__add__one__self__le__self2,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.33 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_add_one_self_le_self2
% 5.02/5.33 thf(fact_6385_ln__one__minus__pos__upper__bound,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.33 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X2 ) ) @ ( uminus_uminus_real @ X2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_one_minus_pos_upper_bound
% 5.02/5.33 thf(fact_6386_ln__sqrt,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ln_ln_real @ ( sqrt @ X2 ) )
% 5.02/5.33 = ( divide_divide_real @ ( ln_ln_real @ X2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_sqrt
% 5.02/5.33 thf(fact_6387_arsinh__real__def,axiom,
% 5.02/5.33 ( arsinh_real
% 5.02/5.33 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % arsinh_real_def
% 5.02/5.33 thf(fact_6388_one__or__eq,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( bit_se1080825931792720795nteger @ one_one_Code_integer @ A )
% 5.02/5.33 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % one_or_eq
% 5.02/5.33 thf(fact_6389_one__or__eq,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ A )
% 5.02/5.33 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % one_or_eq
% 5.02/5.33 thf(fact_6390_one__or__eq,axiom,
% 5.02/5.33 ! [A: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ one_one_nat @ A )
% 5.02/5.33 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % one_or_eq
% 5.02/5.33 thf(fact_6391_or__one__eq,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( bit_se1080825931792720795nteger @ A @ one_one_Code_integer )
% 5.02/5.33 = ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_one_eq
% 5.02/5.33 thf(fact_6392_or__one__eq,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ A @ one_one_int )
% 5.02/5.33 = ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_one_eq
% 5.02/5.33 thf(fact_6393_or__one__eq,axiom,
% 5.02/5.33 ! [A: nat] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ A @ one_one_nat )
% 5.02/5.33 = ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_one_eq
% 5.02/5.33 thf(fact_6394_OR__upper,axiom,
% 5.02/5.33 ! [X2: int,N2: nat,Y: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.33 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.33 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.33 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % OR_upper
% 5.02/5.33 thf(fact_6395_or__int__rec,axiom,
% 5.02/5.33 ( bit_se1409905431419307370or_int
% 5.02/5.33 = ( ^ [K3: int,L2: int] :
% 5.02/5.33 ( plus_plus_int
% 5.02/5.33 @ ( zero_n2684676970156552555ol_int
% 5.02/5.33 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.02/5.33 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.02/5.33 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_int_rec
% 5.02/5.33 thf(fact_6396_ln__one__plus__pos__lower__bound,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.33 => ( ord_less_eq_real @ ( minus_minus_real @ X2 @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % ln_one_plus_pos_lower_bound
% 5.02/5.33 thf(fact_6397_arcosh__real__def,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.02/5.33 => ( ( arcosh_real @ X2 )
% 5.02/5.33 = ( ln_ln_real @ ( plus_plus_real @ X2 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % arcosh_real_def
% 5.02/5.33 thf(fact_6398_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.33 => ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.02/5.33 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.02/5.33 thf(fact_6399_tanh__ln__real,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( tanh_real @ ( ln_ln_real @ X2 ) )
% 5.02/5.33 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % tanh_ln_real
% 5.02/5.33 thf(fact_6400_pred__subset__eq2,axiom,
% 5.02/5.33 ! [R: set_Pr448751882837621926eger_o,S3: set_Pr448751882837621926eger_o] :
% 5.02/5.33 ( ( ord_le2162486998276636481er_o_o
% 5.02/5.33 @ ^ [X: code_integer,Y6: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y6 ) @ R )
% 5.02/5.33 @ ^ [X: code_integer,Y6: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y6 ) @ S3 ) )
% 5.02/5.33 = ( ord_le8980329558974975238eger_o @ R @ S3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_subset_eq2
% 5.02/5.33 thf(fact_6401_pred__subset__eq2,axiom,
% 5.02/5.33 ! [R: set_Pr8218934625190621173um_num,S3: set_Pr8218934625190621173um_num] :
% 5.02/5.33 ( ( ord_le6124364862034508274_num_o
% 5.02/5.33 @ ^ [X: num,Y6: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y6 ) @ R )
% 5.02/5.33 @ ^ [X: num,Y6: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y6 ) @ S3 ) )
% 5.02/5.33 = ( ord_le880128212290418581um_num @ R @ S3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_subset_eq2
% 5.02/5.33 thf(fact_6402_pred__subset__eq2,axiom,
% 5.02/5.33 ! [R: set_Pr6200539531224447659at_num,S3: set_Pr6200539531224447659at_num] :
% 5.02/5.33 ( ( ord_le3404735783095501756_num_o
% 5.02/5.33 @ ^ [X: nat,Y6: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y6 ) @ R )
% 5.02/5.33 @ ^ [X: nat,Y6: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y6 ) @ S3 ) )
% 5.02/5.33 = ( ord_le8085105155179020875at_num @ R @ S3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_subset_eq2
% 5.02/5.33 thf(fact_6403_pred__subset__eq2,axiom,
% 5.02/5.33 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.02/5.33 ( ( ord_le2646555220125990790_nat_o
% 5.02/5.33 @ ^ [X: nat,Y6: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y6 ) @ R )
% 5.02/5.33 @ ^ [X: nat,Y6: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y6 ) @ S3 ) )
% 5.02/5.33 = ( ord_le3146513528884898305at_nat @ R @ S3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_subset_eq2
% 5.02/5.33 thf(fact_6404_pred__subset__eq2,axiom,
% 5.02/5.33 ! [R: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 5.02/5.33 ( ( ord_le6741204236512500942_int_o
% 5.02/5.33 @ ^ [X: int,Y6: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y6 ) @ R )
% 5.02/5.33 @ ^ [X: int,Y6: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y6 ) @ S3 ) )
% 5.02/5.33 = ( ord_le2843351958646193337nt_int @ R @ S3 ) ) ).
% 5.02/5.33
% 5.02/5.33 % pred_subset_eq2
% 5.02/5.33 thf(fact_6405_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.33 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ln_one_plus_x_minus_x_bound
% 5.02/5.33 thf(fact_6406_or__minus__numerals_I5_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_minus_numerals(5)
% 5.02/5.33 thf(fact_6407_or__minus__numerals_I1_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_minus_numerals(1)
% 5.02/5.33 thf(fact_6408_abs__abs,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.02/5.33 = ( abs_abs_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_abs
% 5.02/5.33 thf(fact_6409_abs__abs,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.02/5.33 = ( abs_abs_int @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_abs
% 5.02/5.33 thf(fact_6410_abs__abs,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.02/5.33 = ( abs_abs_Code_integer @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_abs
% 5.02/5.33 thf(fact_6411_abs__idempotent,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.02/5.33 = ( abs_abs_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_idempotent
% 5.02/5.33 thf(fact_6412_abs__idempotent,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.02/5.33 = ( abs_abs_int @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_idempotent
% 5.02/5.33 thf(fact_6413_abs__idempotent,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.02/5.33 = ( abs_abs_Code_integer @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_idempotent
% 5.02/5.33 thf(fact_6414_abs__zero,axiom,
% 5.02/5.33 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.02/5.33 = zero_z3403309356797280102nteger ) ).
% 5.02/5.33
% 5.02/5.33 % abs_zero
% 5.02/5.33 thf(fact_6415_abs__zero,axiom,
% 5.02/5.33 ( ( abs_abs_real @ zero_zero_real )
% 5.02/5.33 = zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % abs_zero
% 5.02/5.33 thf(fact_6416_abs__zero,axiom,
% 5.02/5.33 ( ( abs_abs_rat @ zero_zero_rat )
% 5.02/5.33 = zero_zero_rat ) ).
% 5.02/5.33
% 5.02/5.33 % abs_zero
% 5.02/5.33 thf(fact_6417_abs__zero,axiom,
% 5.02/5.33 ( ( abs_abs_int @ zero_zero_int )
% 5.02/5.33 = zero_zero_int ) ).
% 5.02/5.33
% 5.02/5.33 % abs_zero
% 5.02/5.33 thf(fact_6418_abs__eq__0,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ( abs_abs_Code_integer @ A )
% 5.02/5.33 = zero_z3403309356797280102nteger )
% 5.02/5.33 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0
% 5.02/5.33 thf(fact_6419_abs__eq__0,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ( abs_abs_real @ A )
% 5.02/5.33 = zero_zero_real )
% 5.02/5.33 = ( A = zero_zero_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0
% 5.02/5.33 thf(fact_6420_abs__eq__0,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ( abs_abs_rat @ A )
% 5.02/5.33 = zero_zero_rat )
% 5.02/5.33 = ( A = zero_zero_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0
% 5.02/5.33 thf(fact_6421_abs__eq__0,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ( abs_abs_int @ A )
% 5.02/5.33 = zero_zero_int )
% 5.02/5.33 = ( A = zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0
% 5.02/5.33 thf(fact_6422_abs__0__eq,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( zero_z3403309356797280102nteger
% 5.02/5.33 = ( abs_abs_Code_integer @ A ) )
% 5.02/5.33 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0_eq
% 5.02/5.33 thf(fact_6423_abs__0__eq,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( zero_zero_real
% 5.02/5.33 = ( abs_abs_real @ A ) )
% 5.02/5.33 = ( A = zero_zero_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0_eq
% 5.02/5.33 thf(fact_6424_abs__0__eq,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( zero_zero_rat
% 5.02/5.33 = ( abs_abs_rat @ A ) )
% 5.02/5.33 = ( A = zero_zero_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0_eq
% 5.02/5.33 thf(fact_6425_abs__0__eq,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( zero_zero_int
% 5.02/5.33 = ( abs_abs_int @ A ) )
% 5.02/5.33 = ( A = zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0_eq
% 5.02/5.33 thf(fact_6426_abs__0,axiom,
% 5.02/5.33 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.02/5.33 = zero_z3403309356797280102nteger ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0
% 5.02/5.33 thf(fact_6427_abs__0,axiom,
% 5.02/5.33 ( ( abs_abs_complex @ zero_zero_complex )
% 5.02/5.33 = zero_zero_complex ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0
% 5.02/5.33 thf(fact_6428_abs__0,axiom,
% 5.02/5.33 ( ( abs_abs_real @ zero_zero_real )
% 5.02/5.33 = zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0
% 5.02/5.33 thf(fact_6429_abs__0,axiom,
% 5.02/5.33 ( ( abs_abs_rat @ zero_zero_rat )
% 5.02/5.33 = zero_zero_rat ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0
% 5.02/5.33 thf(fact_6430_abs__0,axiom,
% 5.02/5.33 ( ( abs_abs_int @ zero_zero_int )
% 5.02/5.33 = zero_zero_int ) ).
% 5.02/5.33
% 5.02/5.33 % abs_0
% 5.02/5.33 thf(fact_6431_abs__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 5.02/5.33 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_numeral
% 5.02/5.33 thf(fact_6432_abs__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.33 = ( numeral_numeral_real @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_numeral
% 5.02/5.33 thf(fact_6433_abs__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.02/5.33 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_numeral
% 5.02/5.33 thf(fact_6434_abs__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.33 = ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_numeral
% 5.02/5.33 thf(fact_6435_abs__mult__self__eq,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.02/5.33 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_self_eq
% 5.02/5.33 thf(fact_6436_abs__mult__self__eq,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.02/5.33 = ( times_times_real @ A @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_self_eq
% 5.02/5.33 thf(fact_6437_abs__mult__self__eq,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.02/5.33 = ( times_times_rat @ A @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_self_eq
% 5.02/5.33 thf(fact_6438_abs__mult__self__eq,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.02/5.33 = ( times_times_int @ A @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_self_eq
% 5.02/5.33 thf(fact_6439_abs__1,axiom,
% 5.02/5.33 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.02/5.33 = one_one_Code_integer ) ).
% 5.02/5.33
% 5.02/5.33 % abs_1
% 5.02/5.33 thf(fact_6440_abs__1,axiom,
% 5.02/5.33 ( ( abs_abs_complex @ one_one_complex )
% 5.02/5.33 = one_one_complex ) ).
% 5.02/5.33
% 5.02/5.33 % abs_1
% 5.02/5.33 thf(fact_6441_abs__1,axiom,
% 5.02/5.33 ( ( abs_abs_real @ one_one_real )
% 5.02/5.33 = one_one_real ) ).
% 5.02/5.33
% 5.02/5.33 % abs_1
% 5.02/5.33 thf(fact_6442_abs__1,axiom,
% 5.02/5.33 ( ( abs_abs_rat @ one_one_rat )
% 5.02/5.33 = one_one_rat ) ).
% 5.02/5.33
% 5.02/5.33 % abs_1
% 5.02/5.33 thf(fact_6443_abs__1,axiom,
% 5.02/5.33 ( ( abs_abs_int @ one_one_int )
% 5.02/5.33 = one_one_int ) ).
% 5.02/5.33
% 5.02/5.33 % abs_1
% 5.02/5.33 thf(fact_6444_abs__add__abs,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.02/5.33 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_add_abs
% 5.02/5.33 thf(fact_6445_abs__add__abs,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.02/5.33 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_add_abs
% 5.02/5.33 thf(fact_6446_abs__add__abs,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.02/5.33 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_add_abs
% 5.02/5.33 thf(fact_6447_abs__add__abs,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.02/5.33 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_add_abs
% 5.02/5.33 thf(fact_6448_abs__divide,axiom,
% 5.02/5.33 ! [A: complex,B: complex] :
% 5.02/5.33 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.33 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_divide
% 5.02/5.33 thf(fact_6449_abs__divide,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.33 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_divide
% 5.02/5.33 thf(fact_6450_abs__divide,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.02/5.33 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_divide
% 5.02/5.33 thf(fact_6451_abs__minus,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.02/5.33 = ( abs_abs_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus
% 5.02/5.33 thf(fact_6452_abs__minus,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.02/5.33 = ( abs_abs_int @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus
% 5.02/5.33 thf(fact_6453_abs__minus,axiom,
% 5.02/5.33 ! [A: complex] :
% 5.02/5.33 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.02/5.33 = ( abs_abs_complex @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus
% 5.02/5.33 thf(fact_6454_abs__minus,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.02/5.33 = ( abs_abs_rat @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus
% 5.02/5.33 thf(fact_6455_abs__minus,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.33 = ( abs_abs_Code_integer @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus
% 5.02/5.33 thf(fact_6456_abs__minus__cancel,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.02/5.33 = ( abs_abs_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_cancel
% 5.02/5.33 thf(fact_6457_abs__minus__cancel,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.02/5.33 = ( abs_abs_int @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_cancel
% 5.02/5.33 thf(fact_6458_abs__minus__cancel,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.02/5.33 = ( abs_abs_rat @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_cancel
% 5.02/5.33 thf(fact_6459_abs__minus__cancel,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.02/5.33 = ( abs_abs_Code_integer @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_cancel
% 5.02/5.33 thf(fact_6460_abs__dvd__iff,axiom,
% 5.02/5.33 ! [M: real,K: real] :
% 5.02/5.33 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.02/5.33 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_dvd_iff
% 5.02/5.33 thf(fact_6461_abs__dvd__iff,axiom,
% 5.02/5.33 ! [M: int,K: int] :
% 5.02/5.33 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.02/5.33 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_dvd_iff
% 5.02/5.33 thf(fact_6462_abs__dvd__iff,axiom,
% 5.02/5.33 ! [M: code_integer,K: code_integer] :
% 5.02/5.33 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.02/5.33 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_dvd_iff
% 5.02/5.33 thf(fact_6463_dvd__abs__iff,axiom,
% 5.02/5.33 ! [M: real,K: real] :
% 5.02/5.33 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.02/5.33 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_abs_iff
% 5.02/5.33 thf(fact_6464_dvd__abs__iff,axiom,
% 5.02/5.33 ! [M: int,K: int] :
% 5.02/5.33 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.02/5.33 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_abs_iff
% 5.02/5.33 thf(fact_6465_dvd__abs__iff,axiom,
% 5.02/5.33 ! [M: code_integer,K: code_integer] :
% 5.02/5.33 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.02/5.33 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_abs_iff
% 5.02/5.33 thf(fact_6466_of__int__abs,axiom,
% 5.02/5.33 ! [X2: int] :
% 5.02/5.33 ( ( ring_1_of_int_int @ ( abs_abs_int @ X2 ) )
% 5.02/5.33 = ( abs_abs_int @ ( ring_1_of_int_int @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_abs
% 5.02/5.33 thf(fact_6467_of__int__abs,axiom,
% 5.02/5.33 ! [X2: int] :
% 5.02/5.33 ( ( ring_18347121197199848620nteger @ ( abs_abs_int @ X2 ) )
% 5.02/5.33 = ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_abs
% 5.02/5.33 thf(fact_6468_of__int__abs,axiom,
% 5.02/5.33 ! [X2: int] :
% 5.02/5.33 ( ( ring_1_of_int_real @ ( abs_abs_int @ X2 ) )
% 5.02/5.33 = ( abs_abs_real @ ( ring_1_of_int_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_abs
% 5.02/5.33 thf(fact_6469_of__int__abs,axiom,
% 5.02/5.33 ! [X2: int] :
% 5.02/5.33 ( ( ring_1_of_int_rat @ ( abs_abs_int @ X2 ) )
% 5.02/5.33 = ( abs_abs_rat @ ( ring_1_of_int_rat @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_abs
% 5.02/5.33 thf(fact_6470_abs__bool__eq,axiom,
% 5.02/5.33 ! [P: $o] :
% 5.02/5.33 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.02/5.33 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_bool_eq
% 5.02/5.33 thf(fact_6471_abs__bool__eq,axiom,
% 5.02/5.33 ! [P: $o] :
% 5.02/5.33 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.02/5.33 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_bool_eq
% 5.02/5.33 thf(fact_6472_abs__bool__eq,axiom,
% 5.02/5.33 ! [P: $o] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.02/5.33 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_bool_eq
% 5.02/5.33 thf(fact_6473_tanh__0,axiom,
% 5.02/5.33 ( ( tanh_complex @ zero_zero_complex )
% 5.02/5.33 = zero_zero_complex ) ).
% 5.02/5.33
% 5.02/5.33 % tanh_0
% 5.02/5.33 thf(fact_6474_tanh__0,axiom,
% 5.02/5.33 ( ( tanh_real @ zero_zero_real )
% 5.02/5.33 = zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % tanh_0
% 5.02/5.33 thf(fact_6475_abs__le__zero__iff,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.02/5.33 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_zero_iff
% 5.02/5.33 thf(fact_6476_abs__le__zero__iff,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.02/5.33 = ( A = zero_zero_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_zero_iff
% 5.02/5.33 thf(fact_6477_abs__le__zero__iff,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.02/5.33 = ( A = zero_zero_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_zero_iff
% 5.02/5.33 thf(fact_6478_abs__le__zero__iff,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.02/5.33 = ( A = zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_zero_iff
% 5.02/5.33 thf(fact_6479_abs__le__self__iff,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.02/5.33 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_self_iff
% 5.02/5.33 thf(fact_6480_abs__le__self__iff,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.02/5.33 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_self_iff
% 5.02/5.33 thf(fact_6481_abs__le__self__iff,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.02/5.33 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_self_iff
% 5.02/5.33 thf(fact_6482_abs__le__self__iff,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.02/5.33 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_self_iff
% 5.02/5.33 thf(fact_6483_abs__of__nonneg,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.02/5.33 => ( ( abs_abs_Code_integer @ A )
% 5.02/5.33 = A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_nonneg
% 5.02/5.33 thf(fact_6484_abs__of__nonneg,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.02/5.33 => ( ( abs_abs_real @ A )
% 5.02/5.33 = A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_nonneg
% 5.02/5.33 thf(fact_6485_abs__of__nonneg,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.02/5.33 => ( ( abs_abs_rat @ A )
% 5.02/5.33 = A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_nonneg
% 5.02/5.33 thf(fact_6486_abs__of__nonneg,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.02/5.33 => ( ( abs_abs_int @ A )
% 5.02/5.33 = A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_nonneg
% 5.02/5.33 thf(fact_6487_zero__less__abs__iff,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.02/5.33 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_less_abs_iff
% 5.02/5.33 thf(fact_6488_zero__less__abs__iff,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.02/5.33 = ( A != zero_zero_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_less_abs_iff
% 5.02/5.33 thf(fact_6489_zero__less__abs__iff,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.02/5.33 = ( A != zero_zero_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_less_abs_iff
% 5.02/5.33 thf(fact_6490_zero__less__abs__iff,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.02/5.33 = ( A != zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_less_abs_iff
% 5.02/5.33 thf(fact_6491_abs__neg__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.33 = ( numeral_numeral_real @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_neg_numeral
% 5.02/5.33 thf(fact_6492_abs__neg__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.33 = ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_neg_numeral
% 5.02/5.33 thf(fact_6493_abs__neg__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.02/5.33 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_neg_numeral
% 5.02/5.33 thf(fact_6494_abs__neg__numeral,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.02/5.33 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_neg_numeral
% 5.02/5.33 thf(fact_6495_abs__neg__one,axiom,
% 5.02/5.33 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.33 = one_one_real ) ).
% 5.02/5.33
% 5.02/5.33 % abs_neg_one
% 5.02/5.33 thf(fact_6496_abs__neg__one,axiom,
% 5.02/5.33 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.33 = one_one_int ) ).
% 5.02/5.33
% 5.02/5.33 % abs_neg_one
% 5.02/5.33 thf(fact_6497_abs__neg__one,axiom,
% 5.02/5.33 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.33 = one_one_rat ) ).
% 5.02/5.33
% 5.02/5.33 % abs_neg_one
% 5.02/5.33 thf(fact_6498_abs__neg__one,axiom,
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.33 = one_one_Code_integer ) ).
% 5.02/5.33
% 5.02/5.33 % abs_neg_one
% 5.02/5.33 thf(fact_6499_abs__power__minus,axiom,
% 5.02/5.33 ! [A: real,N2: nat] :
% 5.02/5.33 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.02/5.33 = ( abs_abs_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_power_minus
% 5.02/5.33 thf(fact_6500_abs__power__minus,axiom,
% 5.02/5.33 ! [A: int,N2: nat] :
% 5.02/5.33 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.02/5.33 = ( abs_abs_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_power_minus
% 5.02/5.33 thf(fact_6501_abs__power__minus,axiom,
% 5.02/5.33 ! [A: rat,N2: nat] :
% 5.02/5.33 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.02/5.33 = ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_power_minus
% 5.02/5.33 thf(fact_6502_abs__power__minus,axiom,
% 5.02/5.33 ! [A: code_integer,N2: nat] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.02/5.33 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_power_minus
% 5.02/5.33 thf(fact_6503_real__sqrt__abs2,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( sqrt @ ( times_times_real @ X2 @ X2 ) )
% 5.02/5.33 = ( abs_abs_real @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_abs2
% 5.02/5.33 thf(fact_6504_real__sqrt__mult__self,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.02/5.33 = ( abs_abs_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_mult_self
% 5.02/5.33 thf(fact_6505_zero__le__divide__abs__iff,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.02/5.33 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.02/5.33 | ( B = zero_zero_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_le_divide_abs_iff
% 5.02/5.33 thf(fact_6506_zero__le__divide__abs__iff,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.02/5.33 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.02/5.33 | ( B = zero_zero_rat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_le_divide_abs_iff
% 5.02/5.33 thf(fact_6507_divide__le__0__abs__iff,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.02/5.33 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.02/5.33 | ( B = zero_zero_real ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divide_le_0_abs_iff
% 5.02/5.33 thf(fact_6508_divide__le__0__abs__iff,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.02/5.33 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.02/5.33 | ( B = zero_zero_rat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % divide_le_0_abs_iff
% 5.02/5.33 thf(fact_6509_abs__of__nonpos,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.02/5.33 => ( ( abs_abs_real @ A )
% 5.02/5.33 = ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_nonpos
% 5.02/5.33 thf(fact_6510_abs__of__nonpos,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.02/5.33 => ( ( abs_abs_Code_integer @ A )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_nonpos
% 5.02/5.33 thf(fact_6511_abs__of__nonpos,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.02/5.33 => ( ( abs_abs_rat @ A )
% 5.02/5.33 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_nonpos
% 5.02/5.33 thf(fact_6512_abs__of__nonpos,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.02/5.33 => ( ( abs_abs_int @ A )
% 5.02/5.33 = ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_nonpos
% 5.02/5.33 thf(fact_6513_or__nat__numerals_I2_J,axiom,
% 5.02/5.33 ! [Y: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_nat_numerals(2)
% 5.02/5.33 thf(fact_6514_or__nat__numerals_I4_J,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_nat_numerals(4)
% 5.02/5.33 thf(fact_6515_artanh__minus__real,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.33 => ( ( artanh_real @ ( uminus_uminus_real @ X2 ) )
% 5.02/5.33 = ( uminus_uminus_real @ ( artanh_real @ X2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % artanh_minus_real
% 5.02/5.33 thf(fact_6516_zero__less__power__abs__iff,axiom,
% 5.02/5.33 ! [A: code_integer,N2: nat] :
% 5.02/5.33 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 5.02/5.33 = ( ( A != zero_z3403309356797280102nteger )
% 5.02/5.33 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_less_power_abs_iff
% 5.02/5.33 thf(fact_6517_zero__less__power__abs__iff,axiom,
% 5.02/5.33 ! [A: real,N2: nat] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.02/5.33 = ( ( A != zero_zero_real )
% 5.02/5.33 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_less_power_abs_iff
% 5.02/5.33 thf(fact_6518_zero__less__power__abs__iff,axiom,
% 5.02/5.33 ! [A: rat,N2: nat] :
% 5.02/5.33 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 5.02/5.33 = ( ( A != zero_zero_rat )
% 5.02/5.33 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_less_power_abs_iff
% 5.02/5.33 thf(fact_6519_zero__less__power__abs__iff,axiom,
% 5.02/5.33 ! [A: int,N2: nat] :
% 5.02/5.33 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 5.02/5.33 = ( ( A != zero_zero_int )
% 5.02/5.33 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_less_power_abs_iff
% 5.02/5.33 thf(fact_6520_power2__abs,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.33 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power2_abs
% 5.02/5.33 thf(fact_6521_power2__abs,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.33 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power2_abs
% 5.02/5.33 thf(fact_6522_power2__abs,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.33 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power2_abs
% 5.02/5.33 thf(fact_6523_abs__power2,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_power2
% 5.02/5.33 thf(fact_6524_abs__power2,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_power2
% 5.02/5.33 thf(fact_6525_abs__power2,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_power2
% 5.02/5.33 thf(fact_6526_or__nat__numerals_I1_J,axiom,
% 5.02/5.33 ! [Y: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_nat_numerals(1)
% 5.02/5.33 thf(fact_6527_or__nat__numerals_I3_J,axiom,
% 5.02/5.33 ! [X2: num] :
% 5.02/5.33 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.02/5.33 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_nat_numerals(3)
% 5.02/5.33 thf(fact_6528_power__even__abs__numeral,axiom,
% 5.02/5.33 ! [W: num,A: code_integer] :
% 5.02/5.33 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.02/5.33 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.02/5.33 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_even_abs_numeral
% 5.02/5.33 thf(fact_6529_power__even__abs__numeral,axiom,
% 5.02/5.33 ! [W: num,A: int] :
% 5.02/5.33 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.02/5.33 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.02/5.33 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_even_abs_numeral
% 5.02/5.33 thf(fact_6530_power__even__abs__numeral,axiom,
% 5.02/5.33 ! [W: num,A: real] :
% 5.02/5.33 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.02/5.33 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.02/5.33 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_even_abs_numeral
% 5.02/5.33 thf(fact_6531_real__sqrt__abs,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ( sqrt @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.33 = ( abs_abs_real @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % real_sqrt_abs
% 5.02/5.33 thf(fact_6532_or__minus__numerals_I8_J,axiom,
% 5.02/5.33 ! [N2: num,M: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_minus_numerals(8)
% 5.02/5.33 thf(fact_6533_or__minus__numerals_I4_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_minus_numerals(4)
% 5.02/5.33 thf(fact_6534_or__minus__numerals_I7_J,axiom,
% 5.02/5.33 ! [N2: num,M: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_minus_numerals(7)
% 5.02/5.33 thf(fact_6535_or__minus__numerals_I3_J,axiom,
% 5.02/5.33 ! [M: num,N2: num] :
% 5.02/5.33 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.33 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_minus_numerals(3)
% 5.02/5.33 thf(fact_6536_abs__ge__self,axiom,
% 5.02/5.33 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_self
% 5.02/5.33 thf(fact_6537_abs__ge__self,axiom,
% 5.02/5.33 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_self
% 5.02/5.33 thf(fact_6538_abs__ge__self,axiom,
% 5.02/5.33 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_self
% 5.02/5.33 thf(fact_6539_abs__ge__self,axiom,
% 5.02/5.33 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_self
% 5.02/5.33 thf(fact_6540_abs__le__D1,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_D1
% 5.02/5.33 thf(fact_6541_abs__le__D1,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.02/5.33 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_D1
% 5.02/5.33 thf(fact_6542_abs__le__D1,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_D1
% 5.02/5.33 thf(fact_6543_abs__le__D1,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_D1
% 5.02/5.33 thf(fact_6544_abs__eq__0__iff,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ( abs_abs_Code_integer @ A )
% 5.02/5.33 = zero_z3403309356797280102nteger )
% 5.02/5.33 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0_iff
% 5.02/5.33 thf(fact_6545_abs__eq__0__iff,axiom,
% 5.02/5.33 ! [A: complex] :
% 5.02/5.33 ( ( ( abs_abs_complex @ A )
% 5.02/5.33 = zero_zero_complex )
% 5.02/5.33 = ( A = zero_zero_complex ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0_iff
% 5.02/5.33 thf(fact_6546_abs__eq__0__iff,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ( abs_abs_real @ A )
% 5.02/5.33 = zero_zero_real )
% 5.02/5.33 = ( A = zero_zero_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0_iff
% 5.02/5.33 thf(fact_6547_abs__eq__0__iff,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ( abs_abs_rat @ A )
% 5.02/5.33 = zero_zero_rat )
% 5.02/5.33 = ( A = zero_zero_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0_iff
% 5.02/5.33 thf(fact_6548_abs__eq__0__iff,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ( abs_abs_int @ A )
% 5.02/5.33 = zero_zero_int )
% 5.02/5.33 = ( A = zero_zero_int ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_0_iff
% 5.02/5.33 thf(fact_6549_abs__mult,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.02/5.33 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult
% 5.02/5.33 thf(fact_6550_abs__mult,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.02/5.33 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult
% 5.02/5.33 thf(fact_6551_abs__mult,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.02/5.33 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult
% 5.02/5.33 thf(fact_6552_abs__mult,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.02/5.33 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult
% 5.02/5.33 thf(fact_6553_abs__one,axiom,
% 5.02/5.33 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.02/5.33 = one_one_Code_integer ) ).
% 5.02/5.33
% 5.02/5.33 % abs_one
% 5.02/5.33 thf(fact_6554_abs__one,axiom,
% 5.02/5.33 ( ( abs_abs_real @ one_one_real )
% 5.02/5.33 = one_one_real ) ).
% 5.02/5.33
% 5.02/5.33 % abs_one
% 5.02/5.33 thf(fact_6555_abs__one,axiom,
% 5.02/5.33 ( ( abs_abs_rat @ one_one_rat )
% 5.02/5.33 = one_one_rat ) ).
% 5.02/5.33
% 5.02/5.33 % abs_one
% 5.02/5.33 thf(fact_6556_abs__one,axiom,
% 5.02/5.33 ( ( abs_abs_int @ one_one_int )
% 5.02/5.33 = one_one_int ) ).
% 5.02/5.33
% 5.02/5.33 % abs_one
% 5.02/5.33 thf(fact_6557_abs__minus__commute,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.02/5.33 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_commute
% 5.02/5.33 thf(fact_6558_abs__minus__commute,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.02/5.33 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_commute
% 5.02/5.33 thf(fact_6559_abs__minus__commute,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.02/5.33 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_commute
% 5.02/5.33 thf(fact_6560_abs__minus__commute,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.02/5.33 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_commute
% 5.02/5.33 thf(fact_6561_abs__eq__iff,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ( abs_abs_real @ X2 )
% 5.02/5.33 = ( abs_abs_real @ Y ) )
% 5.02/5.33 = ( ( X2 = Y )
% 5.02/5.33 | ( X2
% 5.02/5.33 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_iff
% 5.02/5.33 thf(fact_6562_abs__eq__iff,axiom,
% 5.02/5.33 ! [X2: int,Y: int] :
% 5.02/5.33 ( ( ( abs_abs_int @ X2 )
% 5.02/5.33 = ( abs_abs_int @ Y ) )
% 5.02/5.33 = ( ( X2 = Y )
% 5.02/5.33 | ( X2
% 5.02/5.33 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_iff
% 5.02/5.33 thf(fact_6563_abs__eq__iff,axiom,
% 5.02/5.33 ! [X2: rat,Y: rat] :
% 5.02/5.33 ( ( ( abs_abs_rat @ X2 )
% 5.02/5.33 = ( abs_abs_rat @ Y ) )
% 5.02/5.33 = ( ( X2 = Y )
% 5.02/5.33 | ( X2
% 5.02/5.33 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_iff
% 5.02/5.33 thf(fact_6564_abs__eq__iff,axiom,
% 5.02/5.33 ! [X2: code_integer,Y: code_integer] :
% 5.02/5.33 ( ( ( abs_abs_Code_integer @ X2 )
% 5.02/5.33 = ( abs_abs_Code_integer @ Y ) )
% 5.02/5.33 = ( ( X2 = Y )
% 5.02/5.33 | ( X2
% 5.02/5.33 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_iff
% 5.02/5.33 thf(fact_6565_power__abs,axiom,
% 5.02/5.33 ! [A: code_integer,N2: nat] :
% 5.02/5.33 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.02/5.33 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_abs
% 5.02/5.33 thf(fact_6566_power__abs,axiom,
% 5.02/5.33 ! [A: int,N2: nat] :
% 5.02/5.33 ( ( abs_abs_int @ ( power_power_int @ A @ N2 ) )
% 5.02/5.33 = ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_abs
% 5.02/5.33 thf(fact_6567_power__abs,axiom,
% 5.02/5.33 ! [A: real,N2: nat] :
% 5.02/5.33 ( ( abs_abs_real @ ( power_power_real @ A @ N2 ) )
% 5.02/5.33 = ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % power_abs
% 5.02/5.33 thf(fact_6568_dvd__if__abs__eq,axiom,
% 5.02/5.33 ! [L: real,K: real] :
% 5.02/5.33 ( ( ( abs_abs_real @ L )
% 5.02/5.33 = ( abs_abs_real @ K ) )
% 5.02/5.33 => ( dvd_dvd_real @ L @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_if_abs_eq
% 5.02/5.33 thf(fact_6569_dvd__if__abs__eq,axiom,
% 5.02/5.33 ! [L: int,K: int] :
% 5.02/5.33 ( ( ( abs_abs_int @ L )
% 5.02/5.33 = ( abs_abs_int @ K ) )
% 5.02/5.33 => ( dvd_dvd_int @ L @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_if_abs_eq
% 5.02/5.33 thf(fact_6570_dvd__if__abs__eq,axiom,
% 5.02/5.33 ! [L: code_integer,K: code_integer] :
% 5.02/5.33 ( ( ( abs_abs_Code_integer @ L )
% 5.02/5.33 = ( abs_abs_Code_integer @ K ) )
% 5.02/5.33 => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 5.02/5.33
% 5.02/5.33 % dvd_if_abs_eq
% 5.02/5.33 thf(fact_6571_or__not__num__neg_Osimps_I1_J,axiom,
% 5.02/5.33 ( ( bit_or_not_num_neg @ one @ one )
% 5.02/5.33 = one ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(1)
% 5.02/5.33 thf(fact_6572_abs__ge__zero,axiom,
% 5.02/5.33 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_zero
% 5.02/5.33 thf(fact_6573_abs__ge__zero,axiom,
% 5.02/5.33 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_zero
% 5.02/5.33 thf(fact_6574_abs__ge__zero,axiom,
% 5.02/5.33 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_zero
% 5.02/5.33 thf(fact_6575_abs__ge__zero,axiom,
% 5.02/5.33 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_zero
% 5.02/5.33 thf(fact_6576_abs__not__less__zero,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.02/5.33
% 5.02/5.33 % abs_not_less_zero
% 5.02/5.33 thf(fact_6577_abs__not__less__zero,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % abs_not_less_zero
% 5.02/5.33 thf(fact_6578_abs__not__less__zero,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.02/5.33
% 5.02/5.33 % abs_not_less_zero
% 5.02/5.33 thf(fact_6579_abs__not__less__zero,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.02/5.33
% 5.02/5.33 % abs_not_less_zero
% 5.02/5.33 thf(fact_6580_abs__of__pos,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.02/5.33 => ( ( abs_abs_Code_integer @ A )
% 5.02/5.33 = A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_pos
% 5.02/5.33 thf(fact_6581_abs__of__pos,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.33 => ( ( abs_abs_real @ A )
% 5.02/5.33 = A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_pos
% 5.02/5.33 thf(fact_6582_abs__of__pos,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.33 => ( ( abs_abs_rat @ A )
% 5.02/5.33 = A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_pos
% 5.02/5.33 thf(fact_6583_abs__of__pos,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ord_less_int @ zero_zero_int @ A )
% 5.02/5.33 => ( ( abs_abs_int @ A )
% 5.02/5.33 = A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_pos
% 5.02/5.33 thf(fact_6584_abs__triangle__ineq,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq
% 5.02/5.33 thf(fact_6585_abs__triangle__ineq,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq
% 5.02/5.33 thf(fact_6586_abs__triangle__ineq,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq
% 5.02/5.33 thf(fact_6587_abs__triangle__ineq,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq
% 5.02/5.33 thf(fact_6588_abs__mult__less,axiom,
% 5.02/5.33 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.02/5.33 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.02/5.33 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.02/5.33 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_less
% 5.02/5.33 thf(fact_6589_abs__mult__less,axiom,
% 5.02/5.33 ! [A: real,C: real,B: real,D: real] :
% 5.02/5.33 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.02/5.33 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.02/5.33 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_less
% 5.02/5.33 thf(fact_6590_abs__mult__less,axiom,
% 5.02/5.33 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.02/5.33 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.02/5.33 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.02/5.33 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_less
% 5.02/5.33 thf(fact_6591_abs__mult__less,axiom,
% 5.02/5.33 ! [A: int,C: int,B: int,D: int] :
% 5.02/5.33 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.02/5.33 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.02/5.33 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_less
% 5.02/5.33 thf(fact_6592_abs__triangle__ineq2,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq2
% 5.02/5.33 thf(fact_6593_abs__triangle__ineq2,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq2
% 5.02/5.33 thf(fact_6594_abs__triangle__ineq2,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq2
% 5.02/5.33 thf(fact_6595_abs__triangle__ineq2,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq2
% 5.02/5.33 thf(fact_6596_abs__triangle__ineq3,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq3
% 5.02/5.33 thf(fact_6597_abs__triangle__ineq3,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq3
% 5.02/5.33 thf(fact_6598_abs__triangle__ineq3,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq3
% 5.02/5.33 thf(fact_6599_abs__triangle__ineq3,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq3
% 5.02/5.33 thf(fact_6600_abs__triangle__ineq2__sym,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq2_sym
% 5.02/5.33 thf(fact_6601_abs__triangle__ineq2__sym,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq2_sym
% 5.02/5.33 thf(fact_6602_abs__triangle__ineq2__sym,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq2_sym
% 5.02/5.33 thf(fact_6603_abs__triangle__ineq2__sym,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq2_sym
% 5.02/5.33 thf(fact_6604_nonzero__abs__divide,axiom,
% 5.02/5.33 ! [B: real,A: real] :
% 5.02/5.33 ( ( B != zero_zero_real )
% 5.02/5.33 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.33 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % nonzero_abs_divide
% 5.02/5.33 thf(fact_6605_nonzero__abs__divide,axiom,
% 5.02/5.33 ! [B: rat,A: rat] :
% 5.02/5.33 ( ( B != zero_zero_rat )
% 5.02/5.33 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.02/5.33 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % nonzero_abs_divide
% 5.02/5.33 thf(fact_6606_abs__leI,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ A @ B )
% 5.02/5.33 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_leI
% 5.02/5.33 thf(fact_6607_abs__leI,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.02/5.33 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.02/5.33 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_leI
% 5.02/5.33 thf(fact_6608_abs__leI,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.33 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_leI
% 5.02/5.33 thf(fact_6609_abs__leI,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ A @ B )
% 5.02/5.33 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_leI
% 5.02/5.33 thf(fact_6610_abs__le__D2,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_D2
% 5.02/5.33 thf(fact_6611_abs__le__D2,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.02/5.33 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_D2
% 5.02/5.33 thf(fact_6612_abs__le__D2,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_D2
% 5.02/5.33 thf(fact_6613_abs__le__D2,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.02/5.33 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_D2
% 5.02/5.33 thf(fact_6614_abs__le__iff,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.02/5.33 = ( ( ord_less_eq_real @ A @ B )
% 5.02/5.33 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_iff
% 5.02/5.33 thf(fact_6615_abs__le__iff,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.02/5.33 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.02/5.33 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_iff
% 5.02/5.33 thf(fact_6616_abs__le__iff,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.02/5.33 = ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.33 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_iff
% 5.02/5.33 thf(fact_6617_abs__le__iff,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.02/5.33 = ( ( ord_less_eq_int @ A @ B )
% 5.02/5.33 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_le_iff
% 5.02/5.33 thf(fact_6618_abs__ge__minus__self,axiom,
% 5.02/5.33 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_minus_self
% 5.02/5.33 thf(fact_6619_abs__ge__minus__self,axiom,
% 5.02/5.33 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_minus_self
% 5.02/5.33 thf(fact_6620_abs__ge__minus__self,axiom,
% 5.02/5.33 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_minus_self
% 5.02/5.33 thf(fact_6621_abs__ge__minus__self,axiom,
% 5.02/5.33 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_ge_minus_self
% 5.02/5.33 thf(fact_6622_abs__less__iff,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.02/5.33 = ( ( ord_less_real @ A @ B )
% 5.02/5.33 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_less_iff
% 5.02/5.33 thf(fact_6623_abs__less__iff,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.02/5.33 = ( ( ord_less_int @ A @ B )
% 5.02/5.33 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_less_iff
% 5.02/5.33 thf(fact_6624_abs__less__iff,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.02/5.33 = ( ( ord_less_rat @ A @ B )
% 5.02/5.33 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_less_iff
% 5.02/5.33 thf(fact_6625_abs__less__iff,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.02/5.33 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.02/5.33 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_less_iff
% 5.02/5.33 thf(fact_6626_tanh__real__lt__1,axiom,
% 5.02/5.33 ! [X2: real] : ( ord_less_real @ ( tanh_real @ X2 ) @ one_one_real ) ).
% 5.02/5.33
% 5.02/5.33 % tanh_real_lt_1
% 5.02/5.33 thf(fact_6627_or__not__num__neg_Osimps_I4_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
% 5.02/5.33 = ( bit0 @ one ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(4)
% 5.02/5.33 thf(fact_6628_or__not__num__neg_Osimps_I6_J,axiom,
% 5.02/5.33 ! [N2: num,M: num] :
% 5.02/5.33 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit1 @ M ) )
% 5.02/5.33 = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(6)
% 5.02/5.33 thf(fact_6629_or__not__num__neg_Osimps_I3_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.02/5.33 = ( bit1 @ M ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(3)
% 5.02/5.33 thf(fact_6630_or__not__num__neg_Osimps_I7_J,axiom,
% 5.02/5.33 ! [N2: num] :
% 5.02/5.33 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ one )
% 5.02/5.33 = one ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(7)
% 5.02/5.33 thf(fact_6631_dense__eq0__I,axiom,
% 5.02/5.33 ! [X2: real] :
% 5.02/5.33 ( ! [E: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ E )
% 5.02/5.33 => ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ E ) )
% 5.02/5.33 => ( X2 = zero_zero_real ) ) ).
% 5.02/5.33
% 5.02/5.33 % dense_eq0_I
% 5.02/5.33 thf(fact_6632_dense__eq0__I,axiom,
% 5.02/5.33 ! [X2: rat] :
% 5.02/5.33 ( ! [E: rat] :
% 5.02/5.33 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.02/5.33 => ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ E ) )
% 5.02/5.33 => ( X2 = zero_zero_rat ) ) ).
% 5.02/5.33
% 5.02/5.33 % dense_eq0_I
% 5.02/5.33 thf(fact_6633_or__not__num__neg_Osimps_I5_J,axiom,
% 5.02/5.33 ! [N2: num,M: num] :
% 5.02/5.33 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit0 @ M ) )
% 5.02/5.33 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(5)
% 5.02/5.33 thf(fact_6634_abs__eq__mult,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.02/5.33 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.02/5.33 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.02/5.33 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.02/5.33 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.02/5.33 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_mult
% 5.02/5.33 thf(fact_6635_abs__eq__mult,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.02/5.33 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.02/5.33 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.02/5.33 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.02/5.33 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.02/5.33 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_mult
% 5.02/5.33 thf(fact_6636_abs__eq__mult,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.02/5.33 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.02/5.33 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.02/5.33 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.02/5.33 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.02/5.33 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_mult
% 5.02/5.33 thf(fact_6637_abs__eq__mult,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.02/5.33 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.02/5.33 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.02/5.33 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.02/5.33 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.02/5.33 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_mult
% 5.02/5.33 thf(fact_6638_abs__mult__pos,axiom,
% 5.02/5.33 ! [X2: code_integer,Y: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X2 )
% 5.02/5.33 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X2 )
% 5.02/5.33 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_pos
% 5.02/5.33 thf(fact_6639_abs__mult__pos,axiom,
% 5.02/5.33 ! [X2: real,Y: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.33 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X2 )
% 5.02/5.33 = ( abs_abs_real @ ( times_times_real @ Y @ X2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_pos
% 5.02/5.33 thf(fact_6640_abs__mult__pos,axiom,
% 5.02/5.33 ! [X2: rat,Y: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ zero_zero_rat @ X2 )
% 5.02/5.33 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X2 )
% 5.02/5.33 = ( abs_abs_rat @ ( times_times_rat @ Y @ X2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_pos
% 5.02/5.33 thf(fact_6641_abs__mult__pos,axiom,
% 5.02/5.33 ! [X2: int,Y: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.33 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X2 )
% 5.02/5.33 = ( abs_abs_int @ ( times_times_int @ Y @ X2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_mult_pos
% 5.02/5.33 thf(fact_6642_abs__minus__le__zero,axiom,
% 5.02/5.33 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_le_zero
% 5.02/5.33 thf(fact_6643_abs__minus__le__zero,axiom,
% 5.02/5.33 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_le_zero
% 5.02/5.33 thf(fact_6644_abs__minus__le__zero,axiom,
% 5.02/5.33 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_le_zero
% 5.02/5.33 thf(fact_6645_abs__minus__le__zero,axiom,
% 5.02/5.33 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.02/5.33
% 5.02/5.33 % abs_minus_le_zero
% 5.02/5.33 thf(fact_6646_eq__abs__iff_H,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( A
% 5.02/5.33 = ( abs_abs_real @ B ) )
% 5.02/5.33 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.02/5.33 & ( ( B = A )
% 5.02/5.33 | ( B
% 5.02/5.33 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % eq_abs_iff'
% 5.02/5.33 thf(fact_6647_eq__abs__iff_H,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( A
% 5.02/5.33 = ( abs_abs_Code_integer @ B ) )
% 5.02/5.33 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.02/5.33 & ( ( B = A )
% 5.02/5.33 | ( B
% 5.02/5.33 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % eq_abs_iff'
% 5.02/5.33 thf(fact_6648_eq__abs__iff_H,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( A
% 5.02/5.33 = ( abs_abs_rat @ B ) )
% 5.02/5.33 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.02/5.33 & ( ( B = A )
% 5.02/5.33 | ( B
% 5.02/5.33 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % eq_abs_iff'
% 5.02/5.33 thf(fact_6649_eq__abs__iff_H,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( A
% 5.02/5.33 = ( abs_abs_int @ B ) )
% 5.02/5.33 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.02/5.33 & ( ( B = A )
% 5.02/5.33 | ( B
% 5.02/5.33 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % eq_abs_iff'
% 5.02/5.33 thf(fact_6650_abs__eq__iff_H,axiom,
% 5.02/5.33 ! [A: real,B: real] :
% 5.02/5.33 ( ( ( abs_abs_real @ A )
% 5.02/5.33 = B )
% 5.02/5.33 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.02/5.33 & ( ( A = B )
% 5.02/5.33 | ( A
% 5.02/5.33 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_iff'
% 5.02/5.33 thf(fact_6651_abs__eq__iff_H,axiom,
% 5.02/5.33 ! [A: code_integer,B: code_integer] :
% 5.02/5.33 ( ( ( abs_abs_Code_integer @ A )
% 5.02/5.33 = B )
% 5.02/5.33 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.02/5.33 & ( ( A = B )
% 5.02/5.33 | ( A
% 5.02/5.33 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_iff'
% 5.02/5.33 thf(fact_6652_abs__eq__iff_H,axiom,
% 5.02/5.33 ! [A: rat,B: rat] :
% 5.02/5.33 ( ( ( abs_abs_rat @ A )
% 5.02/5.33 = B )
% 5.02/5.33 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.02/5.33 & ( ( A = B )
% 5.02/5.33 | ( A
% 5.02/5.33 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_iff'
% 5.02/5.33 thf(fact_6653_abs__eq__iff_H,axiom,
% 5.02/5.33 ! [A: int,B: int] :
% 5.02/5.33 ( ( ( abs_abs_int @ A )
% 5.02/5.33 = B )
% 5.02/5.33 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.02/5.33 & ( ( A = B )
% 5.02/5.33 | ( A
% 5.02/5.33 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_eq_iff'
% 5.02/5.33 thf(fact_6654_zero__le__power__abs,axiom,
% 5.02/5.33 ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_le_power_abs
% 5.02/5.33 thf(fact_6655_zero__le__power__abs,axiom,
% 5.02/5.33 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_le_power_abs
% 5.02/5.33 thf(fact_6656_zero__le__power__abs,axiom,
% 5.02/5.33 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_le_power_abs
% 5.02/5.33 thf(fact_6657_zero__le__power__abs,axiom,
% 5.02/5.33 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % zero_le_power_abs
% 5.02/5.33 thf(fact_6658_abs__div__pos,axiom,
% 5.02/5.33 ! [Y: real,X2: real] :
% 5.02/5.33 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.02/5.33 => ( ( divide_divide_real @ ( abs_abs_real @ X2 ) @ Y )
% 5.02/5.33 = ( abs_abs_real @ ( divide_divide_real @ X2 @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_div_pos
% 5.02/5.33 thf(fact_6659_abs__div__pos,axiom,
% 5.02/5.33 ! [Y: rat,X2: rat] :
% 5.02/5.33 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.02/5.33 => ( ( divide_divide_rat @ ( abs_abs_rat @ X2 ) @ Y )
% 5.02/5.33 = ( abs_abs_rat @ ( divide_divide_rat @ X2 @ Y ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_div_pos
% 5.02/5.33 thf(fact_6660_abs__if__raw,axiom,
% 5.02/5.33 ( abs_abs_real
% 5.02/5.33 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_if_raw
% 5.02/5.33 thf(fact_6661_abs__if__raw,axiom,
% 5.02/5.33 ( abs_abs_int
% 5.02/5.33 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_if_raw
% 5.02/5.33 thf(fact_6662_abs__if__raw,axiom,
% 5.02/5.33 ( abs_abs_rat
% 5.02/5.33 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_if_raw
% 5.02/5.33 thf(fact_6663_abs__if__raw,axiom,
% 5.02/5.33 ( abs_abs_Code_integer
% 5.02/5.33 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_if_raw
% 5.02/5.33 thf(fact_6664_abs__of__neg,axiom,
% 5.02/5.33 ! [A: real] :
% 5.02/5.33 ( ( ord_less_real @ A @ zero_zero_real )
% 5.02/5.33 => ( ( abs_abs_real @ A )
% 5.02/5.33 = ( uminus_uminus_real @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_neg
% 5.02/5.33 thf(fact_6665_abs__of__neg,axiom,
% 5.02/5.33 ! [A: int] :
% 5.02/5.33 ( ( ord_less_int @ A @ zero_zero_int )
% 5.02/5.33 => ( ( abs_abs_int @ A )
% 5.02/5.33 = ( uminus_uminus_int @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_neg
% 5.02/5.33 thf(fact_6666_abs__of__neg,axiom,
% 5.02/5.33 ! [A: rat] :
% 5.02/5.33 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.02/5.33 => ( ( abs_abs_rat @ A )
% 5.02/5.33 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_neg
% 5.02/5.33 thf(fact_6667_abs__of__neg,axiom,
% 5.02/5.33 ! [A: code_integer] :
% 5.02/5.33 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.02/5.33 => ( ( abs_abs_Code_integer @ A )
% 5.02/5.33 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_of_neg
% 5.02/5.33 thf(fact_6668_abs__if,axiom,
% 5.02/5.33 ( abs_abs_real
% 5.02/5.33 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_if
% 5.02/5.33 thf(fact_6669_abs__if,axiom,
% 5.02/5.33 ( abs_abs_int
% 5.02/5.33 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_if
% 5.02/5.33 thf(fact_6670_abs__if,axiom,
% 5.02/5.33 ( abs_abs_rat
% 5.02/5.33 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_if
% 5.02/5.33 thf(fact_6671_abs__if,axiom,
% 5.02/5.33 ( abs_abs_Code_integer
% 5.02/5.33 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_if
% 5.02/5.33 thf(fact_6672_abs__diff__triangle__ineq,axiom,
% 5.02/5.33 ! [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 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_triangle_ineq
% 5.02/5.33 thf(fact_6673_abs__diff__triangle__ineq,axiom,
% 5.02/5.33 ! [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 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_triangle_ineq
% 5.02/5.33 thf(fact_6674_abs__diff__triangle__ineq,axiom,
% 5.02/5.33 ! [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 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_triangle_ineq
% 5.02/5.33 thf(fact_6675_abs__diff__triangle__ineq,axiom,
% 5.02/5.33 ! [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 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_triangle_ineq
% 5.02/5.33 thf(fact_6676_abs__triangle__ineq4,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq4
% 5.02/5.33 thf(fact_6677_abs__triangle__ineq4,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq4
% 5.02/5.33 thf(fact_6678_abs__triangle__ineq4,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq4
% 5.02/5.33 thf(fact_6679_abs__triangle__ineq4,axiom,
% 5.02/5.33 ! [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 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_triangle_ineq4
% 5.02/5.33 thf(fact_6680_abs__diff__le__iff,axiom,
% 5.02/5.33 ! [X2: code_integer,A: code_integer,R2: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R2 )
% 5.02/5.33 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X2 )
% 5.02/5.33 & ( ord_le3102999989581377725nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_le_iff
% 5.02/5.33 thf(fact_6681_abs__diff__le__iff,axiom,
% 5.02/5.33 ! [X2: real,A: real,R2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R2 )
% 5.02/5.33 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R2 ) @ X2 )
% 5.02/5.33 & ( ord_less_eq_real @ X2 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_le_iff
% 5.02/5.33 thf(fact_6682_abs__diff__le__iff,axiom,
% 5.02/5.33 ! [X2: rat,A: rat,R2: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R2 )
% 5.02/5.33 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R2 ) @ X2 )
% 5.02/5.33 & ( ord_less_eq_rat @ X2 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_le_iff
% 5.02/5.33 thf(fact_6683_abs__diff__le__iff,axiom,
% 5.02/5.33 ! [X2: int,A: int,R2: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R2 )
% 5.02/5.33 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R2 ) @ X2 )
% 5.02/5.33 & ( ord_less_eq_int @ X2 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_le_iff
% 5.02/5.33 thf(fact_6684_abs__diff__less__iff,axiom,
% 5.02/5.33 ! [X2: code_integer,A: code_integer,R2: code_integer] :
% 5.02/5.33 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X2 @ A ) ) @ R2 )
% 5.02/5.33 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R2 ) @ X2 )
% 5.02/5.33 & ( ord_le6747313008572928689nteger @ X2 @ ( plus_p5714425477246183910nteger @ A @ R2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_less_iff
% 5.02/5.33 thf(fact_6685_abs__diff__less__iff,axiom,
% 5.02/5.33 ! [X2: real,A: real,R2: real] :
% 5.02/5.33 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ A ) ) @ R2 )
% 5.02/5.33 = ( ( ord_less_real @ ( minus_minus_real @ A @ R2 ) @ X2 )
% 5.02/5.33 & ( ord_less_real @ X2 @ ( plus_plus_real @ A @ R2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_less_iff
% 5.02/5.33 thf(fact_6686_abs__diff__less__iff,axiom,
% 5.02/5.33 ! [X2: rat,A: rat,R2: rat] :
% 5.02/5.33 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ A ) ) @ R2 )
% 5.02/5.33 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R2 ) @ X2 )
% 5.02/5.33 & ( ord_less_rat @ X2 @ ( plus_plus_rat @ A @ R2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_less_iff
% 5.02/5.33 thf(fact_6687_abs__diff__less__iff,axiom,
% 5.02/5.33 ! [X2: int,A: int,R2: int] :
% 5.02/5.33 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ A ) ) @ R2 )
% 5.02/5.33 = ( ( ord_less_int @ ( minus_minus_int @ A @ R2 ) @ X2 )
% 5.02/5.33 & ( ord_less_int @ X2 @ ( plus_plus_int @ A @ R2 ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_diff_less_iff
% 5.02/5.33 thf(fact_6688_or__not__num__neg_Osimps_I9_J,axiom,
% 5.02/5.33 ! [N2: num,M: num] :
% 5.02/5.33 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit1 @ M ) )
% 5.02/5.33 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(9)
% 5.02/5.33 thf(fact_6689_abs__real__def,axiom,
% 5.02/5.33 ( abs_abs_real
% 5.02/5.33 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_real_def
% 5.02/5.33 thf(fact_6690_sin__bound__lemma,axiom,
% 5.02/5.33 ! [X2: real,Y: real,U: real,V: real] :
% 5.02/5.33 ( ( X2 = Y )
% 5.02/5.33 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.02/5.33 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X2 @ U ) @ Y ) ) @ V ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % sin_bound_lemma
% 5.02/5.33 thf(fact_6691_tanh__real__gt__neg1,axiom,
% 5.02/5.33 ! [X2: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X2 ) ) ).
% 5.02/5.33
% 5.02/5.33 % tanh_real_gt_neg1
% 5.02/5.33 thf(fact_6692_abs__add__one__gt__zero,axiom,
% 5.02/5.33 ! [X2: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_add_one_gt_zero
% 5.02/5.33 thf(fact_6693_abs__add__one__gt__zero,axiom,
% 5.02/5.33 ! [X2: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_add_one_gt_zero
% 5.02/5.33 thf(fact_6694_abs__add__one__gt__zero,axiom,
% 5.02/5.33 ! [X2: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_add_one_gt_zero
% 5.02/5.33 thf(fact_6695_abs__add__one__gt__zero,axiom,
% 5.02/5.33 ! [X2: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % abs_add_one_gt_zero
% 5.02/5.33 thf(fact_6696_or__not__num__neg_Osimps_I2_J,axiom,
% 5.02/5.33 ! [M: num] :
% 5.02/5.33 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.02/5.33 = ( bit1 @ M ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(2)
% 5.02/5.33 thf(fact_6697_of__int__leD,axiom,
% 5.02/5.33 ! [N2: int,X2: code_integer] :
% 5.02/5.33 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X2 )
% 5.02/5.33 => ( ( N2 = zero_zero_int )
% 5.02/5.33 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_leD
% 5.02/5.33 thf(fact_6698_of__int__leD,axiom,
% 5.02/5.33 ! [N2: int,X2: real] :
% 5.02/5.33 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X2 )
% 5.02/5.33 => ( ( N2 = zero_zero_int )
% 5.02/5.33 | ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_leD
% 5.02/5.33 thf(fact_6699_of__int__leD,axiom,
% 5.02/5.33 ! [N2: int,X2: rat] :
% 5.02/5.33 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X2 )
% 5.02/5.33 => ( ( N2 = zero_zero_int )
% 5.02/5.33 | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_leD
% 5.02/5.33 thf(fact_6700_of__int__leD,axiom,
% 5.02/5.33 ! [N2: int,X2: int] :
% 5.02/5.33 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X2 )
% 5.02/5.33 => ( ( N2 = zero_zero_int )
% 5.02/5.33 | ( ord_less_eq_int @ one_one_int @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_leD
% 5.02/5.33 thf(fact_6701_of__int__lessD,axiom,
% 5.02/5.33 ! [N2: int,X2: code_integer] :
% 5.02/5.33 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X2 )
% 5.02/5.33 => ( ( N2 = zero_zero_int )
% 5.02/5.33 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_lessD
% 5.02/5.33 thf(fact_6702_of__int__lessD,axiom,
% 5.02/5.33 ! [N2: int,X2: real] :
% 5.02/5.33 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X2 )
% 5.02/5.33 => ( ( N2 = zero_zero_int )
% 5.02/5.33 | ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_lessD
% 5.02/5.33 thf(fact_6703_of__int__lessD,axiom,
% 5.02/5.33 ! [N2: int,X2: rat] :
% 5.02/5.33 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X2 )
% 5.02/5.33 => ( ( N2 = zero_zero_int )
% 5.02/5.33 | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_lessD
% 5.02/5.33 thf(fact_6704_of__int__lessD,axiom,
% 5.02/5.33 ! [N2: int,X2: int] :
% 5.02/5.33 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X2 )
% 5.02/5.33 => ( ( N2 = zero_zero_int )
% 5.02/5.33 | ( ord_less_int @ one_one_int @ X2 ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % of_int_lessD
% 5.02/5.33 thf(fact_6705_or__not__num__neg_Osimps_I8_J,axiom,
% 5.02/5.33 ! [N2: num,M: num] :
% 5.02/5.33 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit0 @ M ) )
% 5.02/5.33 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % or_not_num_neg.simps(8)
% 5.02/5.33 thf(fact_6706_round__diff__minimal,axiom,
% 5.02/5.33 ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_diff_minimal
% 5.02/5.33 thf(fact_6707_round__diff__minimal,axiom,
% 5.02/5.33 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % round_diff_minimal
% 5.02/5.33 thf(fact_6708_bot__empty__eq2,axiom,
% 5.02/5.33 ( bot_bo4731626569425807221er_o_o
% 5.02/5.33 = ( ^ [X: code_integer,Y6: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y6 ) @ bot_bo5379713665208646970eger_o ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % bot_empty_eq2
% 5.02/5.33 thf(fact_6709_bot__empty__eq2,axiom,
% 5.02/5.33 ( bot_bot_num_num_o
% 5.02/5.33 = ( ^ [X: num,Y6: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y6 ) @ bot_bo9056780473022590049um_num ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % bot_empty_eq2
% 5.02/5.33 thf(fact_6710_bot__empty__eq2,axiom,
% 5.02/5.33 ( bot_bot_nat_num_o
% 5.02/5.33 = ( ^ [X: nat,Y6: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y6 ) @ bot_bo7038385379056416535at_num ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % bot_empty_eq2
% 5.02/5.33 thf(fact_6711_bot__empty__eq2,axiom,
% 5.02/5.33 ( bot_bot_nat_nat_o
% 5.02/5.33 = ( ^ [X: nat,Y6: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y6 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % bot_empty_eq2
% 5.02/5.33 thf(fact_6712_bot__empty__eq2,axiom,
% 5.02/5.33 ( bot_bot_int_int_o
% 5.02/5.33 = ( ^ [X: int,Y6: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y6 ) @ bot_bo1796632182523588997nt_int ) ) ) ).
% 5.02/5.33
% 5.02/5.33 % bot_empty_eq2
% 5.02/5.33 thf(fact_6713_pred__equals__eq2,axiom,
% 5.02/5.33 ! [R: set_Pr448751882837621926eger_o,S3: set_Pr448751882837621926eger_o] :
% 5.02/5.33 ( ( ( ^ [X: code_integer,Y6: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y6 ) @ R ) )
% 5.02/5.34 = ( ^ [X: code_integer,Y6: $o] : ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X @ Y6 ) @ S3 ) ) )
% 5.02/5.34 = ( R = S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_equals_eq2
% 5.02/5.34 thf(fact_6714_pred__equals__eq2,axiom,
% 5.02/5.34 ! [R: set_Pr8218934625190621173um_num,S3: set_Pr8218934625190621173um_num] :
% 5.02/5.34 ( ( ( ^ [X: num,Y6: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y6 ) @ R ) )
% 5.02/5.34 = ( ^ [X: num,Y6: num] : ( member7279096912039735102um_num @ ( product_Pair_num_num @ X @ Y6 ) @ S3 ) ) )
% 5.02/5.34 = ( R = S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_equals_eq2
% 5.02/5.34 thf(fact_6715_pred__equals__eq2,axiom,
% 5.02/5.34 ! [R: set_Pr6200539531224447659at_num,S3: set_Pr6200539531224447659at_num] :
% 5.02/5.34 ( ( ( ^ [X: nat,Y6: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y6 ) @ R ) )
% 5.02/5.34 = ( ^ [X: nat,Y6: num] : ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X @ Y6 ) @ S3 ) ) )
% 5.02/5.34 = ( R = S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_equals_eq2
% 5.02/5.34 thf(fact_6716_pred__equals__eq2,axiom,
% 5.02/5.34 ! [R: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat] :
% 5.02/5.34 ( ( ( ^ [X: nat,Y6: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y6 ) @ R ) )
% 5.02/5.34 = ( ^ [X: nat,Y6: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y6 ) @ S3 ) ) )
% 5.02/5.34 = ( R = S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_equals_eq2
% 5.02/5.34 thf(fact_6717_pred__equals__eq2,axiom,
% 5.02/5.34 ! [R: set_Pr958786334691620121nt_int,S3: set_Pr958786334691620121nt_int] :
% 5.02/5.34 ( ( ( ^ [X: int,Y6: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y6 ) @ R ) )
% 5.02/5.34 = ( ^ [X: int,Y6: int] : ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y6 ) @ S3 ) ) )
% 5.02/5.34 = ( R = S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_equals_eq2
% 5.02/5.34 thf(fact_6718_abs__le__square__iff,axiom,
% 5.02/5.34 ! [X2: code_integer,Y: code_integer] :
% 5.02/5.34 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ ( abs_abs_Code_integer @ Y ) )
% 5.02/5.34 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_le_square_iff
% 5.02/5.34 thf(fact_6719_abs__le__square__iff,axiom,
% 5.02/5.34 ! [X2: real,Y: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y ) )
% 5.02/5.34 = ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_le_square_iff
% 5.02/5.34 thf(fact_6720_abs__le__square__iff,axiom,
% 5.02/5.34 ! [X2: rat,Y: rat] :
% 5.02/5.34 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ ( abs_abs_rat @ Y ) )
% 5.02/5.34 = ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_le_square_iff
% 5.02/5.34 thf(fact_6721_abs__le__square__iff,axiom,
% 5.02/5.34 ! [X2: int,Y: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y ) )
% 5.02/5.34 = ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_le_square_iff
% 5.02/5.34 thf(fact_6722_abs__square__eq__1,axiom,
% 5.02/5.34 ! [X2: code_integer] :
% 5.02/5.34 ( ( ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.34 = one_one_Code_integer )
% 5.02/5.34 = ( ( abs_abs_Code_integer @ X2 )
% 5.02/5.34 = one_one_Code_integer ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_eq_1
% 5.02/5.34 thf(fact_6723_abs__square__eq__1,axiom,
% 5.02/5.34 ! [X2: rat] :
% 5.02/5.34 ( ( ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.34 = one_one_rat )
% 5.02/5.34 = ( ( abs_abs_rat @ X2 )
% 5.02/5.34 = one_one_rat ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_eq_1
% 5.02/5.34 thf(fact_6724_abs__square__eq__1,axiom,
% 5.02/5.34 ! [X2: int] :
% 5.02/5.34 ( ( ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.34 = one_one_int )
% 5.02/5.34 = ( ( abs_abs_int @ X2 )
% 5.02/5.34 = one_one_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_eq_1
% 5.02/5.34 thf(fact_6725_abs__square__eq__1,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.34 = one_one_real )
% 5.02/5.34 = ( ( abs_abs_real @ X2 )
% 5.02/5.34 = one_one_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_eq_1
% 5.02/5.34 thf(fact_6726_power__even__abs,axiom,
% 5.02/5.34 ! [N2: nat,A: code_integer] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 )
% 5.02/5.34 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power_even_abs
% 5.02/5.34 thf(fact_6727_power__even__abs,axiom,
% 5.02/5.34 ! [N2: nat,A: int] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N2 )
% 5.02/5.34 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power_even_abs
% 5.02/5.34 thf(fact_6728_power__even__abs,axiom,
% 5.02/5.34 ! [N2: nat,A: real] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N2 )
% 5.02/5.34 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power_even_abs
% 5.02/5.34 thf(fact_6729_or__not__num__neg_Oelims,axiom,
% 5.02/5.34 ! [X2: num,Xa2: num,Y: num] :
% 5.02/5.34 ( ( ( bit_or_not_num_neg @ X2 @ Xa2 )
% 5.02/5.34 = Y )
% 5.02/5.34 => ( ( ( X2 = one )
% 5.02/5.34 => ( ( Xa2 = one )
% 5.02/5.34 => ( Y != one ) ) )
% 5.02/5.34 => ( ( ( X2 = one )
% 5.02/5.34 => ! [M3: num] :
% 5.02/5.34 ( ( Xa2
% 5.02/5.34 = ( bit0 @ M3 ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 != ( bit1 @ M3 ) ) ) )
% 5.02/5.34 => ( ( ( X2 = one )
% 5.02/5.34 => ! [M3: num] :
% 5.02/5.34 ( ( Xa2
% 5.02/5.34 = ( bit1 @ M3 ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 != ( bit1 @ M3 ) ) ) )
% 5.02/5.34 => ( ( ? [N: num] :
% 5.02/5.34 ( X2
% 5.02/5.34 = ( bit0 @ N ) )
% 5.02/5.34 => ( ( Xa2 = one )
% 5.02/5.34 => ( Y
% 5.02/5.34 != ( bit0 @ one ) ) ) )
% 5.02/5.34 => ( ! [N: num] :
% 5.02/5.34 ( ( X2
% 5.02/5.34 = ( bit0 @ N ) )
% 5.02/5.34 => ! [M3: num] :
% 5.02/5.34 ( ( Xa2
% 5.02/5.34 = ( bit0 @ M3 ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 != ( bitM @ ( bit_or_not_num_neg @ N @ M3 ) ) ) ) )
% 5.02/5.34 => ( ! [N: num] :
% 5.02/5.34 ( ( X2
% 5.02/5.34 = ( bit0 @ N ) )
% 5.02/5.34 => ! [M3: num] :
% 5.02/5.34 ( ( Xa2
% 5.02/5.34 = ( bit1 @ M3 ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 != ( bit0 @ ( bit_or_not_num_neg @ N @ M3 ) ) ) ) )
% 5.02/5.34 => ( ( ? [N: num] :
% 5.02/5.34 ( X2
% 5.02/5.34 = ( bit1 @ N ) )
% 5.02/5.34 => ( ( Xa2 = one )
% 5.02/5.34 => ( Y != one ) ) )
% 5.02/5.34 => ( ! [N: num] :
% 5.02/5.34 ( ( X2
% 5.02/5.34 = ( bit1 @ N ) )
% 5.02/5.34 => ! [M3: num] :
% 5.02/5.34 ( ( Xa2
% 5.02/5.34 = ( bit0 @ M3 ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 != ( bitM @ ( bit_or_not_num_neg @ N @ M3 ) ) ) ) )
% 5.02/5.34 => ~ ! [N: num] :
% 5.02/5.34 ( ( X2
% 5.02/5.34 = ( bit1 @ N ) )
% 5.02/5.34 => ! [M3: num] :
% 5.02/5.34 ( ( Xa2
% 5.02/5.34 = ( bit1 @ M3 ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 != ( bitM @ ( bit_or_not_num_neg @ N @ M3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % or_not_num_neg.elims
% 5.02/5.34 thf(fact_6730_power2__le__iff__abs__le,axiom,
% 5.02/5.34 ! [Y: code_integer,X2: code_integer] :
% 5.02/5.34 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.02/5.34 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.34 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power2_le_iff_abs_le
% 5.02/5.34 thf(fact_6731_power2__le__iff__abs__le,axiom,
% 5.02/5.34 ! [Y: real,X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.34 => ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.34 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power2_le_iff_abs_le
% 5.02/5.34 thf(fact_6732_power2__le__iff__abs__le,axiom,
% 5.02/5.34 ! [Y: rat,X2: rat] :
% 5.02/5.34 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.02/5.34 => ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.34 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power2_le_iff_abs_le
% 5.02/5.34 thf(fact_6733_power2__le__iff__abs__le,axiom,
% 5.02/5.34 ! [Y: int,X2: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.34 => ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.34 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power2_le_iff_abs_le
% 5.02/5.34 thf(fact_6734_abs__square__le__1,axiom,
% 5.02/5.34 ! [X2: code_integer] :
% 5.02/5.34 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.02/5.34 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_le_1
% 5.02/5.34 thf(fact_6735_abs__square__le__1,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.02/5.34 = ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_le_1
% 5.02/5.34 thf(fact_6736_abs__square__le__1,axiom,
% 5.02/5.34 ! [X2: rat] :
% 5.02/5.34 ( ( ord_less_eq_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.02/5.34 = ( ord_less_eq_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_le_1
% 5.02/5.34 thf(fact_6737_abs__square__le__1,axiom,
% 5.02/5.34 ! [X2: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.02/5.34 = ( ord_less_eq_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_le_1
% 5.02/5.34 thf(fact_6738_abs__square__less__1,axiom,
% 5.02/5.34 ! [X2: code_integer] :
% 5.02/5.34 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.02/5.34 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X2 ) @ one_one_Code_integer ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_less_1
% 5.02/5.34 thf(fact_6739_abs__square__less__1,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.02/5.34 = ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_less_1
% 5.02/5.34 thf(fact_6740_abs__square__less__1,axiom,
% 5.02/5.34 ! [X2: rat] :
% 5.02/5.34 ( ( ord_less_rat @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.02/5.34 = ( ord_less_rat @ ( abs_abs_rat @ X2 ) @ one_one_rat ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_less_1
% 5.02/5.34 thf(fact_6741_abs__square__less__1,axiom,
% 5.02/5.34 ! [X2: int] :
% 5.02/5.34 ( ( ord_less_int @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.02/5.34 = ( ord_less_int @ ( abs_abs_int @ X2 ) @ one_one_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_square_less_1
% 5.02/5.34 thf(fact_6742_power__mono__even,axiom,
% 5.02/5.34 ! [N2: nat,A: code_integer,B: code_integer] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power_mono_even
% 5.02/5.34 thf(fact_6743_power__mono__even,axiom,
% 5.02/5.34 ! [N2: nat,A: real,B: real] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.02/5.34 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power_mono_even
% 5.02/5.34 thf(fact_6744_power__mono__even,axiom,
% 5.02/5.34 ! [N2: nat,A: rat,B: rat] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power_mono_even
% 5.02/5.34 thf(fact_6745_power__mono__even,axiom,
% 5.02/5.34 ! [N2: nat,A: int,B: int] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.02/5.34 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % power_mono_even
% 5.02/5.34 thf(fact_6746_sqrt__ge__absD,axiom,
% 5.02/5.34 ! [X2: real,Y: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ Y ) )
% 5.02/5.34 => ( ord_less_eq_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 5.02/5.34
% 5.02/5.34 % sqrt_ge_absD
% 5.02/5.34 thf(fact_6747_real__sqrt__ge__abs1,axiom,
% 5.02/5.34 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % real_sqrt_ge_abs1
% 5.02/5.34 thf(fact_6748_real__sqrt__ge__abs2,axiom,
% 5.02/5.34 ! [Y: real,X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % real_sqrt_ge_abs2
% 5.02/5.34 thf(fact_6749_sqrt__sum__squares__le__sum__abs,axiom,
% 5.02/5.34 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sqrt_sum_squares_le_sum_abs
% 5.02/5.34 thf(fact_6750_subrelI,axiom,
% 5.02/5.34 ! [R2: set_Pr448751882837621926eger_o,S2: set_Pr448751882837621926eger_o] :
% 5.02/5.34 ( ! [X5: code_integer,Y3: $o] :
% 5.02/5.34 ( ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X5 @ Y3 ) @ R2 )
% 5.02/5.34 => ( member1379723562493234055eger_o @ ( produc6677183202524767010eger_o @ X5 @ Y3 ) @ S2 ) )
% 5.02/5.34 => ( ord_le8980329558974975238eger_o @ R2 @ S2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % subrelI
% 5.02/5.34 thf(fact_6751_subrelI,axiom,
% 5.02/5.34 ! [R2: set_Pr8218934625190621173um_num,S2: set_Pr8218934625190621173um_num] :
% 5.02/5.34 ( ! [X5: num,Y3: num] :
% 5.02/5.34 ( ( member7279096912039735102um_num @ ( product_Pair_num_num @ X5 @ Y3 ) @ R2 )
% 5.02/5.34 => ( member7279096912039735102um_num @ ( product_Pair_num_num @ X5 @ Y3 ) @ S2 ) )
% 5.02/5.34 => ( ord_le880128212290418581um_num @ R2 @ S2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % subrelI
% 5.02/5.34 thf(fact_6752_subrelI,axiom,
% 5.02/5.34 ! [R2: set_Pr6200539531224447659at_num,S2: set_Pr6200539531224447659at_num] :
% 5.02/5.34 ( ! [X5: nat,Y3: num] :
% 5.02/5.34 ( ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X5 @ Y3 ) @ R2 )
% 5.02/5.34 => ( member9148766508732265716at_num @ ( product_Pair_nat_num @ X5 @ Y3 ) @ S2 ) )
% 5.02/5.34 => ( ord_le8085105155179020875at_num @ R2 @ S2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % subrelI
% 5.02/5.34 thf(fact_6753_subrelI,axiom,
% 5.02/5.34 ! [R2: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 5.02/5.34 ( ! [X5: nat,Y3: nat] :
% 5.02/5.34 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X5 @ Y3 ) @ R2 )
% 5.02/5.34 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X5 @ Y3 ) @ S2 ) )
% 5.02/5.34 => ( ord_le3146513528884898305at_nat @ R2 @ S2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % subrelI
% 5.02/5.34 thf(fact_6754_subrelI,axiom,
% 5.02/5.34 ! [R2: set_Pr958786334691620121nt_int,S2: set_Pr958786334691620121nt_int] :
% 5.02/5.34 ( ! [X5: int,Y3: int] :
% 5.02/5.34 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X5 @ Y3 ) @ R2 )
% 5.02/5.34 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X5 @ Y3 ) @ S2 ) )
% 5.02/5.34 => ( ord_le2843351958646193337nt_int @ R2 @ S2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % subrelI
% 5.02/5.34 thf(fact_6755_or__Suc__0__eq,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.02/5.34 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % or_Suc_0_eq
% 5.02/5.34 thf(fact_6756_Suc__0__or__eq,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.02/5.34 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % Suc_0_or_eq
% 5.02/5.34 thf(fact_6757_or__nat__rec,axiom,
% 5.02/5.34 ( bit_se1412395901928357646or_nat
% 5.02/5.34 = ( ^ [M6: nat,N3: nat] :
% 5.02/5.34 ( plus_plus_nat
% 5.02/5.34 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.34 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.02/5.34 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.02/5.34 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % or_nat_rec
% 5.02/5.34 thf(fact_6758_or__nat__unfold,axiom,
% 5.02/5.34 ( bit_se1412395901928357646or_nat
% 5.02/5.34 = ( ^ [M6: nat,N3: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % or_nat_unfold
% 5.02/5.34 thf(fact_6759_of__int__round__abs__le,axiom,
% 5.02/5.34 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X2 ) ) @ X2 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_round_abs_le
% 5.02/5.34 thf(fact_6760_of__int__round__abs__le,axiom,
% 5.02/5.34 ! [X2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X2 ) ) @ X2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_round_abs_le
% 5.02/5.34 thf(fact_6761_round__unique_H,axiom,
% 5.02/5.34 ! [X2: real,N2: int] :
% 5.02/5.34 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X2 @ ( ring_1_of_int_real @ N2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.34 => ( ( archim8280529875227126926d_real @ X2 )
% 5.02/5.34 = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % round_unique'
% 5.02/5.34 thf(fact_6762_round__unique_H,axiom,
% 5.02/5.34 ! [X2: rat,N2: int] :
% 5.02/5.34 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X2 @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.02/5.34 => ( ( archim7778729529865785530nd_rat @ X2 )
% 5.02/5.34 = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % round_unique'
% 5.02/5.34 thf(fact_6763_cos__x__y__le__one,axiom,
% 5.02/5.34 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.02/5.34
% 5.02/5.34 % cos_x_y_le_one
% 5.02/5.34 thf(fact_6764_real__sqrt__sum__squares__less,axiom,
% 5.02/5.34 ! [X2: real,U: real,Y: real] :
% 5.02/5.34 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.02/5.34 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.02/5.34 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % real_sqrt_sum_squares_less
% 5.02/5.34 thf(fact_6765_pred__subset__eq,axiom,
% 5.02/5.34 ! [R: set_complex,S3: set_complex] :
% 5.02/5.34 ( ( ord_le4573692005234683329plex_o
% 5.02/5.34 @ ^ [X: complex] : ( member_complex @ X @ R )
% 5.02/5.34 @ ^ [X: complex] : ( member_complex @ X @ S3 ) )
% 5.02/5.34 = ( ord_le211207098394363844omplex @ R @ S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_subset_eq
% 5.02/5.34 thf(fact_6766_pred__subset__eq,axiom,
% 5.02/5.34 ! [R: set_real,S3: set_real] :
% 5.02/5.34 ( ( ord_less_eq_real_o
% 5.02/5.34 @ ^ [X: real] : ( member_real @ X @ R )
% 5.02/5.34 @ ^ [X: real] : ( member_real @ X @ S3 ) )
% 5.02/5.34 = ( ord_less_eq_set_real @ R @ S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_subset_eq
% 5.02/5.34 thf(fact_6767_pred__subset__eq,axiom,
% 5.02/5.34 ! [R: set_set_nat,S3: set_set_nat] :
% 5.02/5.34 ( ( ord_le3964352015994296041_nat_o
% 5.02/5.34 @ ^ [X: set_nat] : ( member_set_nat @ X @ R )
% 5.02/5.34 @ ^ [X: set_nat] : ( member_set_nat @ X @ S3 ) )
% 5.02/5.34 = ( ord_le6893508408891458716et_nat @ R @ S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_subset_eq
% 5.02/5.34 thf(fact_6768_pred__subset__eq,axiom,
% 5.02/5.34 ! [R: set_int,S3: set_int] :
% 5.02/5.34 ( ( ord_less_eq_int_o
% 5.02/5.34 @ ^ [X: int] : ( member_int @ X @ R )
% 5.02/5.34 @ ^ [X: int] : ( member_int @ X @ S3 ) )
% 5.02/5.34 = ( ord_less_eq_set_int @ R @ S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_subset_eq
% 5.02/5.34 thf(fact_6769_pred__subset__eq,axiom,
% 5.02/5.34 ! [R: set_nat,S3: set_nat] :
% 5.02/5.34 ( ( ord_less_eq_nat_o
% 5.02/5.34 @ ^ [X: nat] : ( member_nat @ X @ R )
% 5.02/5.34 @ ^ [X: nat] : ( member_nat @ X @ S3 ) )
% 5.02/5.34 = ( ord_less_eq_set_nat @ R @ S3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % pred_subset_eq
% 5.02/5.34 thf(fact_6770_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.34 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.34 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X2 ) ) @ X2 ) ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.02/5.34 thf(fact_6771_abs__sqrt__wlog,axiom,
% 5.02/5.34 ! [P: code_integer > code_integer > $o,X2: code_integer] :
% 5.02/5.34 ( ! [X5: code_integer] :
% 5.02/5.34 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X5 )
% 5.02/5.34 => ( P @ X5 @ ( power_8256067586552552935nteger @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.34 => ( P @ ( abs_abs_Code_integer @ X2 ) @ ( power_8256067586552552935nteger @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_sqrt_wlog
% 5.02/5.34 thf(fact_6772_abs__sqrt__wlog,axiom,
% 5.02/5.34 ! [P: real > real > $o,X2: real] :
% 5.02/5.34 ( ! [X5: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.02/5.34 => ( P @ X5 @ ( power_power_real @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.34 => ( P @ ( abs_abs_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_sqrt_wlog
% 5.02/5.34 thf(fact_6773_abs__sqrt__wlog,axiom,
% 5.02/5.34 ! [P: rat > rat > $o,X2: rat] :
% 5.02/5.34 ( ! [X5: rat] :
% 5.02/5.34 ( ( ord_less_eq_rat @ zero_zero_rat @ X5 )
% 5.02/5.34 => ( P @ X5 @ ( power_power_rat @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.34 => ( P @ ( abs_abs_rat @ X2 ) @ ( power_power_rat @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_sqrt_wlog
% 5.02/5.34 thf(fact_6774_abs__sqrt__wlog,axiom,
% 5.02/5.34 ! [P: int > int > $o,X2: int] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.02/5.34 => ( P @ X5 @ ( power_power_int @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.34 => ( P @ ( abs_abs_int @ X2 ) @ ( power_power_int @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_sqrt_wlog
% 5.02/5.34 thf(fact_6775_arctan__double,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.34 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X2 ) )
% 5.02/5.34 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % arctan_double
% 5.02/5.34 thf(fact_6776_arctan__half,axiom,
% 5.02/5.34 ( arctan
% 5.02/5.34 = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % arctan_half
% 5.02/5.34 thf(fact_6777_int__ge__less__than__def,axiom,
% 5.02/5.34 ( int_ge_less_than
% 5.02/5.34 = ( ^ [D2: int] :
% 5.02/5.34 ( collec213857154873943460nt_int
% 5.02/5.34 @ ( produc4947309494688390418_int_o
% 5.02/5.34 @ ^ [Z5: int,Z6: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ D2 @ Z5 )
% 5.02/5.34 & ( ord_less_int @ Z5 @ Z6 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % int_ge_less_than_def
% 5.02/5.34 thf(fact_6778_int__ge__less__than2__def,axiom,
% 5.02/5.34 ( int_ge_less_than2
% 5.02/5.34 = ( ^ [D2: int] :
% 5.02/5.34 ( collec213857154873943460nt_int
% 5.02/5.34 @ ( produc4947309494688390418_int_o
% 5.02/5.34 @ ^ [Z5: int,Z6: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ D2 @ Z6 )
% 5.02/5.34 & ( ord_less_int @ Z5 @ Z6 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % int_ge_less_than2_def
% 5.02/5.34 thf(fact_6779_signed__take__bit__eq__take__bit__minus,axiom,
% 5.02/5.34 ( bit_ri631733984087533419it_int
% 5.02/5.34 = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N3 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N3 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % signed_take_bit_eq_take_bit_minus
% 5.02/5.34 thf(fact_6780_bit__0__eq,axiom,
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ zero_zero_int )
% 5.02/5.34 = bot_bot_nat_o ) ).
% 5.02/5.34
% 5.02/5.34 % bit_0_eq
% 5.02/5.34 thf(fact_6781_bit__0__eq,axiom,
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ zero_zero_nat )
% 5.02/5.34 = bot_bot_nat_o ) ).
% 5.02/5.34
% 5.02/5.34 % bit_0_eq
% 5.02/5.34 thf(fact_6782_zdvd1__eq,axiom,
% 5.02/5.34 ! [X2: int] :
% 5.02/5.34 ( ( dvd_dvd_int @ X2 @ one_one_int )
% 5.02/5.34 = ( ( abs_abs_int @ X2 )
% 5.02/5.34 = one_one_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % zdvd1_eq
% 5.02/5.34 thf(fact_6783_bit__numeral__Bit0__Suc__iff,axiom,
% 5.02/5.34 ! [M: num,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_Bit0_Suc_iff
% 5.02/5.34 thf(fact_6784_bit__numeral__Bit0__Suc__iff,axiom,
% 5.02/5.34 ! [M: num,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_Bit0_Suc_iff
% 5.02/5.34 thf(fact_6785_bit__numeral__Bit1__Suc__iff,axiom,
% 5.02/5.34 ! [M: num,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_Bit1_Suc_iff
% 5.02/5.34 thf(fact_6786_bit__numeral__Bit1__Suc__iff,axiom,
% 5.02/5.34 ! [M: num,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_Bit1_Suc_iff
% 5.02/5.34 thf(fact_6787_zabs__less__one__iff,axiom,
% 5.02/5.34 ! [Z: int] :
% 5.02/5.34 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.02/5.34 = ( Z = zero_zero_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % zabs_less_one_iff
% 5.02/5.34 thf(fact_6788_signed__take__bit__nonnegative__iff,axiom,
% 5.02/5.34 ! [N2: nat,K: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.02/5.34 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % signed_take_bit_nonnegative_iff
% 5.02/5.34 thf(fact_6789_signed__take__bit__negative__iff,axiom,
% 5.02/5.34 ! [N2: nat,K: int] :
% 5.02/5.34 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % signed_take_bit_negative_iff
% 5.02/5.34 thf(fact_6790_bit__numeral__simps_I2_J,axiom,
% 5.02/5.34 ! [W: num,N2: num] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_simps(2)
% 5.02/5.34 thf(fact_6791_bit__numeral__simps_I2_J,axiom,
% 5.02/5.34 ! [W: num,N2: num] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_simps(2)
% 5.02/5.34 thf(fact_6792_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.02/5.34 ! [W: num,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_minus_numeral_Bit0_Suc_iff
% 5.02/5.34 thf(fact_6793_bit__numeral__simps_I3_J,axiom,
% 5.02/5.34 ! [W: num,N2: num] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_simps(3)
% 5.02/5.34 thf(fact_6794_bit__numeral__simps_I3_J,axiom,
% 5.02/5.34 ! [W: num,N2: num] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_simps(3)
% 5.02/5.34 thf(fact_6795_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.02/5.34 ! [W: num,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N2 ) )
% 5.02/5.34 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_minus_numeral_Bit1_Suc_iff
% 5.02/5.34 thf(fact_6796_bit__0,axiom,
% 5.02/5.34 ! [A: code_integer] :
% 5.02/5.34 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.02/5.34 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_0
% 5.02/5.34 thf(fact_6797_bit__0,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.02/5.34 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_0
% 5.02/5.34 thf(fact_6798_bit__0,axiom,
% 5.02/5.34 ! [A: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.02/5.34 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_0
% 5.02/5.34 thf(fact_6799_bit__minus__numeral__int_I1_J,axiom,
% 5.02/5.34 ! [W: num,N2: num] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_minus_numeral_int(1)
% 5.02/5.34 thf(fact_6800_bit__minus__numeral__int_I2_J,axiom,
% 5.02/5.34 ! [W: num,N2: num] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_minus_numeral_int(2)
% 5.02/5.34 thf(fact_6801_bit__mod__2__iff,axiom,
% 5.02/5.34 ! [A: code_integer,N2: nat] :
% 5.02/5.34 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 )
% 5.02/5.34 = ( ( N2 = zero_zero_nat )
% 5.02/5.34 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_mod_2_iff
% 5.02/5.34 thf(fact_6802_bit__mod__2__iff,axiom,
% 5.02/5.34 ! [A: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 )
% 5.02/5.34 = ( ( N2 = zero_zero_nat )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_mod_2_iff
% 5.02/5.34 thf(fact_6803_bit__mod__2__iff,axiom,
% 5.02/5.34 ! [A: nat,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 5.02/5.34 = ( ( N2 = zero_zero_nat )
% 5.02/5.34 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_mod_2_iff
% 5.02/5.34 thf(fact_6804_bit__numeral__iff,axiom,
% 5.02/5.34 ! [M: num,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 )
% 5.02/5.34 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_iff
% 5.02/5.34 thf(fact_6805_bit__numeral__iff,axiom,
% 5.02/5.34 ! [M: num,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 )
% 5.02/5.34 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_iff
% 5.02/5.34 thf(fact_6806_bit__disjunctive__add__iff,axiom,
% 5.02/5.34 ! [A: int,B: int,N2: nat] :
% 5.02/5.34 ( ! [N: nat] :
% 5.02/5.34 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 5.02/5.34 | ~ ( bit_se1146084159140164899it_int @ B @ N ) )
% 5.02/5.34 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.02/5.34 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.02/5.34 | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_disjunctive_add_iff
% 5.02/5.34 thf(fact_6807_bit__disjunctive__add__iff,axiom,
% 5.02/5.34 ! [A: nat,B: nat,N2: nat] :
% 5.02/5.34 ( ! [N: nat] :
% 5.02/5.34 ( ~ ( bit_se1148574629649215175it_nat @ A @ N )
% 5.02/5.34 | ~ ( bit_se1148574629649215175it_nat @ B @ N ) )
% 5.02/5.34 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.02/5.34 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.02/5.34 | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_disjunctive_add_iff
% 5.02/5.34 thf(fact_6808_bit__or__iff,axiom,
% 5.02/5.34 ! [A: int,B: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ A @ B ) @ N2 )
% 5.02/5.34 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.02/5.34 | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_or_iff
% 5.02/5.34 thf(fact_6809_bit__or__iff,axiom,
% 5.02/5.34 ! [A: nat,B: nat,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( bit_se1412395901928357646or_nat @ A @ B ) @ N2 )
% 5.02/5.34 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.02/5.34 | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_or_iff
% 5.02/5.34 thf(fact_6810_zdvd__antisym__abs,axiom,
% 5.02/5.34 ! [A: int,B: int] :
% 5.02/5.34 ( ( dvd_dvd_int @ A @ B )
% 5.02/5.34 => ( ( dvd_dvd_int @ B @ A )
% 5.02/5.34 => ( ( abs_abs_int @ A )
% 5.02/5.34 = ( abs_abs_int @ B ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % zdvd_antisym_abs
% 5.02/5.34 thf(fact_6811_bit__unset__bit__iff,axiom,
% 5.02/5.34 ! [M: nat,A: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N2 )
% 5.02/5.34 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.02/5.34 & ( M != N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_unset_bit_iff
% 5.02/5.34 thf(fact_6812_bit__unset__bit__iff,axiom,
% 5.02/5.34 ! [M: nat,A: nat,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N2 )
% 5.02/5.34 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.02/5.34 & ( M != N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_unset_bit_iff
% 5.02/5.34 thf(fact_6813_bit__or__int__iff,axiom,
% 5.02/5.34 ! [K: int,L: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N2 )
% 5.02/5.34 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.02/5.34 | ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_or_int_iff
% 5.02/5.34 thf(fact_6814_not__bit__1__Suc,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % not_bit_1_Suc
% 5.02/5.34 thf(fact_6815_not__bit__1__Suc,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % not_bit_1_Suc
% 5.02/5.34 thf(fact_6816_bit__1__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ one_one_int @ N2 )
% 5.02/5.34 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_1_iff
% 5.02/5.34 thf(fact_6817_bit__1__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N2 )
% 5.02/5.34 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_1_iff
% 5.02/5.34 thf(fact_6818_bit__numeral__simps_I1_J,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_simps(1)
% 5.02/5.34 thf(fact_6819_bit__numeral__simps_I1_J,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_numeral_simps(1)
% 5.02/5.34 thf(fact_6820_disjunctive__add,axiom,
% 5.02/5.34 ! [A: int,B: int] :
% 5.02/5.34 ( ! [N: nat] :
% 5.02/5.34 ( ~ ( bit_se1146084159140164899it_int @ A @ N )
% 5.02/5.34 | ~ ( bit_se1146084159140164899it_int @ B @ N ) )
% 5.02/5.34 => ( ( plus_plus_int @ A @ B )
% 5.02/5.34 = ( bit_se1409905431419307370or_int @ A @ B ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % disjunctive_add
% 5.02/5.34 thf(fact_6821_disjunctive__add,axiom,
% 5.02/5.34 ! [A: nat,B: nat] :
% 5.02/5.34 ( ! [N: nat] :
% 5.02/5.34 ( ~ ( bit_se1148574629649215175it_nat @ A @ N )
% 5.02/5.34 | ~ ( bit_se1148574629649215175it_nat @ B @ N ) )
% 5.02/5.34 => ( ( plus_plus_nat @ A @ B )
% 5.02/5.34 = ( bit_se1412395901928357646or_nat @ A @ B ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % disjunctive_add
% 5.02/5.34 thf(fact_6822_bit__take__bit__iff,axiom,
% 5.02/5.34 ! [M: nat,A: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N2 )
% 5.02/5.34 = ( ( ord_less_nat @ N2 @ M )
% 5.02/5.34 & ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_take_bit_iff
% 5.02/5.34 thf(fact_6823_bit__take__bit__iff,axiom,
% 5.02/5.34 ! [M: nat,A: nat,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N2 )
% 5.02/5.34 = ( ( ord_less_nat @ N2 @ M )
% 5.02/5.34 & ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_take_bit_iff
% 5.02/5.34 thf(fact_6824_bit__of__bool__iff,axiom,
% 5.02/5.34 ! [B: $o,N2: nat] :
% 5.02/5.34 ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N2 )
% 5.02/5.34 = ( B
% 5.02/5.34 & ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_of_bool_iff
% 5.02/5.34 thf(fact_6825_bit__of__bool__iff,axiom,
% 5.02/5.34 ! [B: $o,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N2 )
% 5.02/5.34 = ( B
% 5.02/5.34 & ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_of_bool_iff
% 5.02/5.34 thf(fact_6826_bit__of__bool__iff,axiom,
% 5.02/5.34 ! [B: $o,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N2 )
% 5.02/5.34 = ( B
% 5.02/5.34 & ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_of_bool_iff
% 5.02/5.34 thf(fact_6827_signed__take__bit__eq__if__positive,axiom,
% 5.02/5.34 ! [A: int,N2: nat] :
% 5.02/5.34 ( ~ ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.02/5.34 => ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 5.02/5.34 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % signed_take_bit_eq_if_positive
% 5.02/5.34 thf(fact_6828_abs__zmult__eq__1,axiom,
% 5.02/5.34 ! [M: int,N2: int] :
% 5.02/5.34 ( ( ( abs_abs_int @ ( times_times_int @ M @ N2 ) )
% 5.02/5.34 = one_one_int )
% 5.02/5.34 => ( ( abs_abs_int @ M )
% 5.02/5.34 = one_one_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_zmult_eq_1
% 5.02/5.34 thf(fact_6829_abs__div,axiom,
% 5.02/5.34 ! [Y: int,X2: int] :
% 5.02/5.34 ( ( dvd_dvd_int @ Y @ X2 )
% 5.02/5.34 => ( ( abs_abs_int @ ( divide_divide_int @ X2 @ Y ) )
% 5.02/5.34 = ( divide_divide_int @ ( abs_abs_int @ X2 ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_div
% 5.02/5.34 thf(fact_6830_bit__not__int__iff_H,axiom,
% 5.02/5.34 ! [K: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N2 )
% 5.02/5.34 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_not_int_iff'
% 5.02/5.34 thf(fact_6831_zabs__def,axiom,
% 5.02/5.34 ( abs_abs_int
% 5.02/5.34 = ( ^ [I5: int] : ( if_int @ ( ord_less_int @ I5 @ zero_zero_int ) @ ( uminus_uminus_int @ I5 ) @ I5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % zabs_def
% 5.02/5.34 thf(fact_6832_dvd__imp__le__int,axiom,
% 5.02/5.34 ! [I3: int,D: int] :
% 5.02/5.34 ( ( I3 != zero_zero_int )
% 5.02/5.34 => ( ( dvd_dvd_int @ D @ I3 )
% 5.02/5.34 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % dvd_imp_le_int
% 5.02/5.34 thf(fact_6833_abs__mod__less,axiom,
% 5.02/5.34 ! [L: int,K: int] :
% 5.02/5.34 ( ( L != zero_zero_int )
% 5.02/5.34 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_mod_less
% 5.02/5.34 thf(fact_6834_flip__bit__eq__if,axiom,
% 5.02/5.34 ( bit_se2159334234014336723it_int
% 5.02/5.34 = ( ^ [N3: nat,A5: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A5 @ N3 ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N3 @ A5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % flip_bit_eq_if
% 5.02/5.34 thf(fact_6835_flip__bit__eq__if,axiom,
% 5.02/5.34 ( bit_se2161824704523386999it_nat
% 5.02/5.34 = ( ^ [N3: nat,A5: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A5 @ N3 ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N3 @ A5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % flip_bit_eq_if
% 5.02/5.34 thf(fact_6836_bit__imp__take__bit__positive,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,K: int] :
% 5.02/5.34 ( ( ord_less_nat @ N2 @ M )
% 5.02/5.34 => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.02/5.34 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_imp_take_bit_positive
% 5.02/5.34 thf(fact_6837_bit__concat__bit__iff,axiom,
% 5.02/5.34 ! [M: nat,K: int,L: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N2 )
% 5.02/5.34 = ( ( ( ord_less_nat @ N2 @ M )
% 5.02/5.34 & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 5.02/5.34 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_concat_bit_iff
% 5.02/5.34 thf(fact_6838_zdvd__mult__cancel1,axiom,
% 5.02/5.34 ! [M: int,N2: int] :
% 5.02/5.34 ( ( M != zero_zero_int )
% 5.02/5.34 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N2 ) @ M )
% 5.02/5.34 = ( ( abs_abs_int @ N2 )
% 5.02/5.34 = one_one_int ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % zdvd_mult_cancel1
% 5.02/5.34 thf(fact_6839_signed__take__bit__eq__concat__bit,axiom,
% 5.02/5.34 ( bit_ri631733984087533419it_int
% 5.02/5.34 = ( ^ [N3: nat,K3: int] : ( bit_concat_bit @ N3 @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % signed_take_bit_eq_concat_bit
% 5.02/5.34 thf(fact_6840_exp__eq__0__imp__not__bit,axiom,
% 5.02/5.34 ! [N2: nat,A: int] :
% 5.02/5.34 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 = zero_zero_int )
% 5.02/5.34 => ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_eq_0_imp_not_bit
% 5.02/5.34 thf(fact_6841_exp__eq__0__imp__not__bit,axiom,
% 5.02/5.34 ! [N2: nat,A: nat] :
% 5.02/5.34 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 = zero_zero_nat )
% 5.02/5.34 => ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_eq_0_imp_not_bit
% 5.02/5.34 thf(fact_6842_bit__Suc,axiom,
% 5.02/5.34 ! [A: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_Suc
% 5.02/5.34 thf(fact_6843_bit__Suc,axiom,
% 5.02/5.34 ! [A: nat,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_Suc
% 5.02/5.34 thf(fact_6844_bit__iff__idd__imp__stable,axiom,
% 5.02/5.34 ! [A: code_integer] :
% 5.02/5.34 ( ! [N: nat] :
% 5.02/5.34 ( ( bit_se9216721137139052372nteger @ A @ N )
% 5.02/5.34 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.02/5.34 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.34 = A ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_iff_idd_imp_stable
% 5.02/5.34 thf(fact_6845_bit__iff__idd__imp__stable,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ! [N: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ A @ N )
% 5.02/5.34 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.02/5.34 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.34 = A ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_iff_idd_imp_stable
% 5.02/5.34 thf(fact_6846_bit__iff__idd__imp__stable,axiom,
% 5.02/5.34 ! [A: nat] :
% 5.02/5.34 ( ! [N: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ A @ N )
% 5.02/5.34 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.02/5.34 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.34 = A ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_iff_idd_imp_stable
% 5.02/5.34 thf(fact_6847_stable__imp__bit__iff__odd,axiom,
% 5.02/5.34 ! [A: code_integer,N2: nat] :
% 5.02/5.34 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.34 = A )
% 5.02/5.34 => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.02/5.34 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % stable_imp_bit_iff_odd
% 5.02/5.34 thf(fact_6848_stable__imp__bit__iff__odd,axiom,
% 5.02/5.34 ! [A: int,N2: nat] :
% 5.02/5.34 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.34 = A )
% 5.02/5.34 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.02/5.34 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % stable_imp_bit_iff_odd
% 5.02/5.34 thf(fact_6849_stable__imp__bit__iff__odd,axiom,
% 5.02/5.34 ! [A: nat,N2: nat] :
% 5.02/5.34 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.34 = A )
% 5.02/5.34 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.02/5.34 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % stable_imp_bit_iff_odd
% 5.02/5.34 thf(fact_6850_int__bit__bound,axiom,
% 5.02/5.34 ! [K: int] :
% 5.02/5.34 ~ ! [N: nat] :
% 5.02/5.34 ( ! [M2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ N @ M2 )
% 5.02/5.34 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.02/5.34 = ( bit_se1146084159140164899it_int @ K @ N ) ) )
% 5.02/5.34 => ~ ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.02/5.34 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.02/5.34 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % int_bit_bound
% 5.02/5.34 thf(fact_6851_even__add__abs__iff,axiom,
% 5.02/5.34 ! [K: int,L: int] :
% 5.02/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 5.02/5.34 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_add_abs_iff
% 5.02/5.34 thf(fact_6852_even__abs__add__iff,axiom,
% 5.02/5.34 ! [K: int,L: int] :
% 5.02/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 5.02/5.34 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_abs_add_iff
% 5.02/5.34 thf(fact_6853_bit__iff__odd,axiom,
% 5.02/5.34 ( bit_se9216721137139052372nteger
% 5.02/5.34 = ( ^ [A5: code_integer,N3: nat] :
% 5.02/5.34 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A5 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_iff_odd
% 5.02/5.34 thf(fact_6854_bit__iff__odd,axiom,
% 5.02/5.34 ( bit_se1146084159140164899it_int
% 5.02/5.34 = ( ^ [A5: int,N3: nat] :
% 5.02/5.34 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A5 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_iff_odd
% 5.02/5.34 thf(fact_6855_bit__iff__odd,axiom,
% 5.02/5.34 ( bit_se1148574629649215175it_nat
% 5.02/5.34 = ( ^ [A5: nat,N3: nat] :
% 5.02/5.34 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_iff_odd
% 5.02/5.34 thf(fact_6856_bit__int__def,axiom,
% 5.02/5.34 ( bit_se1146084159140164899it_int
% 5.02/5.34 = ( ^ [K3: int,N3: nat] :
% 5.02/5.34 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_int_def
% 5.02/5.34 thf(fact_6857_nat__intermed__int__val,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > int,K: int] :
% 5.02/5.34 ( ! [I2: nat] :
% 5.02/5.34 ( ( ( ord_less_eq_nat @ M @ I2 )
% 5.02/5.34 & ( ord_less_nat @ I2 @ N2 ) )
% 5.02/5.34 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.02/5.34 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.02/5.34 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.02/5.34 => ? [I2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ I2 )
% 5.02/5.34 & ( ord_less_eq_nat @ I2 @ N2 )
% 5.02/5.34 & ( ( F @ I2 )
% 5.02/5.34 = K ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % nat_intermed_int_val
% 5.02/5.34 thf(fact_6858_decr__lemma,axiom,
% 5.02/5.34 ! [D: int,X2: int,Z: int] :
% 5.02/5.34 ( ( ord_less_int @ zero_zero_int @ D )
% 5.02/5.34 => ( ord_less_int @ ( minus_minus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.02/5.34
% 5.02/5.34 % decr_lemma
% 5.02/5.34 thf(fact_6859_incr__lemma,axiom,
% 5.02/5.34 ! [D: int,Z: int,X2: int] :
% 5.02/5.34 ( ( ord_less_int @ zero_zero_int @ D )
% 5.02/5.34 => ( ord_less_int @ Z @ ( plus_plus_int @ X2 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X2 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % incr_lemma
% 5.02/5.34 thf(fact_6860_even__bit__succ__iff,axiom,
% 5.02/5.34 ! [A: code_integer,N2: nat] :
% 5.02/5.34 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N2 )
% 5.02/5.34 = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.02/5.34 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_bit_succ_iff
% 5.02/5.34 thf(fact_6861_even__bit__succ__iff,axiom,
% 5.02/5.34 ! [A: int,N2: nat] :
% 5.02/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 5.02/5.34 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.02/5.34 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_bit_succ_iff
% 5.02/5.34 thf(fact_6862_even__bit__succ__iff,axiom,
% 5.02/5.34 ! [A: nat,N2: nat] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 5.02/5.34 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.02/5.34 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_bit_succ_iff
% 5.02/5.34 thf(fact_6863_odd__bit__iff__bit__pred,axiom,
% 5.02/5.34 ! [A: code_integer,N2: nat] :
% 5.02/5.34 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.02/5.34 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N2 )
% 5.02/5.34 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % odd_bit_iff_bit_pred
% 5.02/5.34 thf(fact_6864_odd__bit__iff__bit__pred,axiom,
% 5.02/5.34 ! [A: int,N2: nat] :
% 5.02/5.34 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.02/5.34 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N2 )
% 5.02/5.34 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % odd_bit_iff_bit_pred
% 5.02/5.34 thf(fact_6865_odd__bit__iff__bit__pred,axiom,
% 5.02/5.34 ! [A: nat,N2: nat] :
% 5.02/5.34 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.02/5.34 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N2 )
% 5.02/5.34 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % odd_bit_iff_bit_pred
% 5.02/5.34 thf(fact_6866_nat__ivt__aux,axiom,
% 5.02/5.34 ! [N2: nat,F: nat > int,K: int] :
% 5.02/5.34 ( ! [I2: nat] :
% 5.02/5.34 ( ( ord_less_nat @ I2 @ N2 )
% 5.02/5.34 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I2 ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.02/5.34 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.02/5.34 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.02/5.34 => ? [I2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.02/5.34 & ( ( F @ I2 )
% 5.02/5.34 = K ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % nat_ivt_aux
% 5.02/5.34 thf(fact_6867_bit__sum__mult__2__cases,axiom,
% 5.02/5.34 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.02/5.34 ( ! [J2: nat] :
% 5.02/5.34 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 5.02/5.34 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.02/5.34 = ( ( ( N2 = zero_zero_nat )
% 5.02/5.34 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.34 & ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_sum_mult_2_cases
% 5.02/5.34 thf(fact_6868_bit__sum__mult__2__cases,axiom,
% 5.02/5.34 ! [A: int,B: int,N2: nat] :
% 5.02/5.34 ( ! [J2: nat] :
% 5.02/5.34 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 5.02/5.34 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.02/5.34 = ( ( ( N2 = zero_zero_nat )
% 5.02/5.34 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.34 & ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_sum_mult_2_cases
% 5.02/5.34 thf(fact_6869_bit__sum__mult__2__cases,axiom,
% 5.02/5.34 ! [A: nat,B: nat,N2: nat] :
% 5.02/5.34 ( ! [J2: nat] :
% 5.02/5.34 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 5.02/5.34 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.02/5.34 = ( ( ( N2 = zero_zero_nat )
% 5.02/5.34 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.02/5.34 & ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_sum_mult_2_cases
% 5.02/5.34 thf(fact_6870_bit__rec,axiom,
% 5.02/5.34 ( bit_se9216721137139052372nteger
% 5.02/5.34 = ( ^ [A5: code_integer,N3: nat] :
% 5.02/5.34 ( ( ( N3 = zero_zero_nat )
% 5.02/5.34 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) )
% 5.02/5.34 & ( ( N3 != zero_zero_nat )
% 5.02/5.34 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_rec
% 5.02/5.34 thf(fact_6871_bit__rec,axiom,
% 5.02/5.34 ( bit_se1146084159140164899it_int
% 5.02/5.34 = ( ^ [A5: int,N3: nat] :
% 5.02/5.34 ( ( ( N3 = zero_zero_nat )
% 5.02/5.34 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) )
% 5.02/5.34 & ( ( N3 != zero_zero_nat )
% 5.02/5.34 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_rec
% 5.02/5.34 thf(fact_6872_bit__rec,axiom,
% 5.02/5.34 ( bit_se1148574629649215175it_nat
% 5.02/5.34 = ( ^ [A5: nat,N3: nat] :
% 5.02/5.34 ( ( ( N3 = zero_zero_nat )
% 5.02/5.34 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) )
% 5.02/5.34 & ( ( N3 != zero_zero_nat )
% 5.02/5.34 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_rec
% 5.02/5.34 thf(fact_6873_nat0__intermed__int__val,axiom,
% 5.02/5.34 ! [N2: nat,F: nat > int,K: int] :
% 5.02/5.34 ( ! [I2: nat] :
% 5.02/5.34 ( ( ord_less_nat @ I2 @ N2 )
% 5.02/5.34 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F @ I2 ) ) ) @ one_one_int ) )
% 5.02/5.34 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.02/5.34 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.02/5.34 => ? [I2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.02/5.34 & ( ( F @ I2 )
% 5.02/5.34 = K ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % nat0_intermed_int_val
% 5.02/5.34 thf(fact_6874_set__bit__eq,axiom,
% 5.02/5.34 ( bit_se7879613467334960850it_int
% 5.02/5.34 = ( ^ [N3: nat,K3: int] :
% 5.02/5.34 ( plus_plus_int @ K3
% 5.02/5.34 @ ( times_times_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N3 ) )
% 5.02/5.34 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_bit_eq
% 5.02/5.34 thf(fact_6875_unset__bit__eq,axiom,
% 5.02/5.34 ( bit_se4203085406695923979it_int
% 5.02/5.34 = ( ^ [N3: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N3 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % unset_bit_eq
% 5.02/5.34 thf(fact_6876_arctan__add,axiom,
% 5.02/5.34 ! [X2: real,Y: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.34 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.02/5.34 => ( ( plus_plus_real @ ( arctan @ X2 ) @ ( arctan @ Y ) )
% 5.02/5.34 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X2 @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % arctan_add
% 5.02/5.34 thf(fact_6877_take__bit__Suc__from__most,axiom,
% 5.02/5.34 ! [N2: nat,K: int] :
% 5.02/5.34 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 5.02/5.34 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_Suc_from_most
% 5.02/5.34 thf(fact_6878_Sum__Icc__int,axiom,
% 5.02/5.34 ! [M: int,N2: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ M @ N2 )
% 5.02/5.34 => ( ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [X: int] : X
% 5.02/5.34 @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 5.02/5.34 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % Sum_Icc_int
% 5.02/5.34 thf(fact_6879_mask__numeral,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_numeral
% 5.02/5.34 thf(fact_6880_mask__numeral,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_numeral
% 5.02/5.34 thf(fact_6881_tanh__real__altdef,axiom,
% 5.02/5.34 ( tanh_real
% 5.02/5.34 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % tanh_real_altdef
% 5.02/5.34 thf(fact_6882_and__int__unfold,axiom,
% 5.02/5.34 ( bit_se725231765392027082nd_int
% 5.02/5.34 = ( ^ [K3: int,L2: int] :
% 5.02/5.34 ( if_int
% 5.02/5.34 @ ( ( K3 = zero_zero_int )
% 5.02/5.34 | ( L2 = zero_zero_int ) )
% 5.02/5.34 @ zero_zero_int
% 5.02/5.34 @ ( if_int
% 5.02/5.34 @ ( K3
% 5.02/5.34 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 @ L2
% 5.02/5.34 @ ( if_int
% 5.02/5.34 @ ( L2
% 5.02/5.34 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 @ K3
% 5.02/5.34 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_int_unfold
% 5.02/5.34 thf(fact_6883_machin,axiom,
% 5.02/5.34 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.34 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % machin
% 5.02/5.34 thf(fact_6884_machin__Euler,axiom,
% 5.02/5.34 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.02/5.34 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % machin_Euler
% 5.02/5.34 thf(fact_6885_and_Oidem,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.02/5.34 = A ) ).
% 5.02/5.34
% 5.02/5.34 % and.idem
% 5.02/5.34 thf(fact_6886_and_Oidem,axiom,
% 5.02/5.34 ! [A: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.02/5.34 = A ) ).
% 5.02/5.34
% 5.02/5.34 % and.idem
% 5.02/5.34 thf(fact_6887_and_Oleft__idem,axiom,
% 5.02/5.34 ! [A: int,B: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.02/5.34 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.left_idem
% 5.02/5.34 thf(fact_6888_and_Oleft__idem,axiom,
% 5.02/5.34 ! [A: nat,B: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.02/5.34 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.left_idem
% 5.02/5.34 thf(fact_6889_and_Oright__idem,axiom,
% 5.02/5.34 ! [A: int,B: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.02/5.34 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.right_idem
% 5.02/5.34 thf(fact_6890_and_Oright__idem,axiom,
% 5.02/5.34 ! [A: nat,B: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.02/5.34 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.right_idem
% 5.02/5.34 thf(fact_6891_mask__nat__positive__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_nat_positive_iff
% 5.02/5.34 thf(fact_6892_bit_Oconj__zero__right,axiom,
% 5.02/5.34 ! [X2: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ X2 @ zero_zero_int )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % bit.conj_zero_right
% 5.02/5.34 thf(fact_6893_bit_Oconj__zero__left,axiom,
% 5.02/5.34 ! [X2: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X2 )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % bit.conj_zero_left
% 5.02/5.34 thf(fact_6894_zero__and__eq,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % zero_and_eq
% 5.02/5.34 thf(fact_6895_zero__and__eq,axiom,
% 5.02/5.34 ! [A: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % zero_and_eq
% 5.02/5.34 thf(fact_6896_and__zero__eq,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_zero_eq
% 5.02/5.34 thf(fact_6897_and__zero__eq,axiom,
% 5.02/5.34 ! [A: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_zero_eq
% 5.02/5.34 thf(fact_6898_take__bit__and,axiom,
% 5.02/5.34 ! [N2: nat,A: int,B: int] :
% 5.02/5.34 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.02/5.34 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_and
% 5.02/5.34 thf(fact_6899_take__bit__and,axiom,
% 5.02/5.34 ! [N2: nat,A: nat,B: nat] :
% 5.02/5.34 ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.02/5.34 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_and
% 5.02/5.34 thf(fact_6900_exp__zero,axiom,
% 5.02/5.34 ( ( exp_complex @ zero_zero_complex )
% 5.02/5.34 = one_one_complex ) ).
% 5.02/5.34
% 5.02/5.34 % exp_zero
% 5.02/5.34 thf(fact_6901_exp__zero,axiom,
% 5.02/5.34 ( ( exp_real @ zero_zero_real )
% 5.02/5.34 = one_one_real ) ).
% 5.02/5.34
% 5.02/5.34 % exp_zero
% 5.02/5.34 thf(fact_6902_and_Oleft__neutral,axiom,
% 5.02/5.34 ! [A: code_integer] :
% 5.02/5.34 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.02/5.34 = A ) ).
% 5.02/5.34
% 5.02/5.34 % and.left_neutral
% 5.02/5.34 thf(fact_6903_and_Oleft__neutral,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.02/5.34 = A ) ).
% 5.02/5.34
% 5.02/5.34 % and.left_neutral
% 5.02/5.34 thf(fact_6904_and_Oright__neutral,axiom,
% 5.02/5.34 ! [A: code_integer] :
% 5.02/5.34 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.34 = A ) ).
% 5.02/5.34
% 5.02/5.34 % and.right_neutral
% 5.02/5.34 thf(fact_6905_and_Oright__neutral,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 = A ) ).
% 5.02/5.34
% 5.02/5.34 % and.right_neutral
% 5.02/5.34 thf(fact_6906_bit_Oconj__one__right,axiom,
% 5.02/5.34 ! [X2: code_integer] :
% 5.02/5.34 ( ( bit_se3949692690581998587nteger @ X2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.34 = X2 ) ).
% 5.02/5.34
% 5.02/5.34 % bit.conj_one_right
% 5.02/5.34 thf(fact_6907_bit_Oconj__one__right,axiom,
% 5.02/5.34 ! [X2: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ X2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 = X2 ) ).
% 5.02/5.34
% 5.02/5.34 % bit.conj_one_right
% 5.02/5.34 thf(fact_6908_mask__eq__0__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ( bit_se2002935070580805687sk_nat @ N2 )
% 5.02/5.34 = zero_zero_nat )
% 5.02/5.34 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_eq_0_iff
% 5.02/5.34 thf(fact_6909_mask__eq__0__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ( bit_se2000444600071755411sk_int @ N2 )
% 5.02/5.34 = zero_zero_int )
% 5.02/5.34 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_eq_0_iff
% 5.02/5.34 thf(fact_6910_mask__0,axiom,
% 5.02/5.34 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % mask_0
% 5.02/5.34 thf(fact_6911_mask__0,axiom,
% 5.02/5.34 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % mask_0
% 5.02/5.34 thf(fact_6912_exp__eq__one__iff,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ( exp_real @ X2 )
% 5.02/5.34 = one_one_real )
% 5.02/5.34 = ( X2 = zero_zero_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_eq_one_iff
% 5.02/5.34 thf(fact_6913_and__nonnegative__int__iff,axiom,
% 5.02/5.34 ! [K: int,L: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.02/5.34 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.34 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_nonnegative_int_iff
% 5.02/5.34 thf(fact_6914_and__negative__int__iff,axiom,
% 5.02/5.34 ! [K: int,L: int] :
% 5.02/5.34 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.02/5.34 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.02/5.34 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_negative_int_iff
% 5.02/5.34 thf(fact_6915_and__numerals_I8_J,axiom,
% 5.02/5.34 ! [X2: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ one_one_int )
% 5.02/5.34 = one_one_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(8)
% 5.02/5.34 thf(fact_6916_and__numerals_I8_J,axiom,
% 5.02/5.34 ! [X2: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ one_one_nat )
% 5.02/5.34 = one_one_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(8)
% 5.02/5.34 thf(fact_6917_and__numerals_I2_J,axiom,
% 5.02/5.34 ! [Y: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.02/5.34 = one_one_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(2)
% 5.02/5.34 thf(fact_6918_and__numerals_I2_J,axiom,
% 5.02/5.34 ! [Y: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.34 = one_one_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(2)
% 5.02/5.34 thf(fact_6919_mask__Suc__0,axiom,
% 5.02/5.34 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.02/5.34 = one_one_nat ) ).
% 5.02/5.34
% 5.02/5.34 % mask_Suc_0
% 5.02/5.34 thf(fact_6920_mask__Suc__0,axiom,
% 5.02/5.34 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.02/5.34 = one_one_int ) ).
% 5.02/5.34
% 5.02/5.34 % mask_Suc_0
% 5.02/5.34 thf(fact_6921_exp__less__one__iff,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.02/5.34 = ( ord_less_real @ X2 @ zero_zero_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_less_one_iff
% 5.02/5.34 thf(fact_6922_one__less__exp__iff,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.02/5.34 = ( ord_less_real @ zero_zero_real @ X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % one_less_exp_iff
% 5.02/5.34 thf(fact_6923_exp__le__one__iff,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( exp_real @ X2 ) @ one_one_real )
% 5.02/5.34 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_le_one_iff
% 5.02/5.34 thf(fact_6924_one__le__exp__iff,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X2 ) )
% 5.02/5.34 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % one_le_exp_iff
% 5.02/5.34 thf(fact_6925_take__bit__minus__one__eq__mask,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se1745604003318907178nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.34 = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_minus_one_eq_mask
% 5.02/5.34 thf(fact_6926_take__bit__minus__one__eq__mask,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_minus_one_eq_mask
% 5.02/5.34 thf(fact_6927_of__int__sum,axiom,
% 5.02/5.34 ! [F: complex > int,A3: set_complex] :
% 5.02/5.34 ( ( ring_17405671764205052669omplex @ ( groups5690904116761175830ex_int @ F @ A3 ) )
% 5.02/5.34 = ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [X: complex] : ( ring_17405671764205052669omplex @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_sum
% 5.02/5.34 thf(fact_6928_of__int__sum,axiom,
% 5.02/5.34 ! [F: nat > int,A3: set_nat] :
% 5.02/5.34 ( ( ring_1_of_int_real @ ( groups3539618377306564664at_int @ F @ A3 ) )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [X: nat] : ( ring_1_of_int_real @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_sum
% 5.02/5.34 thf(fact_6929_of__int__sum,axiom,
% 5.02/5.34 ! [F: int > int,A3: set_int] :
% 5.02/5.34 ( ( ring_1_of_int_real @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.02/5.34 = ( groups8778361861064173332t_real
% 5.02/5.34 @ ^ [X: int] : ( ring_1_of_int_real @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_sum
% 5.02/5.34 thf(fact_6930_of__int__sum,axiom,
% 5.02/5.34 ! [F: int > int,A3: set_int] :
% 5.02/5.34 ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.02/5.34 = ( groups3906332499630173760nt_rat
% 5.02/5.34 @ ^ [X: int] : ( ring_1_of_int_rat @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_sum
% 5.02/5.34 thf(fact_6931_of__int__sum,axiom,
% 5.02/5.34 ! [F: int > int,A3: set_int] :
% 5.02/5.34 ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.02/5.34 = ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [X: int] : ( ring_1_of_int_int @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_sum
% 5.02/5.34 thf(fact_6932_and__numerals_I1_J,axiom,
% 5.02/5.34 ! [Y: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(1)
% 5.02/5.34 thf(fact_6933_and__numerals_I1_J,axiom,
% 5.02/5.34 ! [Y: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(1)
% 5.02/5.34 thf(fact_6934_and__numerals_I5_J,axiom,
% 5.02/5.34 ! [X2: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ one_one_int )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(5)
% 5.02/5.34 thf(fact_6935_and__numerals_I5_J,axiom,
% 5.02/5.34 ! [X2: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ one_one_nat )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(5)
% 5.02/5.34 thf(fact_6936_and__numerals_I3_J,axiom,
% 5.02/5.34 ! [X2: num,Y: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.02/5.34 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(3)
% 5.02/5.34 thf(fact_6937_and__numerals_I3_J,axiom,
% 5.02/5.34 ! [X2: num,Y: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.34 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(3)
% 5.02/5.34 thf(fact_6938_and__minus__numerals_I6_J,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.02/5.34 = one_one_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_minus_numerals(6)
% 5.02/5.34 thf(fact_6939_and__minus__numerals_I2_J,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.34 = one_one_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_minus_numerals(2)
% 5.02/5.34 thf(fact_6940_and__numerals_I4_J,axiom,
% 5.02/5.34 ! [X2: num,Y: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.02/5.34 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(4)
% 5.02/5.34 thf(fact_6941_and__numerals_I4_J,axiom,
% 5.02/5.34 ! [X2: num,Y: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.34 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(4)
% 5.02/5.34 thf(fact_6942_and__numerals_I6_J,axiom,
% 5.02/5.34 ! [X2: num,Y: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.02/5.34 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(6)
% 5.02/5.34 thf(fact_6943_and__numerals_I6_J,axiom,
% 5.02/5.34 ! [X2: num,Y: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.34 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(6)
% 5.02/5.34 thf(fact_6944_and__minus__numerals_I1_J,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_minus_numerals(1)
% 5.02/5.34 thf(fact_6945_and__minus__numerals_I5_J,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % and_minus_numerals(5)
% 5.02/5.34 thf(fact_6946_and__numerals_I7_J,axiom,
% 5.02/5.34 ! [X2: num,Y: num] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X2 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.02/5.34 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X2 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(7)
% 5.02/5.34 thf(fact_6947_and__numerals_I7_J,axiom,
% 5.02/5.34 ! [X2: num,Y: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.34 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X2 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_numerals(7)
% 5.02/5.34 thf(fact_6948_of__int__and__eq,axiom,
% 5.02/5.34 ! [K: int,L: int] :
% 5.02/5.34 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.02/5.34 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_and_eq
% 5.02/5.34 thf(fact_6949_of__int__mask__eq,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.02/5.34 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_mask_eq
% 5.02/5.34 thf(fact_6950_take__bit__eq__mask,axiom,
% 5.02/5.34 ( bit_se2923211474154528505it_int
% 5.02/5.34 = ( ^ [N3: nat,A5: int] : ( bit_se725231765392027082nd_int @ A5 @ ( bit_se2000444600071755411sk_int @ N3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_eq_mask
% 5.02/5.34 thf(fact_6951_take__bit__eq__mask,axiom,
% 5.02/5.34 ( bit_se2925701944663578781it_nat
% 5.02/5.34 = ( ^ [N3: nat,A5: nat] : ( bit_se727722235901077358nd_nat @ A5 @ ( bit_se2002935070580805687sk_nat @ N3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_eq_mask
% 5.02/5.34 thf(fact_6952_and_Oassoc,axiom,
% 5.02/5.34 ! [A: int,B: int,C: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.02/5.34 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.assoc
% 5.02/5.34 thf(fact_6953_and_Oassoc,axiom,
% 5.02/5.34 ! [A: nat,B: nat,C: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.02/5.34 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.assoc
% 5.02/5.34 thf(fact_6954_and_Ocommute,axiom,
% 5.02/5.34 ( bit_se725231765392027082nd_int
% 5.02/5.34 = ( ^ [A5: int,B5: int] : ( bit_se725231765392027082nd_int @ B5 @ A5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.commute
% 5.02/5.34 thf(fact_6955_and_Ocommute,axiom,
% 5.02/5.34 ( bit_se727722235901077358nd_nat
% 5.02/5.34 = ( ^ [A5: nat,B5: nat] : ( bit_se727722235901077358nd_nat @ B5 @ A5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.commute
% 5.02/5.34 thf(fact_6956_and_Oleft__commute,axiom,
% 5.02/5.34 ! [B: int,A: int,C: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.02/5.34 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.left_commute
% 5.02/5.34 thf(fact_6957_and_Oleft__commute,axiom,
% 5.02/5.34 ! [B: nat,A: nat,C: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.02/5.34 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and.left_commute
% 5.02/5.34 thf(fact_6958_bit__and__iff,axiom,
% 5.02/5.34 ! [A: int,B: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N2 )
% 5.02/5.34 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.02/5.34 & ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_and_iff
% 5.02/5.34 thf(fact_6959_bit__and__iff,axiom,
% 5.02/5.34 ! [A: nat,B: nat,N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N2 )
% 5.02/5.34 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.02/5.34 & ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_and_iff
% 5.02/5.34 thf(fact_6960_exp__not__eq__zero,axiom,
% 5.02/5.34 ! [X2: complex] :
% 5.02/5.34 ( ( exp_complex @ X2 )
% 5.02/5.34 != zero_zero_complex ) ).
% 5.02/5.34
% 5.02/5.34 % exp_not_eq_zero
% 5.02/5.34 thf(fact_6961_exp__not__eq__zero,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( exp_real @ X2 )
% 5.02/5.34 != zero_zero_real ) ).
% 5.02/5.34
% 5.02/5.34 % exp_not_eq_zero
% 5.02/5.34 thf(fact_6962_bit_Oconj__disj__distrib,axiom,
% 5.02/5.34 ! [X2: int,Y: int,Z: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ X2 @ ( bit_se1409905431419307370or_int @ Y @ Z ) )
% 5.02/5.34 = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ ( bit_se725231765392027082nd_int @ X2 @ Z ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit.conj_disj_distrib
% 5.02/5.34 thf(fact_6963_bit_Odisj__conj__distrib,axiom,
% 5.02/5.34 ! [X2: int,Y: int,Z: int] :
% 5.02/5.34 ( ( bit_se1409905431419307370or_int @ X2 @ ( bit_se725231765392027082nd_int @ Y @ Z ) )
% 5.02/5.34 = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ X2 @ Y ) @ ( bit_se1409905431419307370or_int @ X2 @ Z ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit.disj_conj_distrib
% 5.02/5.34 thf(fact_6964_bit_Oconj__disj__distrib2,axiom,
% 5.02/5.34 ! [Y: int,Z: int,X2: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y @ Z ) @ X2 )
% 5.02/5.34 = ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y @ X2 ) @ ( bit_se725231765392027082nd_int @ Z @ X2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit.conj_disj_distrib2
% 5.02/5.34 thf(fact_6965_bit_Odisj__conj__distrib2,axiom,
% 5.02/5.34 ! [Y: int,Z: int,X2: int] :
% 5.02/5.34 ( ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ Y @ Z ) @ X2 )
% 5.02/5.34 = ( bit_se725231765392027082nd_int @ ( bit_se1409905431419307370or_int @ Y @ X2 ) @ ( bit_se1409905431419307370or_int @ Z @ X2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit.disj_conj_distrib2
% 5.02/5.34 thf(fact_6966_exp__times__arg__commute,axiom,
% 5.02/5.34 ! [A3: complex] :
% 5.02/5.34 ( ( times_times_complex @ ( exp_complex @ A3 ) @ A3 )
% 5.02/5.34 = ( times_times_complex @ A3 @ ( exp_complex @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_times_arg_commute
% 5.02/5.34 thf(fact_6967_exp__times__arg__commute,axiom,
% 5.02/5.34 ! [A3: real] :
% 5.02/5.34 ( ( times_times_real @ ( exp_real @ A3 ) @ A3 )
% 5.02/5.34 = ( times_times_real @ A3 @ ( exp_real @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_times_arg_commute
% 5.02/5.34 thf(fact_6968_bit__and__int__iff,axiom,
% 5.02/5.34 ! [K: int,L: int,N2: nat] :
% 5.02/5.34 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N2 )
% 5.02/5.34 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.02/5.34 & ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_and_int_iff
% 5.02/5.34 thf(fact_6969_less__eq__mask,axiom,
% 5.02/5.34 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % less_eq_mask
% 5.02/5.34 thf(fact_6970_mod__sum__eq,axiom,
% 5.02/5.34 ! [F: int > int,A: int,A3: set_int] :
% 5.02/5.34 ( ( modulo_modulo_int
% 5.02/5.34 @ ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [I5: int] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 5.02/5.34 @ A3 )
% 5.02/5.34 @ A )
% 5.02/5.34 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ A ) ) ).
% 5.02/5.34
% 5.02/5.34 % mod_sum_eq
% 5.02/5.34 thf(fact_6971_mod__sum__eq,axiom,
% 5.02/5.34 ! [F: nat > nat,A: nat,A3: set_nat] :
% 5.02/5.34 ( ( modulo_modulo_nat
% 5.02/5.34 @ ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [I5: nat] : ( modulo_modulo_nat @ ( F @ I5 ) @ A )
% 5.02/5.34 @ A3 )
% 5.02/5.34 @ A )
% 5.02/5.34 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ A ) ) ).
% 5.02/5.34
% 5.02/5.34 % mod_sum_eq
% 5.02/5.34 thf(fact_6972_and__eq__minus__1__iff,axiom,
% 5.02/5.34 ! [A: code_integer,B: code_integer] :
% 5.02/5.34 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.02/5.34 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.34 = ( ( A
% 5.02/5.34 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.34 & ( B
% 5.02/5.34 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_eq_minus_1_iff
% 5.02/5.34 thf(fact_6973_and__eq__minus__1__iff,axiom,
% 5.02/5.34 ! [A: int,B: int] :
% 5.02/5.34 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.02/5.34 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 = ( ( A
% 5.02/5.34 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 & ( B
% 5.02/5.34 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_eq_minus_1_iff
% 5.02/5.34 thf(fact_6974_not__bit__Suc__0__Suc,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % not_bit_Suc_0_Suc
% 5.02/5.34 thf(fact_6975_bit__Suc__0__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.02/5.34 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_Suc_0_iff
% 5.02/5.34 thf(fact_6976_AND__lower,axiom,
% 5.02/5.34 ! [X2: int,Y: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.34 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % AND_lower
% 5.02/5.34 thf(fact_6977_AND__upper1,axiom,
% 5.02/5.34 ! [X2: int,Y: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.34 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % AND_upper1
% 5.02/5.34 thf(fact_6978_AND__upper2,axiom,
% 5.02/5.34 ! [Y: int,X2: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.34 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Y ) ) ).
% 5.02/5.34
% 5.02/5.34 % AND_upper2
% 5.02/5.34 thf(fact_6979_AND__upper1_H,axiom,
% 5.02/5.34 ! [Y: int,Z: int,Ya: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.34 => ( ( ord_less_eq_int @ Y @ Z )
% 5.02/5.34 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % AND_upper1'
% 5.02/5.34 thf(fact_6980_AND__upper2_H,axiom,
% 5.02/5.34 ! [Y: int,Z: int,X2: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.34 => ( ( ord_less_eq_int @ Y @ Z )
% 5.02/5.34 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Z ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % AND_upper2'
% 5.02/5.34 thf(fact_6981_mult__exp__exp,axiom,
% 5.02/5.34 ! [X2: complex,Y: complex] :
% 5.02/5.34 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y ) )
% 5.02/5.34 = ( exp_complex @ ( plus_plus_complex @ X2 @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mult_exp_exp
% 5.02/5.34 thf(fact_6982_mult__exp__exp,axiom,
% 5.02/5.34 ! [X2: real,Y: real] :
% 5.02/5.34 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) )
% 5.02/5.34 = ( exp_real @ ( plus_plus_real @ X2 @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mult_exp_exp
% 5.02/5.34 thf(fact_6983_exp__add__commuting,axiom,
% 5.02/5.34 ! [X2: complex,Y: complex] :
% 5.02/5.34 ( ( ( times_times_complex @ X2 @ Y )
% 5.02/5.34 = ( times_times_complex @ Y @ X2 ) )
% 5.02/5.34 => ( ( exp_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.02/5.34 = ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_add_commuting
% 5.02/5.34 thf(fact_6984_exp__add__commuting,axiom,
% 5.02/5.34 ! [X2: real,Y: real] :
% 5.02/5.34 ( ( ( times_times_real @ X2 @ Y )
% 5.02/5.34 = ( times_times_real @ Y @ X2 ) )
% 5.02/5.34 => ( ( exp_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.02/5.34 = ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_add_commuting
% 5.02/5.34 thf(fact_6985_exp__diff,axiom,
% 5.02/5.34 ! [X2: complex,Y: complex] :
% 5.02/5.34 ( ( exp_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.02/5.34 = ( divide1717551699836669952omplex @ ( exp_complex @ X2 ) @ ( exp_complex @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_diff
% 5.02/5.34 thf(fact_6986_exp__diff,axiom,
% 5.02/5.34 ! [X2: real,Y: real] :
% 5.02/5.34 ( ( exp_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.02/5.34 = ( divide_divide_real @ ( exp_real @ X2 ) @ ( exp_real @ Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_diff
% 5.02/5.34 thf(fact_6987_plus__and__or,axiom,
% 5.02/5.34 ! [X2: int,Y: int] :
% 5.02/5.34 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ ( bit_se1409905431419307370or_int @ X2 @ Y ) )
% 5.02/5.34 = ( plus_plus_int @ X2 @ Y ) ) ).
% 5.02/5.34
% 5.02/5.34 % plus_and_or
% 5.02/5.34 thf(fact_6988_mask__nonnegative__int,axiom,
% 5.02/5.34 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_nonnegative_int
% 5.02/5.34 thf(fact_6989_not__mask__negative__int,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % not_mask_negative_int
% 5.02/5.34 thf(fact_6990_not__bit__Suc__0__numeral,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % not_bit_Suc_0_numeral
% 5.02/5.34 thf(fact_6991_exp__gt__one,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.34 => ( ord_less_real @ one_one_real @ ( exp_real @ X2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_gt_one
% 5.02/5.34 thf(fact_6992_exp__ge__add__one__self,axiom,
% 5.02/5.34 ! [X2: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_ge_add_one_self
% 5.02/5.34 thf(fact_6993_and__less__eq,axiom,
% 5.02/5.34 ! [L: int,K: int] :
% 5.02/5.34 ( ( ord_less_int @ L @ zero_zero_int )
% 5.02/5.34 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_less_eq
% 5.02/5.34 thf(fact_6994_AND__upper1_H_H,axiom,
% 5.02/5.34 ! [Y: int,Z: int,Ya: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.34 => ( ( ord_less_int @ Y @ Z )
% 5.02/5.34 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % AND_upper1''
% 5.02/5.34 thf(fact_6995_AND__upper2_H_H,axiom,
% 5.02/5.34 ! [Y: int,Z: int,X2: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.34 => ( ( ord_less_int @ Y @ Z )
% 5.02/5.34 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X2 @ Y ) @ Z ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % AND_upper2''
% 5.02/5.34 thf(fact_6996_exp__minus__inverse,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( times_times_real @ ( exp_real @ X2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) )
% 5.02/5.34 = one_one_real ) ).
% 5.02/5.34
% 5.02/5.34 % exp_minus_inverse
% 5.02/5.34 thf(fact_6997_exp__minus__inverse,axiom,
% 5.02/5.34 ! [X2: complex] :
% 5.02/5.34 ( ( times_times_complex @ ( exp_complex @ X2 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X2 ) ) )
% 5.02/5.34 = one_one_complex ) ).
% 5.02/5.34
% 5.02/5.34 % exp_minus_inverse
% 5.02/5.34 thf(fact_6998_less__mask,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.02/5.34 => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % less_mask
% 5.02/5.34 thf(fact_6999_even__and__iff,axiom,
% 5.02/5.34 ! [A: code_integer,B: code_integer] :
% 5.02/5.34 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.02/5.34 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_and_iff
% 5.02/5.34 thf(fact_7000_even__and__iff,axiom,
% 5.02/5.34 ! [A: int,B: int] :
% 5.02/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.02/5.34 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_and_iff
% 5.02/5.34 thf(fact_7001_even__and__iff,axiom,
% 5.02/5.34 ! [A: nat,B: nat] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.02/5.34 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.02/5.34 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_and_iff
% 5.02/5.34 thf(fact_7002_bit_Ocomplement__unique,axiom,
% 5.02/5.34 ! [A: code_integer,X2: code_integer,Y: code_integer] :
% 5.02/5.34 ( ( ( bit_se3949692690581998587nteger @ A @ X2 )
% 5.02/5.34 = zero_z3403309356797280102nteger )
% 5.02/5.34 => ( ( ( bit_se1080825931792720795nteger @ A @ X2 )
% 5.02/5.34 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.34 => ( ( ( bit_se3949692690581998587nteger @ A @ Y )
% 5.02/5.34 = zero_z3403309356797280102nteger )
% 5.02/5.34 => ( ( ( bit_se1080825931792720795nteger @ A @ Y )
% 5.02/5.34 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.02/5.34 => ( X2 = Y ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit.complement_unique
% 5.02/5.34 thf(fact_7003_bit_Ocomplement__unique,axiom,
% 5.02/5.34 ! [A: int,X2: int,Y: int] :
% 5.02/5.34 ( ( ( bit_se725231765392027082nd_int @ A @ X2 )
% 5.02/5.34 = zero_zero_int )
% 5.02/5.34 => ( ( ( bit_se1409905431419307370or_int @ A @ X2 )
% 5.02/5.34 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 => ( ( ( bit_se725231765392027082nd_int @ A @ Y )
% 5.02/5.34 = zero_zero_int )
% 5.02/5.34 => ( ( ( bit_se1409905431419307370or_int @ A @ Y )
% 5.02/5.34 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.34 => ( X2 = Y ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit.complement_unique
% 5.02/5.34 thf(fact_7004_exp__ge__add__one__self__aux,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.34 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( exp_real @ X2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_ge_add_one_self_aux
% 5.02/5.34 thf(fact_7005_even__and__iff__int,axiom,
% 5.02/5.34 ! [K: int,L: int] :
% 5.02/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.02/5.34 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.02/5.34 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % even_and_iff_int
% 5.02/5.34 thf(fact_7006_lemma__exp__total,axiom,
% 5.02/5.34 ! [Y: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.02/5.34 => ? [X5: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.02/5.34 & ( ord_less_eq_real @ X5 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.02/5.34 & ( ( exp_real @ X5 )
% 5.02/5.34 = Y ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % lemma_exp_total
% 5.02/5.34 thf(fact_7007_ln__x__over__x__mono,axiom,
% 5.02/5.34 ! [X2: real,Y: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X2 )
% 5.02/5.34 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.34 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X2 ) @ X2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % ln_x_over_x_mono
% 5.02/5.34 thf(fact_7008_pi__less__4,axiom,
% 5.02/5.34 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % pi_less_4
% 5.02/5.34 thf(fact_7009_pi__ge__two,axiom,
% 5.02/5.34 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.02/5.34
% 5.02/5.34 % pi_ge_two
% 5.02/5.34 thf(fact_7010_pi__half__neq__two,axiom,
% 5.02/5.34 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.34 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % pi_half_neq_two
% 5.02/5.34 thf(fact_7011_one__and__eq,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.02/5.34 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % one_and_eq
% 5.02/5.34 thf(fact_7012_one__and__eq,axiom,
% 5.02/5.34 ! [A: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.02/5.34 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % one_and_eq
% 5.02/5.34 thf(fact_7013_and__one__eq,axiom,
% 5.02/5.34 ! [A: int] :
% 5.02/5.34 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.02/5.34 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_one_eq
% 5.02/5.34 thf(fact_7014_and__one__eq,axiom,
% 5.02/5.34 ! [A: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.02/5.34 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_one_eq
% 5.02/5.34 thf(fact_7015_exp__le,axiom,
% 5.02/5.34 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_le
% 5.02/5.34 thf(fact_7016_take__bit__eq__mask__iff,axiom,
% 5.02/5.34 ! [N2: nat,K: int] :
% 5.02/5.34 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.02/5.34 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.02/5.34 = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.02/5.34 = zero_zero_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_eq_mask_iff
% 5.02/5.34 thf(fact_7017_pi__half__neq__zero,axiom,
% 5.02/5.34 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.34 != zero_zero_real ) ).
% 5.02/5.34
% 5.02/5.34 % pi_half_neq_zero
% 5.02/5.34 thf(fact_7018_pi__half__less__two,axiom,
% 5.02/5.34 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.02/5.34
% 5.02/5.34 % pi_half_less_two
% 5.02/5.34 thf(fact_7019_pi__half__le__two,axiom,
% 5.02/5.34 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.02/5.34
% 5.02/5.34 % pi_half_le_two
% 5.02/5.34 thf(fact_7020_tanh__altdef,axiom,
% 5.02/5.34 ( tanh_real
% 5.02/5.34 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % tanh_altdef
% 5.02/5.34 thf(fact_7021_tanh__altdef,axiom,
% 5.02/5.34 ( tanh_complex
% 5.02/5.34 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % tanh_altdef
% 5.02/5.34 thf(fact_7022_and__exp__eq__0__iff__not__bit,axiom,
% 5.02/5.34 ! [A: int,N2: nat] :
% 5.02/5.34 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.34 = zero_zero_int )
% 5.02/5.34 = ( ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_exp_eq_0_iff_not_bit
% 5.02/5.34 thf(fact_7023_and__exp__eq__0__iff__not__bit,axiom,
% 5.02/5.34 ! [A: nat,N2: nat] :
% 5.02/5.34 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.34 = zero_zero_nat )
% 5.02/5.34 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_exp_eq_0_iff_not_bit
% 5.02/5.34 thf(fact_7024_Suc__mask__eq__exp,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.02/5.34 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % Suc_mask_eq_exp
% 5.02/5.34 thf(fact_7025_exp__half__le2,axiom,
% 5.02/5.34 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_half_le2
% 5.02/5.34 thf(fact_7026_mask__nat__less__exp,axiom,
% 5.02/5.34 ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_nat_less_exp
% 5.02/5.34 thf(fact_7027_bit__nat__def,axiom,
% 5.02/5.34 ( bit_se1148574629649215175it_nat
% 5.02/5.34 = ( ^ [M6: nat,N3: nat] :
% 5.02/5.34 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % bit_nat_def
% 5.02/5.34 thf(fact_7028_exp__double,axiom,
% 5.02/5.34 ! [Z: complex] :
% 5.02/5.34 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.02/5.34 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_double
% 5.02/5.34 thf(fact_7029_exp__double,axiom,
% 5.02/5.34 ! [Z: real] :
% 5.02/5.34 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.02/5.34 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_double
% 5.02/5.34 thf(fact_7030_pi__half__gt__zero,axiom,
% 5.02/5.34 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % pi_half_gt_zero
% 5.02/5.34 thf(fact_7031_pi__half__ge__zero,axiom,
% 5.02/5.34 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % pi_half_ge_zero
% 5.02/5.34 thf(fact_7032_m2pi__less__pi,axiom,
% 5.02/5.34 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.02/5.34
% 5.02/5.34 % m2pi_less_pi
% 5.02/5.34 thf(fact_7033_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N2 ) )
% 5.02/5.34 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % semiring_bit_operations_class.even_mask_iff
% 5.02/5.34 thf(fact_7034_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.02/5.34 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % semiring_bit_operations_class.even_mask_iff
% 5.02/5.34 thf(fact_7035_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.02/5.34 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % semiring_bit_operations_class.even_mask_iff
% 5.02/5.34 thf(fact_7036_arctan__ubound,axiom,
% 5.02/5.34 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % arctan_ubound
% 5.02/5.34 thf(fact_7037_arctan__one,axiom,
% 5.02/5.34 ( ( arctan @ one_one_real )
% 5.02/5.34 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % arctan_one
% 5.02/5.34 thf(fact_7038_mask__nat__def,axiom,
% 5.02/5.34 ( bit_se2002935070580805687sk_nat
% 5.02/5.34 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_nat_def
% 5.02/5.34 thf(fact_7039_mask__half__int,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.34 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_half_int
% 5.02/5.34 thf(fact_7040_mask__int__def,axiom,
% 5.02/5.34 ( bit_se2000444600071755411sk_int
% 5.02/5.34 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_int_def
% 5.02/5.34 thf(fact_7041_minus__pi__half__less__zero,axiom,
% 5.02/5.34 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.02/5.34
% 5.02/5.34 % minus_pi_half_less_zero
% 5.02/5.34 thf(fact_7042_arctan__bounded,axiom,
% 5.02/5.34 ! [Y: real] :
% 5.02/5.34 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.02/5.34 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % arctan_bounded
% 5.02/5.34 thf(fact_7043_arctan__lbound,axiom,
% 5.02/5.34 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.02/5.34
% 5.02/5.34 % arctan_lbound
% 5.02/5.34 thf(fact_7044_mask__eq__exp__minus__1,axiom,
% 5.02/5.34 ( bit_se2002935070580805687sk_nat
% 5.02/5.34 = ( ^ [N3: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_eq_exp_minus_1
% 5.02/5.34 thf(fact_7045_mask__eq__exp__minus__1,axiom,
% 5.02/5.34 ( bit_se2000444600071755411sk_int
% 5.02/5.34 = ( ^ [N3: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) @ one_one_int ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_eq_exp_minus_1
% 5.02/5.34 thf(fact_7046_mask__Suc__exp,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1412395901928357646or_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_Suc_exp
% 5.02/5.34 thf(fact_7047_mask__Suc__exp,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se2000444600071755411sk_int @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1409905431419307370or_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_Suc_exp
% 5.02/5.34 thf(fact_7048_exp__bound,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.34 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.34 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_bound
% 5.02/5.34 thf(fact_7049_and__int__rec,axiom,
% 5.02/5.34 ( bit_se725231765392027082nd_int
% 5.02/5.34 = ( ^ [K3: int,L2: int] :
% 5.02/5.34 ( plus_plus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.02/5.34 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_int_rec
% 5.02/5.34 thf(fact_7050_real__exp__bound__lemma,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.34 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.34 => ( ord_less_eq_real @ ( exp_real @ X2 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % real_exp_bound_lemma
% 5.02/5.34 thf(fact_7051_mask__Suc__double,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se2002935070580805687sk_nat @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1412395901928357646or_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_Suc_double
% 5.02/5.34 thf(fact_7052_mask__Suc__double,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se2000444600071755411sk_int @ ( suc @ N2 ) )
% 5.02/5.34 = ( bit_se1409905431419307370or_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_Suc_double
% 5.02/5.34 thf(fact_7053_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.02/5.34 ! [N2: nat,K: int] :
% 5.02/5.34 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.02/5.34 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.02/5.34 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % take_bit_eq_mask_iff_exp_dvd
% 5.02/5.34 thf(fact_7054_exp__lower__Taylor__quadratic,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.34 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X2 ) @ ( divide_divide_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % exp_lower_Taylor_quadratic
% 5.02/5.34 thf(fact_7055_sum__abs__ge__zero,axiom,
% 5.02/5.34 ! [F: int > int,A3: set_int] :
% 5.02/5.34 ( ord_less_eq_int @ zero_zero_int
% 5.02/5.34 @ ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_abs_ge_zero
% 5.02/5.34 thf(fact_7056_sum__abs__ge__zero,axiom,
% 5.02/5.34 ! [F: nat > real,A3: set_nat] :
% 5.02/5.34 ( ord_less_eq_real @ zero_zero_real
% 5.02/5.34 @ ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_abs_ge_zero
% 5.02/5.34 thf(fact_7057_sum__abs,axiom,
% 5.02/5.34 ! [F: int > int,A3: set_int] :
% 5.02/5.34 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.02/5.34 @ ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_abs
% 5.02/5.34 thf(fact_7058_sum__abs,axiom,
% 5.02/5.34 ! [F: nat > real,A3: set_nat] :
% 5.02/5.34 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A3 ) )
% 5.02/5.34 @ ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_abs
% 5.02/5.34 thf(fact_7059_sum_Oempty,axiom,
% 5.02/5.34 ! [G: nat > complex] :
% 5.02/5.34 ( ( groups2073611262835488442omplex @ G @ bot_bot_set_nat )
% 5.02/5.34 = zero_zero_complex ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7060_sum_Oempty,axiom,
% 5.02/5.34 ! [G: nat > rat] :
% 5.02/5.34 ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 5.02/5.34 = zero_zero_rat ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7061_sum_Oempty,axiom,
% 5.02/5.34 ! [G: nat > int] :
% 5.02/5.34 ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7062_sum_Oempty,axiom,
% 5.02/5.34 ! [G: int > complex] :
% 5.02/5.34 ( ( groups3049146728041665814omplex @ G @ bot_bot_set_int )
% 5.02/5.34 = zero_zero_complex ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7063_sum_Oempty,axiom,
% 5.02/5.34 ! [G: int > real] :
% 5.02/5.34 ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 5.02/5.34 = zero_zero_real ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7064_sum_Oempty,axiom,
% 5.02/5.34 ! [G: int > rat] :
% 5.02/5.34 ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 5.02/5.34 = zero_zero_rat ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7065_sum_Oempty,axiom,
% 5.02/5.34 ! [G: int > nat] :
% 5.02/5.34 ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7066_sum_Oempty,axiom,
% 5.02/5.34 ! [G: real > complex] :
% 5.02/5.34 ( ( groups5754745047067104278omplex @ G @ bot_bot_set_real )
% 5.02/5.34 = zero_zero_complex ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7067_sum_Oempty,axiom,
% 5.02/5.34 ! [G: real > real] :
% 5.02/5.34 ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 5.02/5.34 = zero_zero_real ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7068_sum_Oempty,axiom,
% 5.02/5.34 ! [G: real > rat] :
% 5.02/5.34 ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 5.02/5.34 = zero_zero_rat ) ).
% 5.02/5.34
% 5.02/5.34 % sum.empty
% 5.02/5.34 thf(fact_7069_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_complex,X2: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.02/5.34 ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ I6 )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups6621422865394947399nteger @ X2 @ I6 )
% 5.02/5.34 = one_one_Code_integer )
% 5.02/5.34 => ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ I6 )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_le3102999989581377725nteger
% 5.02/5.34 @ ( abs_abs_Code_integer
% 5.02/5.34 @ ( minus_8373710615458151222nteger
% 5.02/5.34 @ ( groups6621422865394947399nteger
% 5.02/5.34 @ ^ [I5: complex] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7070_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_real,X2: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.02/5.34 ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ I6 )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups7713935264441627589nteger @ X2 @ I6 )
% 5.02/5.34 = one_one_Code_integer )
% 5.02/5.34 => ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ I6 )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_le3102999989581377725nteger
% 5.02/5.34 @ ( abs_abs_Code_integer
% 5.02/5.34 @ ( minus_8373710615458151222nteger
% 5.02/5.34 @ ( groups7713935264441627589nteger
% 5.02/5.34 @ ^ [I5: real] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7071_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_nat,X2: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.02/5.34 ( ! [I2: nat] :
% 5.02/5.34 ( ( member_nat @ I2 @ I6 )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups7501900531339628137nteger @ X2 @ I6 )
% 5.02/5.34 = one_one_Code_integer )
% 5.02/5.34 => ( ! [I2: nat] :
% 5.02/5.34 ( ( member_nat @ I2 @ I6 )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_le3102999989581377725nteger
% 5.02/5.34 @ ( abs_abs_Code_integer
% 5.02/5.34 @ ( minus_8373710615458151222nteger
% 5.02/5.34 @ ( groups7501900531339628137nteger
% 5.02/5.34 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7072_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_int,X2: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.02/5.34 ( ! [I2: int] :
% 5.02/5.34 ( ( member_int @ I2 @ I6 )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups7873554091576472773nteger @ X2 @ I6 )
% 5.02/5.34 = one_one_Code_integer )
% 5.02/5.34 => ( ! [I2: int] :
% 5.02/5.34 ( ( member_int @ I2 @ I6 )
% 5.02/5.34 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_le3102999989581377725nteger
% 5.02/5.34 @ ( abs_abs_Code_integer
% 5.02/5.34 @ ( minus_8373710615458151222nteger
% 5.02/5.34 @ ( groups7873554091576472773nteger
% 5.02/5.34 @ ^ [I5: int] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7073_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_complex,X2: complex > real,A: complex > real,B: real,Delta: real] :
% 5.02/5.34 ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups5808333547571424918x_real @ X2 @ I6 )
% 5.02/5.34 = one_one_real )
% 5.02/5.34 => ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_less_eq_real
% 5.02/5.34 @ ( abs_abs_real
% 5.02/5.34 @ ( minus_minus_real
% 5.02/5.34 @ ( groups5808333547571424918x_real
% 5.02/5.34 @ ^ [I5: complex] : ( times_times_real @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7074_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_real,X2: real > real,A: real > real,B: real,Delta: real] :
% 5.02/5.34 ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups8097168146408367636l_real @ X2 @ I6 )
% 5.02/5.34 = one_one_real )
% 5.02/5.34 => ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_less_eq_real
% 5.02/5.34 @ ( abs_abs_real
% 5.02/5.34 @ ( minus_minus_real
% 5.02/5.34 @ ( groups8097168146408367636l_real
% 5.02/5.34 @ ^ [I5: real] : ( times_times_real @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7075_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_int,X2: int > real,A: int > real,B: real,Delta: real] :
% 5.02/5.34 ( ! [I2: int] :
% 5.02/5.34 ( ( member_int @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups8778361861064173332t_real @ X2 @ I6 )
% 5.02/5.34 = one_one_real )
% 5.02/5.34 => ( ! [I2: int] :
% 5.02/5.34 ( ( member_int @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_less_eq_real
% 5.02/5.34 @ ( abs_abs_real
% 5.02/5.34 @ ( minus_minus_real
% 5.02/5.34 @ ( groups8778361861064173332t_real
% 5.02/5.34 @ ^ [I5: int] : ( times_times_real @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7076_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_complex,X2: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.02/5.34 ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups5058264527183730370ex_rat @ X2 @ I6 )
% 5.02/5.34 = one_one_rat )
% 5.02/5.34 => ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_less_eq_rat
% 5.02/5.34 @ ( abs_abs_rat
% 5.02/5.34 @ ( minus_minus_rat
% 5.02/5.34 @ ( groups5058264527183730370ex_rat
% 5.02/5.34 @ ^ [I5: complex] : ( times_times_rat @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7077_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_real,X2: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.02/5.34 ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups1300246762558778688al_rat @ X2 @ I6 )
% 5.02/5.34 = one_one_rat )
% 5.02/5.34 => ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_less_eq_rat
% 5.02/5.34 @ ( abs_abs_rat
% 5.02/5.34 @ ( minus_minus_rat
% 5.02/5.34 @ ( groups1300246762558778688al_rat
% 5.02/5.34 @ ^ [I5: real] : ( times_times_rat @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7078_convex__sum__bound__le,axiom,
% 5.02/5.34 ! [I6: set_nat,X2: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.02/5.34 ( ! [I2: nat] :
% 5.02/5.34 ( ( member_nat @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( X2 @ I2 ) ) )
% 5.02/5.34 => ( ( ( groups2906978787729119204at_rat @ X2 @ I6 )
% 5.02/5.34 = one_one_rat )
% 5.02/5.34 => ( ! [I2: nat] :
% 5.02/5.34 ( ( member_nat @ I2 @ I6 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 5.02/5.34 => ( ord_less_eq_rat
% 5.02/5.34 @ ( abs_abs_rat
% 5.02/5.34 @ ( minus_minus_rat
% 5.02/5.34 @ ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( X2 @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 @ B ) )
% 5.02/5.34 @ Delta ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % convex_sum_bound_le
% 5.02/5.34 thf(fact_7079_sum_Oneutral__const,axiom,
% 5.02/5.34 ! [A3: set_int] :
% 5.02/5.34 ( ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [Uu3: int] : zero_zero_int
% 5.02/5.34 @ A3 )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % sum.neutral_const
% 5.02/5.34 thf(fact_7080_sum_Oneutral__const,axiom,
% 5.02/5.34 ! [A3: set_complex] :
% 5.02/5.34 ( ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [Uu3: complex] : zero_zero_complex
% 5.02/5.34 @ A3 )
% 5.02/5.34 = zero_zero_complex ) ).
% 5.02/5.34
% 5.02/5.34 % sum.neutral_const
% 5.02/5.34 thf(fact_7081_sum_Oneutral__const,axiom,
% 5.02/5.34 ! [A3: set_nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [Uu3: nat] : zero_zero_nat
% 5.02/5.34 @ A3 )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % sum.neutral_const
% 5.02/5.34 thf(fact_7082_sum_Oneutral__const,axiom,
% 5.02/5.34 ! [A3: set_nat] :
% 5.02/5.34 ( ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [Uu3: nat] : zero_zero_real
% 5.02/5.34 @ A3 )
% 5.02/5.34 = zero_zero_real ) ).
% 5.02/5.34
% 5.02/5.34 % sum.neutral_const
% 5.02/5.34 thf(fact_7083_and__int_Oelims,axiom,
% 5.02/5.34 ! [X2: int,Xa2: int,Y: int] :
% 5.02/5.34 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.02/5.34 = Y )
% 5.02/5.34 => ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.02/5.34 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 = ( uminus_uminus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.02/5.34 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.02/5.34 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 = ( plus_plus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.02/5.34 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_int.elims
% 5.02/5.34 thf(fact_7084_insert__subset,axiom,
% 5.02/5.34 ! [X2: complex,A3: set_complex,B4: set_complex] :
% 5.02/5.34 ( ( ord_le211207098394363844omplex @ ( insert_complex @ X2 @ A3 ) @ B4 )
% 5.02/5.34 = ( ( member_complex @ X2 @ B4 )
% 5.02/5.34 & ( ord_le211207098394363844omplex @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % insert_subset
% 5.02/5.34 thf(fact_7085_insert__subset,axiom,
% 5.02/5.34 ! [X2: real,A3: set_real,B4: set_real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ ( insert_real @ X2 @ A3 ) @ B4 )
% 5.02/5.34 = ( ( member_real @ X2 @ B4 )
% 5.02/5.34 & ( ord_less_eq_set_real @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % insert_subset
% 5.02/5.34 thf(fact_7086_insert__subset,axiom,
% 5.02/5.34 ! [X2: set_nat,A3: set_set_nat,B4: set_set_nat] :
% 5.02/5.34 ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X2 @ A3 ) @ B4 )
% 5.02/5.34 = ( ( member_set_nat @ X2 @ B4 )
% 5.02/5.34 & ( ord_le6893508408891458716et_nat @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % insert_subset
% 5.02/5.34 thf(fact_7087_insert__subset,axiom,
% 5.02/5.34 ! [X2: int,A3: set_int,B4: set_int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ ( insert_int @ X2 @ A3 ) @ B4 )
% 5.02/5.34 = ( ( member_int @ X2 @ B4 )
% 5.02/5.34 & ( ord_less_eq_set_int @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % insert_subset
% 5.02/5.34 thf(fact_7088_insert__subset,axiom,
% 5.02/5.34 ! [X2: nat,A3: set_nat,B4: set_nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ ( insert_nat @ X2 @ A3 ) @ B4 )
% 5.02/5.34 = ( ( member_nat @ X2 @ B4 )
% 5.02/5.34 & ( ord_less_eq_set_nat @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % insert_subset
% 5.02/5.34 thf(fact_7089_singleton__insert__inj__eq_H,axiom,
% 5.02/5.34 ! [A: int,A3: set_int,B: int] :
% 5.02/5.34 ( ( ( insert_int @ A @ A3 )
% 5.02/5.34 = ( insert_int @ B @ bot_bot_set_int ) )
% 5.02/5.34 = ( ( A = B )
% 5.02/5.34 & ( ord_less_eq_set_int @ A3 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % singleton_insert_inj_eq'
% 5.02/5.34 thf(fact_7090_singleton__insert__inj__eq_H,axiom,
% 5.02/5.34 ! [A: real,A3: set_real,B: real] :
% 5.02/5.34 ( ( ( insert_real @ A @ A3 )
% 5.02/5.34 = ( insert_real @ B @ bot_bot_set_real ) )
% 5.02/5.34 = ( ( A = B )
% 5.02/5.34 & ( ord_less_eq_set_real @ A3 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % singleton_insert_inj_eq'
% 5.02/5.34 thf(fact_7091_singleton__insert__inj__eq_H,axiom,
% 5.02/5.34 ! [A: nat,A3: set_nat,B: nat] :
% 5.02/5.34 ( ( ( insert_nat @ A @ A3 )
% 5.02/5.34 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 5.02/5.34 = ( ( A = B )
% 5.02/5.34 & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % singleton_insert_inj_eq'
% 5.02/5.34 thf(fact_7092_singleton__insert__inj__eq,axiom,
% 5.02/5.34 ! [B: int,A: int,A3: set_int] :
% 5.02/5.34 ( ( ( insert_int @ B @ bot_bot_set_int )
% 5.02/5.34 = ( insert_int @ A @ A3 ) )
% 5.02/5.34 = ( ( A = B )
% 5.02/5.34 & ( ord_less_eq_set_int @ A3 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % singleton_insert_inj_eq
% 5.02/5.34 thf(fact_7093_singleton__insert__inj__eq,axiom,
% 5.02/5.34 ! [B: real,A: real,A3: set_real] :
% 5.02/5.34 ( ( ( insert_real @ B @ bot_bot_set_real )
% 5.02/5.34 = ( insert_real @ A @ A3 ) )
% 5.02/5.34 = ( ( A = B )
% 5.02/5.34 & ( ord_less_eq_set_real @ A3 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % singleton_insert_inj_eq
% 5.02/5.34 thf(fact_7094_singleton__insert__inj__eq,axiom,
% 5.02/5.34 ! [B: nat,A: nat,A3: set_nat] :
% 5.02/5.34 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 5.02/5.34 = ( insert_nat @ A @ A3 ) )
% 5.02/5.34 = ( ( A = B )
% 5.02/5.34 & ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % singleton_insert_inj_eq
% 5.02/5.34 thf(fact_7095_and__nat__numerals_I3_J,axiom,
% 5.02/5.34 ! [X2: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_nat_numerals(3)
% 5.02/5.34 thf(fact_7096_and__nat__numerals_I1_J,axiom,
% 5.02/5.34 ! [Y: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_nat_numerals(1)
% 5.02/5.34 thf(fact_7097_subset__Compl__singleton,axiom,
% 5.02/5.34 ! [A3: set_complex,B: complex] :
% 5.02/5.34 ( ( ord_le211207098394363844omplex @ A3 @ ( uminus8566677241136511917omplex @ ( insert_complex @ B @ bot_bot_set_complex ) ) )
% 5.02/5.34 = ( ~ ( member_complex @ B @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Compl_singleton
% 5.02/5.34 thf(fact_7098_subset__Compl__singleton,axiom,
% 5.02/5.34 ! [A3: set_set_nat,B: set_nat] :
% 5.02/5.34 ( ( ord_le6893508408891458716et_nat @ A3 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 5.02/5.34 = ( ~ ( member_set_nat @ B @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Compl_singleton
% 5.02/5.34 thf(fact_7099_subset__Compl__singleton,axiom,
% 5.02/5.34 ! [A3: set_int,B: int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 5.02/5.34 = ( ~ ( member_int @ B @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Compl_singleton
% 5.02/5.34 thf(fact_7100_subset__Compl__singleton,axiom,
% 5.02/5.34 ! [A3: set_real,B: real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ A3 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 5.02/5.34 = ( ~ ( member_real @ B @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Compl_singleton
% 5.02/5.34 thf(fact_7101_subset__Compl__singleton,axiom,
% 5.02/5.34 ! [A3: set_nat,B: nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 5.02/5.34 = ( ~ ( member_nat @ B @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Compl_singleton
% 5.02/5.34 thf(fact_7102_sum_Ocl__ivl__Suc,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,G: nat > complex] :
% 5.02/5.34 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = zero_zero_complex ) )
% 5.02/5.34 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.cl_ivl_Suc
% 5.02/5.34 thf(fact_7103_sum_Ocl__ivl__Suc,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,G: nat > rat] :
% 5.02/5.34 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = zero_zero_rat ) )
% 5.02/5.34 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.cl_ivl_Suc
% 5.02/5.34 thf(fact_7104_sum_Ocl__ivl__Suc,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,G: nat > int] :
% 5.02/5.34 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = zero_zero_int ) )
% 5.02/5.34 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.cl_ivl_Suc
% 5.02/5.34 thf(fact_7105_sum_Ocl__ivl__Suc,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,G: nat > nat] :
% 5.02/5.34 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = zero_zero_nat ) )
% 5.02/5.34 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.cl_ivl_Suc
% 5.02/5.34 thf(fact_7106_sum_Ocl__ivl__Suc,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,G: nat > real] :
% 5.02/5.34 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = zero_zero_real ) )
% 5.02/5.34 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.cl_ivl_Suc
% 5.02/5.34 thf(fact_7107_and__nat__numerals_I4_J,axiom,
% 5.02/5.34 ! [X2: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.02/5.34 = one_one_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_nat_numerals(4)
% 5.02/5.34 thf(fact_7108_and__nat__numerals_I2_J,axiom,
% 5.02/5.34 ! [Y: num] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.34 = one_one_nat ) ).
% 5.02/5.34
% 5.02/5.34 % and_nat_numerals(2)
% 5.02/5.34 thf(fact_7109_set__replicate,axiom,
% 5.02/5.34 ! [N2: nat,X2: vEBT_VEBT] :
% 5.02/5.34 ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X2 ) )
% 5.02/5.34 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate
% 5.02/5.34 thf(fact_7110_set__replicate,axiom,
% 5.02/5.34 ! [N2: nat,X2: nat] :
% 5.02/5.34 ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X2 ) )
% 5.02/5.34 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate
% 5.02/5.34 thf(fact_7111_set__replicate,axiom,
% 5.02/5.34 ! [N2: nat,X2: int] :
% 5.02/5.34 ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( ( set_int2 @ ( replicate_int @ N2 @ X2 ) )
% 5.02/5.34 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate
% 5.02/5.34 thf(fact_7112_set__replicate,axiom,
% 5.02/5.34 ! [N2: nat,X2: real] :
% 5.02/5.34 ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( ( set_real2 @ ( replicate_real @ N2 @ X2 ) )
% 5.02/5.34 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate
% 5.02/5.34 thf(fact_7113_Suc__0__and__eq,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.02/5.34 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % Suc_0_and_eq
% 5.02/5.34 thf(fact_7114_and__Suc__0__eq,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.02/5.34 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_Suc_0_eq
% 5.02/5.34 thf(fact_7115_insert__mono,axiom,
% 5.02/5.34 ! [C5: set_int,D4: set_int,A: int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ C5 @ D4 )
% 5.02/5.34 => ( ord_less_eq_set_int @ ( insert_int @ A @ C5 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % insert_mono
% 5.02/5.34 thf(fact_7116_insert__mono,axiom,
% 5.02/5.34 ! [C5: set_real,D4: set_real,A: real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ C5 @ D4 )
% 5.02/5.34 => ( ord_less_eq_set_real @ ( insert_real @ A @ C5 ) @ ( insert_real @ A @ D4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % insert_mono
% 5.02/5.34 thf(fact_7117_insert__mono,axiom,
% 5.02/5.34 ! [C5: set_nat,D4: set_nat,A: nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ C5 @ D4 )
% 5.02/5.34 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C5 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % insert_mono
% 5.02/5.34 thf(fact_7118_subset__insert,axiom,
% 5.02/5.34 ! [X2: complex,A3: set_complex,B4: set_complex] :
% 5.02/5.34 ( ~ ( member_complex @ X2 @ A3 )
% 5.02/5.34 => ( ( ord_le211207098394363844omplex @ A3 @ ( insert_complex @ X2 @ B4 ) )
% 5.02/5.34 = ( ord_le211207098394363844omplex @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert
% 5.02/5.34 thf(fact_7119_subset__insert,axiom,
% 5.02/5.34 ! [X2: real,A3: set_real,B4: set_real] :
% 5.02/5.34 ( ~ ( member_real @ X2 @ A3 )
% 5.02/5.34 => ( ( ord_less_eq_set_real @ A3 @ ( insert_real @ X2 @ B4 ) )
% 5.02/5.34 = ( ord_less_eq_set_real @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert
% 5.02/5.34 thf(fact_7120_subset__insert,axiom,
% 5.02/5.34 ! [X2: set_nat,A3: set_set_nat,B4: set_set_nat] :
% 5.02/5.34 ( ~ ( member_set_nat @ X2 @ A3 )
% 5.02/5.34 => ( ( ord_le6893508408891458716et_nat @ A3 @ ( insert_set_nat @ X2 @ B4 ) )
% 5.02/5.34 = ( ord_le6893508408891458716et_nat @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert
% 5.02/5.34 thf(fact_7121_subset__insert,axiom,
% 5.02/5.34 ! [X2: int,A3: set_int,B4: set_int] :
% 5.02/5.34 ( ~ ( member_int @ X2 @ A3 )
% 5.02/5.34 => ( ( ord_less_eq_set_int @ A3 @ ( insert_int @ X2 @ B4 ) )
% 5.02/5.34 = ( ord_less_eq_set_int @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert
% 5.02/5.34 thf(fact_7122_subset__insert,axiom,
% 5.02/5.34 ! [X2: nat,A3: set_nat,B4: set_nat] :
% 5.02/5.34 ( ~ ( member_nat @ X2 @ A3 )
% 5.02/5.34 => ( ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ X2 @ B4 ) )
% 5.02/5.34 = ( ord_less_eq_set_nat @ A3 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert
% 5.02/5.34 thf(fact_7123_subset__insertI,axiom,
% 5.02/5.34 ! [B4: set_int,A: int] : ( ord_less_eq_set_int @ B4 @ ( insert_int @ A @ B4 ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insertI
% 5.02/5.34 thf(fact_7124_subset__insertI,axiom,
% 5.02/5.34 ! [B4: set_real,A: real] : ( ord_less_eq_set_real @ B4 @ ( insert_real @ A @ B4 ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insertI
% 5.02/5.34 thf(fact_7125_subset__insertI,axiom,
% 5.02/5.34 ! [B4: set_nat,A: nat] : ( ord_less_eq_set_nat @ B4 @ ( insert_nat @ A @ B4 ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insertI
% 5.02/5.34 thf(fact_7126_subset__insertI2,axiom,
% 5.02/5.34 ! [A3: set_int,B4: set_int,B: int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ A3 @ B4 )
% 5.02/5.34 => ( ord_less_eq_set_int @ A3 @ ( insert_int @ B @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insertI2
% 5.02/5.34 thf(fact_7127_subset__insertI2,axiom,
% 5.02/5.34 ! [A3: set_real,B4: set_real,B: real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ A3 @ B4 )
% 5.02/5.34 => ( ord_less_eq_set_real @ A3 @ ( insert_real @ B @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insertI2
% 5.02/5.34 thf(fact_7128_subset__insertI2,axiom,
% 5.02/5.34 ! [A3: set_nat,B4: set_nat,B: nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ A3 @ B4 )
% 5.02/5.34 => ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ B @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insertI2
% 5.02/5.34 thf(fact_7129_sum__cong__Suc,axiom,
% 5.02/5.34 ! [A3: set_nat,F: nat > nat,G: nat > nat] :
% 5.02/5.34 ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 5.02/5.34 => ( ! [X5: nat] :
% 5.02/5.34 ( ( member_nat @ ( suc @ X5 ) @ A3 )
% 5.02/5.34 => ( ( F @ ( suc @ X5 ) )
% 5.02/5.34 = ( G @ ( suc @ X5 ) ) ) )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat @ F @ A3 )
% 5.02/5.34 = ( groups3542108847815614940at_nat @ G @ A3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_cong_Suc
% 5.02/5.34 thf(fact_7130_sum__cong__Suc,axiom,
% 5.02/5.34 ! [A3: set_nat,F: nat > real,G: nat > real] :
% 5.02/5.34 ( ~ ( member_nat @ zero_zero_nat @ A3 )
% 5.02/5.34 => ( ! [X5: nat] :
% 5.02/5.34 ( ( member_nat @ ( suc @ X5 ) @ A3 )
% 5.02/5.34 => ( ( F @ ( suc @ X5 ) )
% 5.02/5.34 = ( G @ ( suc @ X5 ) ) ) )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ F @ A3 )
% 5.02/5.34 = ( groups6591440286371151544t_real @ G @ A3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_cong_Suc
% 5.02/5.34 thf(fact_7131_sum__subtractf__nat,axiom,
% 5.02/5.34 ! [A3: set_complex,G: complex > nat,F: complex > nat] :
% 5.02/5.34 ( ! [X5: complex] :
% 5.02/5.34 ( ( member_complex @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ( groups5693394587270226106ex_nat
% 5.02/5.34 @ ^ [X: complex] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ ( groups5693394587270226106ex_nat @ G @ A3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_subtractf_nat
% 5.02/5.34 thf(fact_7132_sum__subtractf__nat,axiom,
% 5.02/5.34 ! [A3: set_real,G: real > nat,F: real > nat] :
% 5.02/5.34 ( ! [X5: real] :
% 5.02/5.34 ( ( member_real @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ( groups1935376822645274424al_nat
% 5.02/5.34 @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ ( groups1935376822645274424al_nat @ G @ A3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_subtractf_nat
% 5.02/5.34 thf(fact_7133_sum__subtractf__nat,axiom,
% 5.02/5.34 ! [A3: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 5.02/5.34 ( ! [X5: set_nat] :
% 5.02/5.34 ( ( member_set_nat @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ( groups8294997508430121362at_nat
% 5.02/5.34 @ ^ [X: set_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A3 ) @ ( groups8294997508430121362at_nat @ G @ A3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_subtractf_nat
% 5.02/5.34 thf(fact_7134_sum__subtractf__nat,axiom,
% 5.02/5.34 ! [A3: set_int,G: int > nat,F: int > nat] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( member_int @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ( groups4541462559716669496nt_nat
% 5.02/5.34 @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_subtractf_nat
% 5.02/5.34 thf(fact_7135_sum__subtractf__nat,axiom,
% 5.02/5.34 ! [A3: set_nat,G: nat > nat,F: nat > nat] :
% 5.02/5.34 ( ! [X5: nat] :
% 5.02/5.34 ( ( member_nat @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ G @ A3 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_subtractf_nat
% 5.02/5.34 thf(fact_7136_sum__SucD,axiom,
% 5.02/5.34 ! [F: nat > nat,A3: set_nat,N2: nat] :
% 5.02/5.34 ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 5.02/5.34 = ( suc @ N2 ) )
% 5.02/5.34 => ? [X5: nat] :
% 5.02/5.34 ( ( member_nat @ X5 @ A3 )
% 5.02/5.34 & ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_SucD
% 5.02/5.34 thf(fact_7137_subset__singleton__iff,axiom,
% 5.02/5.34 ! [X8: set_int,A: int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 5.02/5.34 = ( ( X8 = bot_bot_set_int )
% 5.02/5.34 | ( X8
% 5.02/5.34 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_singleton_iff
% 5.02/5.34 thf(fact_7138_subset__singleton__iff,axiom,
% 5.02/5.34 ! [X8: set_real,A: real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 5.02/5.34 = ( ( X8 = bot_bot_set_real )
% 5.02/5.34 | ( X8
% 5.02/5.34 = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_singleton_iff
% 5.02/5.34 thf(fact_7139_subset__singleton__iff,axiom,
% 5.02/5.34 ! [X8: set_nat,A: nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 5.02/5.34 = ( ( X8 = bot_bot_set_nat )
% 5.02/5.34 | ( X8
% 5.02/5.34 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_singleton_iff
% 5.02/5.34 thf(fact_7140_subset__singletonD,axiom,
% 5.02/5.34 ! [A3: set_int,X2: int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 5.02/5.34 => ( ( A3 = bot_bot_set_int )
% 5.02/5.34 | ( A3
% 5.02/5.34 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_singletonD
% 5.02/5.34 thf(fact_7141_subset__singletonD,axiom,
% 5.02/5.34 ! [A3: set_real,X2: real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) )
% 5.02/5.34 => ( ( A3 = bot_bot_set_real )
% 5.02/5.34 | ( A3
% 5.02/5.34 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_singletonD
% 5.02/5.34 thf(fact_7142_subset__singletonD,axiom,
% 5.02/5.34 ! [A3: set_nat,X2: nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 5.02/5.34 => ( ( A3 = bot_bot_set_nat )
% 5.02/5.34 | ( A3
% 5.02/5.34 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_singletonD
% 5.02/5.34 thf(fact_7143_subset__Diff__insert,axiom,
% 5.02/5.34 ! [A3: set_complex,B4: set_complex,X2: complex,C5: set_complex] :
% 5.02/5.34 ( ( ord_le211207098394363844omplex @ A3 @ ( minus_811609699411566653omplex @ B4 @ ( insert_complex @ X2 @ C5 ) ) )
% 5.02/5.34 = ( ( ord_le211207098394363844omplex @ A3 @ ( minus_811609699411566653omplex @ B4 @ C5 ) )
% 5.02/5.34 & ~ ( member_complex @ X2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Diff_insert
% 5.02/5.34 thf(fact_7144_subset__Diff__insert,axiom,
% 5.02/5.34 ! [A3: set_real,B4: set_real,X2: real,C5: set_real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ A3 @ ( minus_minus_set_real @ B4 @ ( insert_real @ X2 @ C5 ) ) )
% 5.02/5.34 = ( ( ord_less_eq_set_real @ A3 @ ( minus_minus_set_real @ B4 @ C5 ) )
% 5.02/5.34 & ~ ( member_real @ X2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Diff_insert
% 5.02/5.34 thf(fact_7145_subset__Diff__insert,axiom,
% 5.02/5.34 ! [A3: set_set_nat,B4: set_set_nat,X2: set_nat,C5: set_set_nat] :
% 5.02/5.34 ( ( ord_le6893508408891458716et_nat @ A3 @ ( minus_2163939370556025621et_nat @ B4 @ ( insert_set_nat @ X2 @ C5 ) ) )
% 5.02/5.34 = ( ( ord_le6893508408891458716et_nat @ A3 @ ( minus_2163939370556025621et_nat @ B4 @ C5 ) )
% 5.02/5.34 & ~ ( member_set_nat @ X2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Diff_insert
% 5.02/5.34 thf(fact_7146_subset__Diff__insert,axiom,
% 5.02/5.34 ! [A3: set_int,B4: set_int,X2: int,C5: set_int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ A3 @ ( minus_minus_set_int @ B4 @ ( insert_int @ X2 @ C5 ) ) )
% 5.02/5.34 = ( ( ord_less_eq_set_int @ A3 @ ( minus_minus_set_int @ B4 @ C5 ) )
% 5.02/5.34 & ~ ( member_int @ X2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Diff_insert
% 5.02/5.34 thf(fact_7147_subset__Diff__insert,axiom,
% 5.02/5.34 ! [A3: set_nat,B4: set_nat,X2: nat,C5: set_nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ A3 @ ( minus_minus_set_nat @ B4 @ ( insert_nat @ X2 @ C5 ) ) )
% 5.02/5.34 = ( ( ord_less_eq_set_nat @ A3 @ ( minus_minus_set_nat @ B4 @ C5 ) )
% 5.02/5.34 & ~ ( member_nat @ X2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_Diff_insert
% 5.02/5.34 thf(fact_7148_sum__nth__roots,axiom,
% 5.02/5.34 ! [N2: nat,C: complex] :
% 5.02/5.34 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.02/5.34 => ( ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [X: complex] : X
% 5.02/5.34 @ ( collect_complex
% 5.02/5.34 @ ^ [Z6: complex] :
% 5.02/5.34 ( ( power_power_complex @ Z6 @ N2 )
% 5.02/5.34 = C ) ) )
% 5.02/5.34 = zero_zero_complex ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nth_roots
% 5.02/5.34 thf(fact_7149_sum__roots__unity,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.02/5.34 => ( ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [X: complex] : X
% 5.02/5.34 @ ( collect_complex
% 5.02/5.34 @ ^ [Z6: complex] :
% 5.02/5.34 ( ( power_power_complex @ Z6 @ N2 )
% 5.02/5.34 = one_one_complex ) ) )
% 5.02/5.34 = zero_zero_complex ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_roots_unity
% 5.02/5.34 thf(fact_7150_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.02/5.34 ! [G: nat > nat,M: nat,N2: nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.shift_bounds_cl_Suc_ivl
% 5.02/5.34 thf(fact_7151_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.02/5.34 ! [G: nat > real,M: nat,N2: nat] :
% 5.02/5.34 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.shift_bounds_cl_Suc_ivl
% 5.02/5.34 thf(fact_7152_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.02/5.34 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.shift_bounds_cl_nat_ivl
% 5.02/5.34 thf(fact_7153_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.02/5.34 ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 5.02/5.34 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.shift_bounds_cl_nat_ivl
% 5.02/5.34 thf(fact_7154_Diff__single__insert,axiom,
% 5.02/5.34 ! [A3: set_int,X2: int,B4: set_int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B4 )
% 5.02/5.34 => ( ord_less_eq_set_int @ A3 @ ( insert_int @ X2 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % Diff_single_insert
% 5.02/5.34 thf(fact_7155_Diff__single__insert,axiom,
% 5.02/5.34 ! [A3: set_real,X2: real,B4: set_real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B4 )
% 5.02/5.34 => ( ord_less_eq_set_real @ A3 @ ( insert_real @ X2 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % Diff_single_insert
% 5.02/5.34 thf(fact_7156_Diff__single__insert,axiom,
% 5.02/5.34 ! [A3: set_nat,X2: nat,B4: set_nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B4 )
% 5.02/5.34 => ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ X2 @ B4 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % Diff_single_insert
% 5.02/5.34 thf(fact_7157_subset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_complex,X2: complex,B4: set_complex] :
% 5.02/5.34 ( ( ord_le211207098394363844omplex @ A3 @ ( insert_complex @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_complex @ X2 @ A3 )
% 5.02/5.34 => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_complex @ X2 @ A3 )
% 5.02/5.34 => ( ord_le211207098394363844omplex @ A3 @ B4 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert_iff
% 5.02/5.34 thf(fact_7158_subset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_set_nat,X2: set_nat,B4: set_set_nat] :
% 5.02/5.34 ( ( ord_le6893508408891458716et_nat @ A3 @ ( insert_set_nat @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_set_nat @ X2 @ A3 )
% 5.02/5.34 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_set_nat @ X2 @ A3 )
% 5.02/5.34 => ( ord_le6893508408891458716et_nat @ A3 @ B4 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert_iff
% 5.02/5.34 thf(fact_7159_subset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_int,X2: int,B4: set_int] :
% 5.02/5.34 ( ( ord_less_eq_set_int @ A3 @ ( insert_int @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_int @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_int @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_int @ A3 @ B4 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert_iff
% 5.02/5.34 thf(fact_7160_subset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_real,X2: real,B4: set_real] :
% 5.02/5.34 ( ( ord_less_eq_set_real @ A3 @ ( insert_real @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_real @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_real @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_real @ A3 @ B4 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert_iff
% 5.02/5.34 thf(fact_7161_subset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_nat,X2: nat,B4: set_nat] :
% 5.02/5.34 ( ( ord_less_eq_set_nat @ A3 @ ( insert_nat @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_nat @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_nat @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_nat @ A3 @ B4 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % subset_insert_iff
% 5.02/5.34 thf(fact_7162_set__update__subset__insert,axiom,
% 5.02/5.34 ! [Xs: list_real,I3: nat,X2: real] : ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I3 @ X2 ) ) @ ( insert_real @ X2 @ ( set_real2 @ Xs ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_update_subset_insert
% 5.02/5.34 thf(fact_7163_set__update__subset__insert,axiom,
% 5.02/5.34 ! [Xs: list_int,I3: nat,X2: int] : ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I3 @ X2 ) ) @ ( insert_int @ X2 @ ( set_int2 @ Xs ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_update_subset_insert
% 5.02/5.34 thf(fact_7164_set__update__subset__insert,axiom,
% 5.02/5.34 ! [Xs: list_VEBT_VEBT,I3: nat,X2: vEBT_VEBT] : ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X2 ) ) @ ( insert_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_update_subset_insert
% 5.02/5.34 thf(fact_7165_set__update__subset__insert,axiom,
% 5.02/5.34 ! [Xs: list_nat,I3: nat,X2: nat] : ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I3 @ X2 ) ) @ ( insert_nat @ X2 @ ( set_nat2 @ Xs ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_update_subset_insert
% 5.02/5.34 thf(fact_7166_sum__power__add,axiom,
% 5.02/5.34 ! [X2: complex,M: nat,I6: set_nat] :
% 5.02/5.34 ( ( groups2073611262835488442omplex
% 5.02/5.34 @ ^ [I5: nat] : ( power_power_complex @ X2 @ ( plus_plus_nat @ M @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ I6 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_power_add
% 5.02/5.34 thf(fact_7167_sum__power__add,axiom,
% 5.02/5.34 ! [X2: rat,M: nat,I6: set_nat] :
% 5.02/5.34 ( ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [I5: nat] : ( power_power_rat @ X2 @ ( plus_plus_nat @ M @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ I6 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_power_add
% 5.02/5.34 thf(fact_7168_sum__power__add,axiom,
% 5.02/5.34 ! [X2: int,M: nat,I6: set_nat] :
% 5.02/5.34 ( ( groups3539618377306564664at_int
% 5.02/5.34 @ ^ [I5: nat] : ( power_power_int @ X2 @ ( plus_plus_nat @ M @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ I6 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_power_add
% 5.02/5.34 thf(fact_7169_sum__power__add,axiom,
% 5.02/5.34 ! [X2: real,M: nat,I6: set_nat] :
% 5.02/5.34 ( ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( power_power_real @ X2 @ ( plus_plus_nat @ M @ I5 ) )
% 5.02/5.34 @ I6 )
% 5.02/5.34 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ I6 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_power_add
% 5.02/5.34 thf(fact_7170_sum_OatLeastAtMost__rev,axiom,
% 5.02/5.34 ! [G: nat > nat,N2: nat,M: nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeastAtMost_rev
% 5.02/5.34 thf(fact_7171_sum_OatLeastAtMost__rev,axiom,
% 5.02/5.34 ! [G: nat > real,N2: nat,M: nat] :
% 5.02/5.34 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeastAtMost_rev
% 5.02/5.34 thf(fact_7172_sum__shift__lb__Suc0__0,axiom,
% 5.02/5.34 ! [F: nat > complex,K: nat] :
% 5.02/5.34 ( ( ( F @ zero_zero_nat )
% 5.02/5.34 = zero_zero_complex )
% 5.02/5.34 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.02/5.34 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_shift_lb_Suc0_0
% 5.02/5.34 thf(fact_7173_sum__shift__lb__Suc0__0,axiom,
% 5.02/5.34 ! [F: nat > rat,K: nat] :
% 5.02/5.34 ( ( ( F @ zero_zero_nat )
% 5.02/5.34 = zero_zero_rat )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.02/5.34 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_shift_lb_Suc0_0
% 5.02/5.34 thf(fact_7174_sum__shift__lb__Suc0__0,axiom,
% 5.02/5.34 ! [F: nat > int,K: nat] :
% 5.02/5.34 ( ( ( F @ zero_zero_nat )
% 5.02/5.34 = zero_zero_int )
% 5.02/5.34 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.02/5.34 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_shift_lb_Suc0_0
% 5.02/5.34 thf(fact_7175_sum__shift__lb__Suc0__0,axiom,
% 5.02/5.34 ! [F: nat > nat,K: nat] :
% 5.02/5.34 ( ( ( F @ zero_zero_nat )
% 5.02/5.34 = zero_zero_nat )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_shift_lb_Suc0_0
% 5.02/5.34 thf(fact_7176_sum__shift__lb__Suc0__0,axiom,
% 5.02/5.34 ! [F: nat > real,K: nat] :
% 5.02/5.34 ( ( ( F @ zero_zero_nat )
% 5.02/5.34 = zero_zero_real )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.02/5.34 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_shift_lb_Suc0_0
% 5.02/5.34 thf(fact_7177_sum_OatLeast0__atMost__Suc,axiom,
% 5.02/5.34 ! [G: nat > rat,N2: nat] :
% 5.02/5.34 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeast0_atMost_Suc
% 5.02/5.34 thf(fact_7178_sum_OatLeast0__atMost__Suc,axiom,
% 5.02/5.34 ! [G: nat > int,N2: nat] :
% 5.02/5.34 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeast0_atMost_Suc
% 5.02/5.34 thf(fact_7179_sum_OatLeast0__atMost__Suc,axiom,
% 5.02/5.34 ! [G: nat > nat,N2: nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeast0_atMost_Suc
% 5.02/5.34 thf(fact_7180_sum_OatLeast0__atMost__Suc,axiom,
% 5.02/5.34 ! [G: nat > real,N2: nat] :
% 5.02/5.34 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeast0_atMost_Suc
% 5.02/5.34 thf(fact_7181_sum_Onat__ivl__Suc_H,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > rat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.nat_ivl_Suc'
% 5.02/5.34 thf(fact_7182_sum_Onat__ivl__Suc_H,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > int] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.34 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.nat_ivl_Suc'
% 5.02/5.34 thf(fact_7183_sum_Onat__ivl__Suc_H,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.nat_ivl_Suc'
% 5.02/5.34 thf(fact_7184_sum_Onat__ivl__Suc_H,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > real] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.nat_ivl_Suc'
% 5.02/5.34 thf(fact_7185_sum_OatLeast__Suc__atMost,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > rat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeast_Suc_atMost
% 5.02/5.34 thf(fact_7186_sum_OatLeast__Suc__atMost,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > int] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeast_Suc_atMost
% 5.02/5.34 thf(fact_7187_sum_OatLeast__Suc__atMost,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeast_Suc_atMost
% 5.02/5.34 thf(fact_7188_sum_OatLeast__Suc__atMost,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > real] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.atLeast_Suc_atMost
% 5.02/5.34 thf(fact_7189_psubset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_complex,X2: complex,B4: set_complex] :
% 5.02/5.34 ( ( ord_less_set_complex @ A3 @ ( insert_complex @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_complex @ X2 @ B4 )
% 5.02/5.34 => ( ord_less_set_complex @ A3 @ B4 ) )
% 5.02/5.34 & ( ~ ( member_complex @ X2 @ B4 )
% 5.02/5.34 => ( ( ( member_complex @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A3 @ ( insert_complex @ X2 @ bot_bot_set_complex ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_complex @ X2 @ A3 )
% 5.02/5.34 => ( ord_le211207098394363844omplex @ A3 @ B4 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % psubset_insert_iff
% 5.02/5.34 thf(fact_7190_psubset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_set_nat,X2: set_nat,B4: set_set_nat] :
% 5.02/5.34 ( ( ord_less_set_set_nat @ A3 @ ( insert_set_nat @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_set_nat @ X2 @ B4 )
% 5.02/5.34 => ( ord_less_set_set_nat @ A3 @ B4 ) )
% 5.02/5.34 & ( ~ ( member_set_nat @ X2 @ B4 )
% 5.02/5.34 => ( ( ( member_set_nat @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_set_nat @ X2 @ A3 )
% 5.02/5.34 => ( ord_le6893508408891458716et_nat @ A3 @ B4 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % psubset_insert_iff
% 5.02/5.34 thf(fact_7191_psubset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_int,X2: int,B4: set_int] :
% 5.02/5.34 ( ( ord_less_set_int @ A3 @ ( insert_int @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_int @ X2 @ B4 )
% 5.02/5.34 => ( ord_less_set_int @ A3 @ B4 ) )
% 5.02/5.34 & ( ~ ( member_int @ X2 @ B4 )
% 5.02/5.34 => ( ( ( member_int @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_set_int @ ( minus_minus_set_int @ A3 @ ( insert_int @ X2 @ bot_bot_set_int ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_int @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_int @ A3 @ B4 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % psubset_insert_iff
% 5.02/5.34 thf(fact_7192_psubset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_real,X2: real,B4: set_real] :
% 5.02/5.34 ( ( ord_less_set_real @ A3 @ ( insert_real @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_real @ X2 @ B4 )
% 5.02/5.34 => ( ord_less_set_real @ A3 @ B4 ) )
% 5.02/5.34 & ( ~ ( member_real @ X2 @ B4 )
% 5.02/5.34 => ( ( ( member_real @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_set_real @ ( minus_minus_set_real @ A3 @ ( insert_real @ X2 @ bot_bot_set_real ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_real @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_real @ A3 @ B4 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % psubset_insert_iff
% 5.02/5.34 thf(fact_7193_psubset__insert__iff,axiom,
% 5.02/5.34 ! [A3: set_nat,X2: nat,B4: set_nat] :
% 5.02/5.34 ( ( ord_less_set_nat @ A3 @ ( insert_nat @ X2 @ B4 ) )
% 5.02/5.34 = ( ( ( member_nat @ X2 @ B4 )
% 5.02/5.34 => ( ord_less_set_nat @ A3 @ B4 ) )
% 5.02/5.34 & ( ~ ( member_nat @ X2 @ B4 )
% 5.02/5.34 => ( ( ( member_nat @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A3 @ ( insert_nat @ X2 @ bot_bot_set_nat ) ) @ B4 ) )
% 5.02/5.34 & ( ~ ( member_nat @ X2 @ A3 )
% 5.02/5.34 => ( ord_less_eq_set_nat @ A3 @ B4 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % psubset_insert_iff
% 5.02/5.34 thf(fact_7194_set__replicate__Suc,axiom,
% 5.02/5.34 ! [N2: nat,X2: vEBT_VEBT] :
% 5.02/5.34 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N2 ) @ X2 ) )
% 5.02/5.34 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate_Suc
% 5.02/5.34 thf(fact_7195_set__replicate__Suc,axiom,
% 5.02/5.34 ! [N2: nat,X2: nat] :
% 5.02/5.34 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N2 ) @ X2 ) )
% 5.02/5.34 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate_Suc
% 5.02/5.34 thf(fact_7196_set__replicate__Suc,axiom,
% 5.02/5.34 ! [N2: nat,X2: int] :
% 5.02/5.34 ( ( set_int2 @ ( replicate_int @ ( suc @ N2 ) @ X2 ) )
% 5.02/5.34 = ( insert_int @ X2 @ bot_bot_set_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate_Suc
% 5.02/5.34 thf(fact_7197_set__replicate__Suc,axiom,
% 5.02/5.34 ! [N2: nat,X2: real] :
% 5.02/5.34 ( ( set_real2 @ ( replicate_real @ ( suc @ N2 ) @ X2 ) )
% 5.02/5.34 = ( insert_real @ X2 @ bot_bot_set_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate_Suc
% 5.02/5.34 thf(fact_7198_set__replicate__conv__if,axiom,
% 5.02/5.34 ! [N2: nat,X2: vEBT_VEBT] :
% 5.02/5.34 ( ( ( N2 = zero_zero_nat )
% 5.02/5.34 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X2 ) )
% 5.02/5.34 = bot_bo8194388402131092736T_VEBT ) )
% 5.02/5.34 & ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ X2 ) )
% 5.02/5.34 = ( insert_VEBT_VEBT @ X2 @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate_conv_if
% 5.02/5.34 thf(fact_7199_set__replicate__conv__if,axiom,
% 5.02/5.34 ! [N2: nat,X2: nat] :
% 5.02/5.34 ( ( ( N2 = zero_zero_nat )
% 5.02/5.34 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X2 ) )
% 5.02/5.34 = bot_bot_set_nat ) )
% 5.02/5.34 & ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( ( set_nat2 @ ( replicate_nat @ N2 @ X2 ) )
% 5.02/5.34 = ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate_conv_if
% 5.02/5.34 thf(fact_7200_set__replicate__conv__if,axiom,
% 5.02/5.34 ! [N2: nat,X2: int] :
% 5.02/5.34 ( ( ( N2 = zero_zero_nat )
% 5.02/5.34 => ( ( set_int2 @ ( replicate_int @ N2 @ X2 ) )
% 5.02/5.34 = bot_bot_set_int ) )
% 5.02/5.34 & ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( ( set_int2 @ ( replicate_int @ N2 @ X2 ) )
% 5.02/5.34 = ( insert_int @ X2 @ bot_bot_set_int ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate_conv_if
% 5.02/5.34 thf(fact_7201_set__replicate__conv__if,axiom,
% 5.02/5.34 ! [N2: nat,X2: real] :
% 5.02/5.34 ( ( ( N2 = zero_zero_nat )
% 5.02/5.34 => ( ( set_real2 @ ( replicate_real @ N2 @ X2 ) )
% 5.02/5.34 = bot_bot_set_real ) )
% 5.02/5.34 & ( ( N2 != zero_zero_nat )
% 5.02/5.34 => ( ( set_real2 @ ( replicate_real @ N2 @ X2 ) )
% 5.02/5.34 = ( insert_real @ X2 @ bot_bot_set_real ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % set_replicate_conv_if
% 5.02/5.34 thf(fact_7202_sum_OSuc__reindex__ivl,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > rat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_rat @ ( G @ M )
% 5.02/5.34 @ ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.Suc_reindex_ivl
% 5.02/5.34 thf(fact_7203_sum_OSuc__reindex__ivl,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > int] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_int @ ( G @ M )
% 5.02/5.34 @ ( groups3539618377306564664at_int
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.Suc_reindex_ivl
% 5.02/5.34 thf(fact_7204_sum_OSuc__reindex__ivl,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_nat @ ( G @ M )
% 5.02/5.34 @ ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.Suc_reindex_ivl
% 5.02/5.34 thf(fact_7205_sum_OSuc__reindex__ivl,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > real] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.02/5.34 = ( plus_plus_real @ ( G @ M )
% 5.02/5.34 @ ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.Suc_reindex_ivl
% 5.02/5.34 thf(fact_7206_sum__Suc__diff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > rat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_Suc_diff
% 5.02/5.34 thf(fact_7207_sum__Suc__diff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > int] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.34 => ( ( groups3539618377306564664at_int
% 5.02/5.34 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_Suc_diff
% 5.02/5.34 thf(fact_7208_sum__Suc__diff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > real] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.34 => ( ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_Suc_diff
% 5.02/5.34 thf(fact_7209_atLeastAtMostPlus1__int__conv,axiom,
% 5.02/5.34 ! [M: int,N2: int] :
% 5.02/5.34 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 5.02/5.34 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 5.02/5.34 = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % atLeastAtMostPlus1_int_conv
% 5.02/5.34 thf(fact_7210_simp__from__to,axiom,
% 5.02/5.34 ( set_or1266510415728281911st_int
% 5.02/5.34 = ( ^ [I5: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I5 ) @ bot_bot_set_int @ ( insert_int @ I5 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % simp_from_to
% 5.02/5.34 thf(fact_7211_sum_Oub__add__nat,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > rat,P2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.02/5.34 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.ub_add_nat
% 5.02/5.34 thf(fact_7212_sum_Oub__add__nat,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > int,P2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.02/5.34 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.02/5.34 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.ub_add_nat
% 5.02/5.34 thf(fact_7213_sum_Oub__add__nat,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > nat,P2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.02/5.34 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.ub_add_nat
% 5.02/5.34 thf(fact_7214_sum_Oub__add__nat,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,G: nat > real,P2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.02/5.34 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.ub_add_nat
% 5.02/5.34 thf(fact_7215_sum__natinterval__diff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > complex] :
% 5.02/5.34 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups2073611262835488442omplex
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.02/5.34 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups2073611262835488442omplex
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = zero_zero_complex ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_natinterval_diff
% 5.02/5.34 thf(fact_7216_sum__natinterval__diff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > rat] :
% 5.02/5.34 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.02/5.34 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = zero_zero_rat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_natinterval_diff
% 5.02/5.34 thf(fact_7217_sum__natinterval__diff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > int] :
% 5.02/5.34 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups3539618377306564664at_int
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.02/5.34 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups3539618377306564664at_int
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = zero_zero_int ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_natinterval_diff
% 5.02/5.34 thf(fact_7218_sum__natinterval__diff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > real] :
% 5.02/5.34 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.02/5.34 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = zero_zero_real ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_natinterval_diff
% 5.02/5.34 thf(fact_7219_sum__telescope_H_H,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > rat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.02/5.34 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_telescope''
% 5.02/5.34 thf(fact_7220_sum__telescope_H_H,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > int] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups3539618377306564664at_int
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.02/5.34 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_telescope''
% 5.02/5.34 thf(fact_7221_sum__telescope_H_H,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,F: nat > real] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.02/5.34 = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_telescope''
% 5.02/5.34 thf(fact_7222_sum_Oneutral,axiom,
% 5.02/5.34 ! [A3: set_int,G: int > int] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( member_int @ X5 @ A3 )
% 5.02/5.34 => ( ( G @ X5 )
% 5.02/5.34 = zero_zero_int ) )
% 5.02/5.34 => ( ( groups4538972089207619220nt_int @ G @ A3 )
% 5.02/5.34 = zero_zero_int ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.neutral
% 5.02/5.34 thf(fact_7223_sum_Oneutral,axiom,
% 5.02/5.34 ! [A3: set_complex,G: complex > complex] :
% 5.02/5.34 ( ! [X5: complex] :
% 5.02/5.34 ( ( member_complex @ X5 @ A3 )
% 5.02/5.34 => ( ( G @ X5 )
% 5.02/5.34 = zero_zero_complex ) )
% 5.02/5.34 => ( ( groups7754918857620584856omplex @ G @ A3 )
% 5.02/5.34 = zero_zero_complex ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.neutral
% 5.02/5.34 thf(fact_7224_sum_Oneutral,axiom,
% 5.02/5.34 ! [A3: set_nat,G: nat > nat] :
% 5.02/5.34 ( ! [X5: nat] :
% 5.02/5.34 ( ( member_nat @ X5 @ A3 )
% 5.02/5.34 => ( ( G @ X5 )
% 5.02/5.34 = zero_zero_nat ) )
% 5.02/5.34 => ( ( groups3542108847815614940at_nat @ G @ A3 )
% 5.02/5.34 = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.neutral
% 5.02/5.34 thf(fact_7225_sum_Oneutral,axiom,
% 5.02/5.34 ! [A3: set_nat,G: nat > real] :
% 5.02/5.34 ( ! [X5: nat] :
% 5.02/5.34 ( ( member_nat @ X5 @ A3 )
% 5.02/5.34 => ( ( G @ X5 )
% 5.02/5.34 = zero_zero_real ) )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ G @ A3 )
% 5.02/5.34 = zero_zero_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.neutral
% 5.02/5.34 thf(fact_7226_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: real > complex,A3: set_real] :
% 5.02/5.34 ( ( ( groups5754745047067104278omplex @ G @ A3 )
% 5.02/5.34 != zero_zero_complex )
% 5.02/5.34 => ~ ! [A4: real] :
% 5.02/5.34 ( ( member_real @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_complex ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7227_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: nat > complex,A3: set_nat] :
% 5.02/5.34 ( ( ( groups2073611262835488442omplex @ G @ A3 )
% 5.02/5.34 != zero_zero_complex )
% 5.02/5.34 => ~ ! [A4: nat] :
% 5.02/5.34 ( ( member_nat @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_complex ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7228_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: int > complex,A3: set_int] :
% 5.02/5.34 ( ( ( groups3049146728041665814omplex @ G @ A3 )
% 5.02/5.34 != zero_zero_complex )
% 5.02/5.34 => ~ ! [A4: int] :
% 5.02/5.34 ( ( member_int @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_complex ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7229_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: complex > real,A3: set_complex] :
% 5.02/5.34 ( ( ( groups5808333547571424918x_real @ G @ A3 )
% 5.02/5.34 != zero_zero_real )
% 5.02/5.34 => ~ ! [A4: complex] :
% 5.02/5.34 ( ( member_complex @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_real ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7230_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: real > real,A3: set_real] :
% 5.02/5.34 ( ( ( groups8097168146408367636l_real @ G @ A3 )
% 5.02/5.34 != zero_zero_real )
% 5.02/5.34 => ~ ! [A4: real] :
% 5.02/5.34 ( ( member_real @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_real ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7231_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: int > real,A3: set_int] :
% 5.02/5.34 ( ( ( groups8778361861064173332t_real @ G @ A3 )
% 5.02/5.34 != zero_zero_real )
% 5.02/5.34 => ~ ! [A4: int] :
% 5.02/5.34 ( ( member_int @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_real ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7232_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: complex > rat,A3: set_complex] :
% 5.02/5.34 ( ( ( groups5058264527183730370ex_rat @ G @ A3 )
% 5.02/5.34 != zero_zero_rat )
% 5.02/5.34 => ~ ! [A4: complex] :
% 5.02/5.34 ( ( member_complex @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_rat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7233_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: real > rat,A3: set_real] :
% 5.02/5.34 ( ( ( groups1300246762558778688al_rat @ G @ A3 )
% 5.02/5.34 != zero_zero_rat )
% 5.02/5.34 => ~ ! [A4: real] :
% 5.02/5.34 ( ( member_real @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_rat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7234_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: nat > rat,A3: set_nat] :
% 5.02/5.34 ( ( ( groups2906978787729119204at_rat @ G @ A3 )
% 5.02/5.34 != zero_zero_rat )
% 5.02/5.34 => ~ ! [A4: nat] :
% 5.02/5.34 ( ( member_nat @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_rat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7235_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.34 ! [G: int > rat,A3: set_int] :
% 5.02/5.34 ( ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 5.02/5.34 != zero_zero_rat )
% 5.02/5.34 => ~ ! [A4: int] :
% 5.02/5.34 ( ( member_int @ A4 @ A3 )
% 5.02/5.34 => ( ( G @ A4 )
% 5.02/5.34 = zero_zero_rat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.not_neutral_contains_not_neutral
% 5.02/5.34 thf(fact_7236_mask__eq__sum__exp,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 5.02/5.34 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.34 @ ( collect_nat
% 5.02/5.34 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_eq_sum_exp
% 5.02/5.34 thf(fact_7237_mask__eq__sum__exp,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 5.02/5.34 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.34 @ ( collect_nat
% 5.02/5.34 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_eq_sum_exp
% 5.02/5.34 thf(fact_7238_sum__gp__multiplied,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,X2: complex] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.02/5.34 = ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_gp_multiplied
% 5.02/5.34 thf(fact_7239_sum__gp__multiplied,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,X2: rat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.02/5.34 = ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_gp_multiplied
% 5.02/5.34 thf(fact_7240_sum__gp__multiplied,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,X2: int] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.02/5.34 = ( minus_minus_int @ ( power_power_int @ X2 @ M ) @ ( power_power_int @ X2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_gp_multiplied
% 5.02/5.34 thf(fact_7241_sum__gp__multiplied,axiom,
% 5.02/5.34 ! [M: nat,N2: nat,X2: real] :
% 5.02/5.34 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.34 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.02/5.34 = ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_gp_multiplied
% 5.02/5.34 thf(fact_7242_sum_Oin__pairs,axiom,
% 5.02/5.34 ! [G: nat > rat,M: nat,N2: nat] :
% 5.02/5.34 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.34 = ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.in_pairs
% 5.02/5.34 thf(fact_7243_sum_Oin__pairs,axiom,
% 5.02/5.34 ! [G: nat > int,M: nat,N2: nat] :
% 5.02/5.34 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.34 = ( groups3539618377306564664at_int
% 5.02/5.34 @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.in_pairs
% 5.02/5.34 thf(fact_7244_sum_Oin__pairs,axiom,
% 5.02/5.34 ! [G: nat > nat,M: nat,N2: nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.in_pairs
% 5.02/5.34 thf(fact_7245_sum_Oin__pairs,axiom,
% 5.02/5.34 ! [G: nat > real,M: nat,N2: nat] :
% 5.02/5.34 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.in_pairs
% 5.02/5.34 thf(fact_7246_and__nat__unfold,axiom,
% 5.02/5.34 ( bit_se727722235901077358nd_nat
% 5.02/5.34 = ( ^ [M6: nat,N3: nat] :
% 5.02/5.34 ( if_nat
% 5.02/5.34 @ ( ( M6 = zero_zero_nat )
% 5.02/5.34 | ( N3 = zero_zero_nat ) )
% 5.02/5.34 @ zero_zero_nat
% 5.02/5.34 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_nat_unfold
% 5.02/5.34 thf(fact_7247_and__nat__rec,axiom,
% 5.02/5.34 ( bit_se727722235901077358nd_nat
% 5.02/5.34 = ( ^ [M6: nat,N3: nat] :
% 5.02/5.34 ( plus_plus_nat
% 5.02/5.34 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.34 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.02/5.34 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.02/5.34 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_nat_rec
% 5.02/5.34 thf(fact_7248_mask__eq__sum__exp__nat,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.34 @ ( collect_nat
% 5.02/5.34 @ ^ [Q4: nat] : ( ord_less_nat @ Q4 @ N2 ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % mask_eq_sum_exp_nat
% 5.02/5.34 thf(fact_7249_gauss__sum__nat,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [X: nat] : X
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.34 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % gauss_sum_nat
% 5.02/5.34 thf(fact_7250_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.02/5.34 ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7251_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.02/5.34 ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7252_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.02/5.34 ( ! [I2: nat] :
% 5.02/5.34 ( ( member_nat @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7253_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.02/5.34 ( ! [I2: int] :
% 5.02/5.34 ( ( member_int @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7254_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.02/5.34 ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7255_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.02/5.34 ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7256_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.02/5.34 ( ! [I2: int] :
% 5.02/5.34 ( ( member_int @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7257_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.02/5.34 ( ! [I2: complex] :
% 5.02/5.34 ( ( member_complex @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7258_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_real,F: real > int,G: real > int] :
% 5.02/5.34 ( ! [I2: real] :
% 5.02/5.34 ( ( member_real @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7259_sum__mono,axiom,
% 5.02/5.34 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.02/5.34 ( ! [I2: nat] :
% 5.02/5.34 ( ( member_nat @ I2 @ K5 )
% 5.02/5.34 => ( ord_less_eq_int @ ( F @ I2 ) @ ( G @ I2 ) ) )
% 5.02/5.34 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_mono
% 5.02/5.34 thf(fact_7260_sum__distrib__left,axiom,
% 5.02/5.34 ! [R2: int,F: int > int,A3: set_int] :
% 5.02/5.34 ( ( times_times_int @ R2 @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.02/5.34 = ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [N3: int] : ( times_times_int @ R2 @ ( F @ N3 ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_distrib_left
% 5.02/5.34 thf(fact_7261_sum__distrib__left,axiom,
% 5.02/5.34 ! [R2: complex,F: complex > complex,A3: set_complex] :
% 5.02/5.34 ( ( times_times_complex @ R2 @ ( groups7754918857620584856omplex @ F @ A3 ) )
% 5.02/5.34 = ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [N3: complex] : ( times_times_complex @ R2 @ ( F @ N3 ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_distrib_left
% 5.02/5.34 thf(fact_7262_sum__distrib__left,axiom,
% 5.02/5.34 ! [R2: nat,F: nat > nat,A3: set_nat] :
% 5.02/5.34 ( ( times_times_nat @ R2 @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [N3: nat] : ( times_times_nat @ R2 @ ( F @ N3 ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_distrib_left
% 5.02/5.34 thf(fact_7263_sum__distrib__left,axiom,
% 5.02/5.34 ! [R2: real,F: nat > real,A3: set_nat] :
% 5.02/5.34 ( ( times_times_real @ R2 @ ( groups6591440286371151544t_real @ F @ A3 ) )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [N3: nat] : ( times_times_real @ R2 @ ( F @ N3 ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_distrib_left
% 5.02/5.34 thf(fact_7264_sum__distrib__right,axiom,
% 5.02/5.34 ! [F: int > int,A3: set_int,R2: int] :
% 5.02/5.34 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ R2 )
% 5.02/5.34 = ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [N3: int] : ( times_times_int @ ( F @ N3 ) @ R2 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_distrib_right
% 5.02/5.34 thf(fact_7265_sum__distrib__right,axiom,
% 5.02/5.34 ! [F: complex > complex,A3: set_complex,R2: complex] :
% 5.02/5.34 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A3 ) @ R2 )
% 5.02/5.34 = ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [N3: complex] : ( times_times_complex @ ( F @ N3 ) @ R2 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_distrib_right
% 5.02/5.34 thf(fact_7266_sum__distrib__right,axiom,
% 5.02/5.34 ! [F: nat > nat,A3: set_nat,R2: nat] :
% 5.02/5.34 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ R2 )
% 5.02/5.34 = ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [N3: nat] : ( times_times_nat @ ( F @ N3 ) @ R2 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_distrib_right
% 5.02/5.34 thf(fact_7267_sum__distrib__right,axiom,
% 5.02/5.34 ! [F: nat > real,A3: set_nat,R2: real] :
% 5.02/5.34 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A3 ) @ R2 )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ R2 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_distrib_right
% 5.02/5.34 thf(fact_7268_sum__product,axiom,
% 5.02/5.34 ! [F: int > int,A3: set_int,G: int > int,B4: set_int] :
% 5.02/5.34 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ ( groups4538972089207619220nt_int @ G @ B4 ) )
% 5.02/5.34 = ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [I5: int] :
% 5.02/5.34 ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [J3: int] : ( times_times_int @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.02/5.34 @ B4 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_product
% 5.02/5.34 thf(fact_7269_sum__product,axiom,
% 5.02/5.34 ! [F: complex > complex,A3: set_complex,G: complex > complex,B4: set_complex] :
% 5.02/5.34 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A3 ) @ ( groups7754918857620584856omplex @ G @ B4 ) )
% 5.02/5.34 = ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [I5: complex] :
% 5.02/5.34 ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.02/5.34 @ B4 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_product
% 5.02/5.34 thf(fact_7270_sum__product,axiom,
% 5.02/5.34 ! [F: nat > nat,A3: set_nat,G: nat > nat,B4: set_nat] :
% 5.02/5.34 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ G @ B4 ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [I5: nat] :
% 5.02/5.34 ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.02/5.34 @ B4 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_product
% 5.02/5.34 thf(fact_7271_sum__product,axiom,
% 5.02/5.34 ! [F: nat > real,A3: set_nat,G: nat > real,B4: set_nat] :
% 5.02/5.34 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A3 ) @ ( groups6591440286371151544t_real @ G @ B4 ) )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [I5: nat] :
% 5.02/5.34 ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [J3: nat] : ( times_times_real @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.02/5.34 @ B4 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_product
% 5.02/5.34 thf(fact_7272_sum_Odistrib,axiom,
% 5.02/5.34 ! [G: int > int,H2: int > int,A3: set_int] :
% 5.02/5.34 ( ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [X: int] : ( plus_plus_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A3 ) @ ( groups4538972089207619220nt_int @ H2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.distrib
% 5.02/5.34 thf(fact_7273_sum_Odistrib,axiom,
% 5.02/5.34 ! [G: complex > complex,H2: complex > complex,A3: set_complex] :
% 5.02/5.34 ( ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [X: complex] : ( plus_plus_complex @ ( G @ X ) @ ( H2 @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A3 ) @ ( groups7754918857620584856omplex @ H2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.distrib
% 5.02/5.34 thf(fact_7274_sum_Odistrib,axiom,
% 5.02/5.34 ! [G: nat > nat,H2: nat > nat,A3: set_nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [X: nat] : ( plus_plus_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A3 ) @ ( groups3542108847815614940at_nat @ H2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.distrib
% 5.02/5.34 thf(fact_7275_sum_Odistrib,axiom,
% 5.02/5.34 ! [G: nat > real,H2: nat > real,A3: set_nat] :
% 5.02/5.34 ( ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [X: nat] : ( plus_plus_real @ ( G @ X ) @ ( H2 @ X ) )
% 5.02/5.34 @ A3 )
% 5.02/5.34 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A3 ) @ ( groups6591440286371151544t_real @ H2 @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum.distrib
% 5.02/5.34 thf(fact_7276_sum__divide__distrib,axiom,
% 5.02/5.34 ! [F: complex > complex,A3: set_complex,R2: complex] :
% 5.02/5.34 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A3 ) @ R2 )
% 5.02/5.34 = ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [N3: complex] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ R2 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_divide_distrib
% 5.02/5.34 thf(fact_7277_sum__divide__distrib,axiom,
% 5.02/5.34 ! [F: nat > real,A3: set_nat,R2: real] :
% 5.02/5.34 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A3 ) @ R2 )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ R2 )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_divide_distrib
% 5.02/5.34 thf(fact_7278_arith__series__nat,axiom,
% 5.02/5.34 ! [A: nat,D: nat,N2: nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I5 @ D ) )
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.34 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % arith_series_nat
% 5.02/5.34 thf(fact_7279_Sum__Icc__nat,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [X: nat] : X
% 5.02/5.34 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % Sum_Icc_nat
% 5.02/5.34 thf(fact_7280_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_complex,F: complex > real] :
% 5.02/5.34 ( ! [X5: complex] :
% 5.02/5.34 ( ( member_complex @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7281_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_real,F: real > real] :
% 5.02/5.34 ( ! [X5: real] :
% 5.02/5.34 ( ( member_real @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7282_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_int,F: int > real] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( member_int @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7283_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_complex,F: complex > rat] :
% 5.02/5.34 ( ! [X5: complex] :
% 5.02/5.34 ( ( member_complex @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7284_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_real,F: real > rat] :
% 5.02/5.34 ( ! [X5: real] :
% 5.02/5.34 ( ( member_real @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7285_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_nat,F: nat > rat] :
% 5.02/5.34 ( ! [X5: nat] :
% 5.02/5.34 ( ( member_nat @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7286_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_int,F: int > rat] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( member_int @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7287_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_complex,F: complex > nat] :
% 5.02/5.34 ( ! [X5: complex] :
% 5.02/5.34 ( ( member_complex @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7288_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_real,F: real > nat] :
% 5.02/5.34 ( ! [X5: real] :
% 5.02/5.34 ( ( member_real @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7289_sum__nonneg,axiom,
% 5.02/5.34 ! [A3: set_int,F: int > nat] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( member_int @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.02/5.34 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonneg
% 5.02/5.34 thf(fact_7290_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_complex,F: complex > real] :
% 5.02/5.34 ( ! [X5: complex] :
% 5.02/5.34 ( ( member_complex @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.02/5.34 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7291_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_real,F: real > real] :
% 5.02/5.34 ( ! [X5: real] :
% 5.02/5.34 ( ( member_real @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.02/5.34 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7292_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_int,F: int > real] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( member_int @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.02/5.34 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A3 ) @ zero_zero_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7293_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_complex,F: complex > rat] :
% 5.02/5.34 ( ! [X5: complex] :
% 5.02/5.34 ( ( member_complex @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7294_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_real,F: real > rat] :
% 5.02/5.34 ( ! [X5: real] :
% 5.02/5.34 ( ( member_real @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7295_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_nat,F: nat > rat] :
% 5.02/5.34 ( ! [X5: nat] :
% 5.02/5.34 ( ( member_nat @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7296_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_int,F: int > rat] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( member_int @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.02/5.34 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7297_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_complex,F: complex > nat] :
% 5.02/5.34 ( ! [X5: complex] :
% 5.02/5.34 ( ( member_complex @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.02/5.34 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7298_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_real,F: real > nat] :
% 5.02/5.34 ( ! [X5: real] :
% 5.02/5.34 ( ( member_real @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.02/5.34 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7299_sum__nonpos,axiom,
% 5.02/5.34 ! [A3: set_int,F: int > nat] :
% 5.02/5.34 ( ! [X5: int] :
% 5.02/5.34 ( ( member_int @ X5 @ A3 )
% 5.02/5.34 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.02/5.34 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_nonpos
% 5.02/5.34 thf(fact_7300_and__int_Osimps,axiom,
% 5.02/5.34 ( bit_se725231765392027082nd_int
% 5.02/5.34 = ( ^ [K3: int,L2: int] :
% 5.02/5.34 ( if_int
% 5.02/5.34 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.02/5.34 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.02/5.34 @ ( uminus_uminus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.02/5.34 @ ( plus_plus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.02/5.34 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_int.simps
% 5.02/5.34 thf(fact_7301_and__int_Opsimps,axiom,
% 5.02/5.34 ! [K: int,L: int] :
% 5.02/5.34 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.02/5.34 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.02/5.34 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.02/5.34 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.02/5.34 = ( uminus_uminus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.02/5.34 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.02/5.34 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.02/5.34 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.02/5.34 = ( plus_plus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.02/5.34 @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_int.psimps
% 5.02/5.34 thf(fact_7302_and__int_Opelims,axiom,
% 5.02/5.34 ! [X2: int,Xa2: int,Y: int] :
% 5.02/5.34 ( ( ( bit_se725231765392027082nd_int @ X2 @ Xa2 )
% 5.02/5.34 = Y )
% 5.02/5.34 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) )
% 5.02/5.34 => ~ ( ( ( ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.02/5.34 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 = ( uminus_uminus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.02/5.34 & ( ~ ( ( member_int @ X2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.02/5.34 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.02/5.34 => ( Y
% 5.02/5.34 = ( plus_plus_int
% 5.02/5.34 @ ( zero_n2684676970156552555ol_int
% 5.02/5.34 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X2 )
% 5.02/5.34 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.02/5.34 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.02/5.34 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % and_int.pelims
% 5.02/5.34 thf(fact_7303_sum__gp,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,X2: complex] :
% 5.02/5.34 ( ( ( ord_less_nat @ N2 @ M )
% 5.02/5.34 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = zero_zero_complex ) )
% 5.02/5.34 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.02/5.34 => ( ( ( X2 = one_one_complex )
% 5.02/5.34 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.02/5.34 & ( ( X2 != one_one_complex )
% 5.02/5.34 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ X2 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_gp
% 5.02/5.34 thf(fact_7304_sum__gp,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,X2: rat] :
% 5.02/5.34 ( ( ( ord_less_nat @ N2 @ M )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = zero_zero_rat ) )
% 5.02/5.34 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.02/5.34 => ( ( ( X2 = one_one_rat )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.02/5.34 & ( ( X2 != one_one_rat )
% 5.02/5.34 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ X2 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_gp
% 5.02/5.34 thf(fact_7305_sum__gp,axiom,
% 5.02/5.34 ! [N2: nat,M: nat,X2: real] :
% 5.02/5.34 ( ( ( ord_less_nat @ N2 @ M )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = zero_zero_real ) )
% 5.02/5.34 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.02/5.34 => ( ( ( X2 = one_one_real )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.02/5.34 & ( ( X2 != one_one_real )
% 5.02/5.34 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.34 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % sum_gp
% 5.02/5.34 thf(fact_7306_cot__less__zero,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.02/5.34 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.02/5.34 => ( ord_less_real @ ( cot_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % cot_less_zero
% 5.02/5.34 thf(fact_7307_cos__npi__int,axiom,
% 5.02/5.34 ! [N2: int] :
% 5.02/5.34 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.02/5.34 = one_one_real ) )
% 5.02/5.34 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.34 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.02/5.34 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % cos_npi_int
% 5.02/5.34 thf(fact_7308_of__nat__eq__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ( semiri1314217659103216013at_int @ M )
% 5.02/5.34 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( M = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_iff
% 5.02/5.34 thf(fact_7309_of__nat__eq__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ( semiri5074537144036343181t_real @ M )
% 5.02/5.34 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.34 = ( M = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_iff
% 5.02/5.34 thf(fact_7310_of__nat__eq__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.02/5.34 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.34 = ( M = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_iff
% 5.02/5.34 thf(fact_7311_of__nat__eq__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ( semiri681578069525770553at_rat @ M )
% 5.02/5.34 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.02/5.34 = ( M = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_iff
% 5.02/5.34 thf(fact_7312_int__eq__iff__numeral,axiom,
% 5.02/5.34 ! [M: nat,V: num] :
% 5.02/5.34 ( ( ( semiri1314217659103216013at_int @ M )
% 5.02/5.34 = ( numeral_numeral_int @ V ) )
% 5.02/5.34 = ( M
% 5.02/5.34 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % int_eq_iff_numeral
% 5.02/5.34 thf(fact_7313_abs__of__nat,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.02/5.34 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_of_nat
% 5.02/5.34 thf(fact_7314_abs__of__nat,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_of_nat
% 5.02/5.34 thf(fact_7315_abs__of__nat,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.34 = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_of_nat
% 5.02/5.34 thf(fact_7316_abs__of__nat,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.02/5.34 = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % abs_of_nat
% 5.02/5.34 thf(fact_7317_negative__eq__positive,axiom,
% 5.02/5.34 ! [N2: nat,M: nat] :
% 5.02/5.34 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( semiri1314217659103216013at_int @ M ) )
% 5.02/5.34 = ( ( N2 = zero_zero_nat )
% 5.02/5.34 & ( M = zero_zero_nat ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % negative_eq_positive
% 5.02/5.34 thf(fact_7318_of__int__of__nat__eq,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ring_1_of_int_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_of_nat_eq
% 5.02/5.34 thf(fact_7319_of__int__of__nat__eq,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ring_1_of_int_real @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_of_nat_eq
% 5.02/5.34 thf(fact_7320_of__int__of__nat__eq,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ring_1_of_int_rat @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_int_of_nat_eq
% 5.02/5.34 thf(fact_7321_negative__zle,axiom,
% 5.02/5.34 ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.02/5.34
% 5.02/5.34 % negative_zle
% 5.02/5.34 thf(fact_7322_int__dvd__int__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % int_dvd_int_iff
% 5.02/5.34 thf(fact_7323_cot__zero,axiom,
% 5.02/5.34 ( ( cot_complex @ zero_zero_complex )
% 5.02/5.34 = zero_zero_complex ) ).
% 5.02/5.34
% 5.02/5.34 % cot_zero
% 5.02/5.34 thf(fact_7324_cot__zero,axiom,
% 5.02/5.34 ( ( cot_real @ zero_zero_real )
% 5.02/5.34 = zero_zero_real ) ).
% 5.02/5.34
% 5.02/5.34 % cot_zero
% 5.02/5.34 thf(fact_7325_of__nat__eq__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ( semiri8010041392384452111omplex @ M )
% 5.02/5.34 = zero_zero_complex )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_0_iff
% 5.02/5.34 thf(fact_7326_of__nat__eq__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ( semiri1314217659103216013at_int @ M )
% 5.02/5.34 = zero_zero_int )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_0_iff
% 5.02/5.34 thf(fact_7327_of__nat__eq__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ( semiri5074537144036343181t_real @ M )
% 5.02/5.34 = zero_zero_real )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_0_iff
% 5.02/5.34 thf(fact_7328_of__nat__eq__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.02/5.34 = zero_zero_nat )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_0_iff
% 5.02/5.34 thf(fact_7329_of__nat__eq__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ( semiri681578069525770553at_rat @ M )
% 5.02/5.34 = zero_zero_rat )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_0_iff
% 5.02/5.34 thf(fact_7330_of__nat__0__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( zero_zero_complex
% 5.02/5.34 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.02/5.34 = ( zero_zero_nat = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_eq_iff
% 5.02/5.34 thf(fact_7331_of__nat__0__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( zero_zero_int
% 5.02/5.34 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( zero_zero_nat = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_eq_iff
% 5.02/5.34 thf(fact_7332_of__nat__0__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( zero_zero_real
% 5.02/5.34 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.34 = ( zero_zero_nat = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_eq_iff
% 5.02/5.34 thf(fact_7333_of__nat__0__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( zero_zero_nat
% 5.02/5.34 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.34 = ( zero_zero_nat = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_eq_iff
% 5.02/5.34 thf(fact_7334_of__nat__0__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( zero_zero_rat
% 5.02/5.34 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.02/5.34 = ( zero_zero_nat = N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_eq_iff
% 5.02/5.34 thf(fact_7335_of__nat__0,axiom,
% 5.02/5.34 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.02/5.34 = zero_zero_complex ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0
% 5.02/5.34 thf(fact_7336_of__nat__0,axiom,
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.02/5.34 = zero_zero_int ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0
% 5.02/5.34 thf(fact_7337_of__nat__0,axiom,
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.02/5.34 = zero_zero_real ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0
% 5.02/5.34 thf(fact_7338_of__nat__0,axiom,
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.02/5.34 = zero_zero_nat ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0
% 5.02/5.34 thf(fact_7339_of__nat__0,axiom,
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.02/5.34 = zero_zero_rat ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0
% 5.02/5.34 thf(fact_7340_of__nat__less__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_less_iff
% 5.02/5.34 thf(fact_7341_of__nat__less__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_less_iff
% 5.02/5.34 thf(fact_7342_of__nat__less__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_less_iff
% 5.02/5.34 thf(fact_7343_of__nat__less__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_less_iff
% 5.02/5.34 thf(fact_7344_of__nat__le__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.34 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_le_iff
% 5.02/5.34 thf(fact_7345_of__nat__le__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.02/5.34 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_le_iff
% 5.02/5.34 thf(fact_7346_of__nat__le__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.34 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_le_iff
% 5.02/5.34 thf(fact_7347_of__nat__le__iff,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_le_iff
% 5.02/5.34 thf(fact_7348_of__nat__numeral,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_numeral
% 5.02/5.34 thf(fact_7349_of__nat__numeral,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_numeral
% 5.02/5.34 thf(fact_7350_of__nat__numeral,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( numeral_numeral_real @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_numeral
% 5.02/5.34 thf(fact_7351_of__nat__numeral,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_numeral
% 5.02/5.34 thf(fact_7352_of__nat__numeral,axiom,
% 5.02/5.34 ! [N2: num] :
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.34 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_numeral
% 5.02/5.34 thf(fact_7353_cos__zero,axiom,
% 5.02/5.34 ( ( cos_complex @ zero_zero_complex )
% 5.02/5.34 = one_one_complex ) ).
% 5.02/5.34
% 5.02/5.34 % cos_zero
% 5.02/5.34 thf(fact_7354_cos__zero,axiom,
% 5.02/5.34 ( ( cos_real @ zero_zero_real )
% 5.02/5.34 = one_one_real ) ).
% 5.02/5.34
% 5.02/5.34 % cos_zero
% 5.02/5.34 thf(fact_7355_of__nat__add,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 5.02/5.34 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_add
% 5.02/5.34 thf(fact_7356_of__nat__add,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 5.02/5.34 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_add
% 5.02/5.34 thf(fact_7357_of__nat__add,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.02/5.34 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_add
% 5.02/5.34 thf(fact_7358_of__nat__add,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 5.02/5.34 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_add
% 5.02/5.34 thf(fact_7359_of__nat__mult,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 5.02/5.34 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_mult
% 5.02/5.34 thf(fact_7360_of__nat__mult,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 5.02/5.34 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_mult
% 5.02/5.34 thf(fact_7361_of__nat__mult,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 5.02/5.34 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_mult
% 5.02/5.34 thf(fact_7362_of__nat__mult,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N2 ) )
% 5.02/5.34 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_mult
% 5.02/5.34 thf(fact_7363_of__nat__eq__1__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ( semiri8010041392384452111omplex @ N2 )
% 5.02/5.34 = one_one_complex )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_1_iff
% 5.02/5.34 thf(fact_7364_of__nat__eq__1__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ( semiri1314217659103216013at_int @ N2 )
% 5.02/5.34 = one_one_int )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_1_iff
% 5.02/5.34 thf(fact_7365_of__nat__eq__1__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ( semiri5074537144036343181t_real @ N2 )
% 5.02/5.34 = one_one_real )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_1_iff
% 5.02/5.34 thf(fact_7366_of__nat__eq__1__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 5.02/5.34 = one_one_nat )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_1_iff
% 5.02/5.34 thf(fact_7367_of__nat__eq__1__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ( semiri681578069525770553at_rat @ N2 )
% 5.02/5.34 = one_one_rat )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_1_iff
% 5.02/5.34 thf(fact_7368_of__nat__1__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( one_one_complex
% 5.02/5.34 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1_eq_iff
% 5.02/5.34 thf(fact_7369_of__nat__1__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( one_one_int
% 5.02/5.34 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1_eq_iff
% 5.02/5.34 thf(fact_7370_of__nat__1__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( one_one_real
% 5.02/5.34 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1_eq_iff
% 5.02/5.34 thf(fact_7371_of__nat__1__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( one_one_nat
% 5.02/5.34 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1_eq_iff
% 5.02/5.34 thf(fact_7372_of__nat__1__eq__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( one_one_rat
% 5.02/5.34 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.02/5.34 = ( N2 = one_one_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1_eq_iff
% 5.02/5.34 thf(fact_7373_of__nat__1,axiom,
% 5.02/5.34 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.02/5.34 = one_one_complex ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1
% 5.02/5.34 thf(fact_7374_of__nat__1,axiom,
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.02/5.34 = one_one_int ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1
% 5.02/5.34 thf(fact_7375_of__nat__1,axiom,
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.02/5.34 = one_one_real ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1
% 5.02/5.34 thf(fact_7376_of__nat__1,axiom,
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.02/5.34 = one_one_nat ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1
% 5.02/5.34 thf(fact_7377_of__nat__1,axiom,
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.02/5.34 = one_one_rat ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_1
% 5.02/5.34 thf(fact_7378_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ( semiri8010041392384452111omplex @ X2 )
% 5.02/5.34 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.02/5.34 = ( X2
% 5.02/5.34 = ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_eq_of_nat_cancel_iff
% 5.02/5.34 thf(fact_7379_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ( semiri1314217659103216013at_int @ X2 )
% 5.02/5.34 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.02/5.34 = ( X2
% 5.02/5.34 = ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_eq_of_nat_cancel_iff
% 5.02/5.34 thf(fact_7380_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ( semiri5074537144036343181t_real @ X2 )
% 5.02/5.34 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.02/5.34 = ( X2
% 5.02/5.34 = ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_eq_of_nat_cancel_iff
% 5.02/5.34 thf(fact_7381_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ( semiri1316708129612266289at_nat @ X2 )
% 5.02/5.34 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.02/5.34 = ( X2
% 5.02/5.34 = ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_eq_of_nat_cancel_iff
% 5.02/5.34 thf(fact_7382_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ( semiri681578069525770553at_rat @ X2 )
% 5.02/5.34 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.02/5.34 = ( X2
% 5.02/5.34 = ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_eq_of_nat_cancel_iff
% 5.02/5.34 thf(fact_7383_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.02/5.34 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.34 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.02/5.34 = ( semiri8010041392384452111omplex @ X2 ) )
% 5.02/5.34 = ( ( power_power_nat @ B @ W )
% 5.02/5.34 = X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_of_nat_power_cancel_iff
% 5.02/5.34 thf(fact_7384_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.02/5.34 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.34 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.02/5.34 = ( semiri1314217659103216013at_int @ X2 ) )
% 5.02/5.34 = ( ( power_power_nat @ B @ W )
% 5.02/5.34 = X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_of_nat_power_cancel_iff
% 5.02/5.34 thf(fact_7385_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.02/5.34 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.34 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.02/5.34 = ( semiri5074537144036343181t_real @ X2 ) )
% 5.02/5.34 = ( ( power_power_nat @ B @ W )
% 5.02/5.34 = X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_of_nat_power_cancel_iff
% 5.02/5.34 thf(fact_7386_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.02/5.34 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.34 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.02/5.34 = ( semiri1316708129612266289at_nat @ X2 ) )
% 5.02/5.34 = ( ( power_power_nat @ B @ W )
% 5.02/5.34 = X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_of_nat_power_cancel_iff
% 5.02/5.34 thf(fact_7387_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.02/5.34 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.34 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 5.02/5.34 = ( semiri681578069525770553at_rat @ X2 ) )
% 5.02/5.34 = ( ( power_power_nat @ B @ W )
% 5.02/5.34 = X2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_eq_of_nat_power_cancel_iff
% 5.02/5.34 thf(fact_7388_of__nat__power,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N2 ) )
% 5.02/5.34 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power
% 5.02/5.34 thf(fact_7389_of__nat__power,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N2 ) )
% 5.02/5.34 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power
% 5.02/5.34 thf(fact_7390_of__nat__power,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N2 ) )
% 5.02/5.34 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power
% 5.02/5.34 thf(fact_7391_of__nat__power,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
% 5.02/5.34 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power
% 5.02/5.34 thf(fact_7392_of__nat__power,axiom,
% 5.02/5.34 ! [M: nat,N2: nat] :
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N2 ) )
% 5.02/5.34 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power
% 5.02/5.34 thf(fact_7393_negative__zless,axiom,
% 5.02/5.34 ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.02/5.34
% 5.02/5.34 % negative_zless
% 5.02/5.34 thf(fact_7394_of__nat__of__bool,axiom,
% 5.02/5.34 ! [P: $o] :
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.02/5.34 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_of_bool
% 5.02/5.34 thf(fact_7395_of__nat__of__bool,axiom,
% 5.02/5.34 ! [P: $o] :
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.02/5.34 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_of_bool
% 5.02/5.34 thf(fact_7396_of__nat__of__bool,axiom,
% 5.02/5.34 ! [P: $o] :
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.02/5.34 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_of_bool
% 5.02/5.34 thf(fact_7397_of__nat__of__bool,axiom,
% 5.02/5.34 ! [P: $o] :
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.02/5.34 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_of_bool
% 5.02/5.34 thf(fact_7398_of__nat__of__bool,axiom,
% 5.02/5.34 ! [P: $o] :
% 5.02/5.34 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.02/5.34 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_of_bool
% 5.02/5.34 thf(fact_7399_of__nat__sum,axiom,
% 5.02/5.34 ! [F: int > nat,A3: set_int] :
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 5.02/5.34 = ( groups4538972089207619220nt_int
% 5.02/5.34 @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_sum
% 5.02/5.34 thf(fact_7400_of__nat__sum,axiom,
% 5.02/5.34 ! [F: complex > nat,A3: set_complex] :
% 5.02/5.34 ( ( semiri8010041392384452111omplex @ ( groups5693394587270226106ex_nat @ F @ A3 ) )
% 5.02/5.34 = ( groups7754918857620584856omplex
% 5.02/5.34 @ ^ [X: complex] : ( semiri8010041392384452111omplex @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_sum
% 5.02/5.34 thf(fact_7401_of__nat__sum,axiom,
% 5.02/5.34 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.34 = ( groups3539618377306564664at_int
% 5.02/5.34 @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_sum
% 5.02/5.34 thf(fact_7402_of__nat__sum,axiom,
% 5.02/5.34 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.34 = ( groups2906978787729119204at_rat
% 5.02/5.34 @ ^ [X: nat] : ( semiri681578069525770553at_rat @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_sum
% 5.02/5.34 thf(fact_7403_of__nat__sum,axiom,
% 5.02/5.34 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.34 = ( groups3542108847815614940at_nat
% 5.02/5.34 @ ^ [X: nat] : ( semiri1316708129612266289at_nat @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_sum
% 5.02/5.34 thf(fact_7404_of__nat__sum,axiom,
% 5.02/5.34 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.34 = ( groups6591440286371151544t_real
% 5.02/5.34 @ ^ [X: nat] : ( semiri5074537144036343181t_real @ ( F @ X ) )
% 5.02/5.34 @ A3 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_sum
% 5.02/5.34 thf(fact_7405_of__nat__le__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_le_0_iff
% 5.02/5.34 thf(fact_7406_of__nat__le__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_le_0_iff
% 5.02/5.34 thf(fact_7407_of__nat__le__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_le_0_iff
% 5.02/5.34 thf(fact_7408_of__nat__le__0__iff,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.02/5.34 = ( M = zero_zero_nat ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_le_0_iff
% 5.02/5.34 thf(fact_7409_of__nat__Suc,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.02/5.34 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_Suc
% 5.02/5.34 thf(fact_7410_of__nat__Suc,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.02/5.34 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_Suc
% 5.02/5.34 thf(fact_7411_of__nat__Suc,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.02/5.34 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_Suc
% 5.02/5.34 thf(fact_7412_of__nat__Suc,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.02/5.34 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_Suc
% 5.02/5.34 thf(fact_7413_of__nat__Suc,axiom,
% 5.02/5.34 ! [M: nat] :
% 5.02/5.34 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.02/5.34 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_Suc
% 5.02/5.34 thf(fact_7414_real__of__nat__less__numeral__iff,axiom,
% 5.02/5.34 ! [N2: nat,W: num] :
% 5.02/5.34 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W ) )
% 5.02/5.34 = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % real_of_nat_less_numeral_iff
% 5.02/5.34 thf(fact_7415_numeral__less__real__of__nat__iff,axiom,
% 5.02/5.34 ! [W: num,N2: nat] :
% 5.02/5.34 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % numeral_less_real_of_nat_iff
% 5.02/5.34 thf(fact_7416_numeral__le__real__of__nat__iff,axiom,
% 5.02/5.34 ! [N2: num,M: nat] :
% 5.02/5.34 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.02/5.34 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 5.02/5.34
% 5.02/5.34 % numeral_le_real_of_nat_iff
% 5.02/5.34 thf(fact_7417_cos__pi,axiom,
% 5.02/5.34 ( ( cos_real @ pi )
% 5.02/5.34 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.34
% 5.02/5.34 % cos_pi
% 5.02/5.34 thf(fact_7418_cos__periodic__pi2,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( cos_real @ ( plus_plus_real @ pi @ X2 ) )
% 5.02/5.34 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % cos_periodic_pi2
% 5.02/5.34 thf(fact_7419_cos__periodic__pi,axiom,
% 5.02/5.34 ! [X2: real] :
% 5.02/5.34 ( ( cos_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.02/5.34 = ( uminus_uminus_real @ ( cos_real @ X2 ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % cos_periodic_pi
% 5.02/5.34 thf(fact_7420_cot__npi,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.02/5.34 = zero_zero_real ) ).
% 5.02/5.34
% 5.02/5.34 % cot_npi
% 5.02/5.34 thf(fact_7421_of__nat__0__less__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_less_iff
% 5.02/5.34 thf(fact_7422_of__nat__0__less__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_less_iff
% 5.02/5.34 thf(fact_7423_of__nat__0__less__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_less_iff
% 5.02/5.34 thf(fact_7424_of__nat__0__less__iff,axiom,
% 5.02/5.34 ! [N2: nat] :
% 5.02/5.34 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.02/5.34 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_0_less_iff
% 5.02/5.34 thf(fact_7425_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.02/5.34 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_less_of_nat_cancel_iff
% 5.02/5.34 thf(fact_7426_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.02/5.34 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_less_of_nat_cancel_iff
% 5.02/5.34 thf(fact_7427_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.02/5.34 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_less_of_nat_cancel_iff
% 5.02/5.34 thf(fact_7428_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.02/5.34 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.34 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.02/5.34 = ( ord_less_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.34
% 5.02/5.34 % of_nat_power_less_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7429_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.02/5.35 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.02/5.35 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_of_nat_power_cancel_iff
% 5.02/5.35 thf(fact_7430_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.02/5.35 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.02/5.35 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_of_nat_power_cancel_iff
% 5.02/5.35 thf(fact_7431_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.02/5.35 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.02/5.35 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_of_nat_power_cancel_iff
% 5.02/5.35 thf(fact_7432_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.02/5.35 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.02/5.35 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_of_nat_power_cancel_iff
% 5.02/5.35 thf(fact_7433_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_power_le_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7434_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.35 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_power_le_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7435_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_power_le_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7436_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,B: nat,W: nat] :
% 5.02/5.35 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_power_le_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7437_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.02/5.35 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_le_of_nat_power_cancel_iff
% 5.02/5.35 thf(fact_7438_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.02/5.35 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_le_of_nat_power_cancel_iff
% 5.02/5.35 thf(fact_7439_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.02/5.35 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_le_of_nat_power_cancel_iff
% 5.02/5.35 thf(fact_7440_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.02/5.35 ! [B: nat,W: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_le_of_nat_power_cancel_iff
% 5.02/5.35 thf(fact_7441_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [Y: nat,X2: num,N2: nat] :
% 5.02/5.35 ( ( ( semiri8010041392384452111omplex @ Y )
% 5.02/5.35 = ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N2 ) )
% 5.02/5.35 = ( Y
% 5.02/5.35 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_eq_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7442_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [Y: nat,X2: num,N2: nat] :
% 5.02/5.35 ( ( ( semiri1314217659103216013at_int @ Y )
% 5.02/5.35 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) )
% 5.02/5.35 = ( Y
% 5.02/5.35 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_eq_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7443_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [Y: nat,X2: num,N2: nat] :
% 5.02/5.35 ( ( ( semiri5074537144036343181t_real @ Y )
% 5.02/5.35 = ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N2 ) )
% 5.02/5.35 = ( Y
% 5.02/5.35 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_eq_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7444_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [Y: nat,X2: num,N2: nat] :
% 5.02/5.35 ( ( ( semiri1316708129612266289at_nat @ Y )
% 5.02/5.35 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) )
% 5.02/5.35 = ( Y
% 5.02/5.35 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_eq_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7445_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [Y: nat,X2: num,N2: nat] :
% 5.02/5.35 ( ( ( semiri681578069525770553at_rat @ Y )
% 5.02/5.35 = ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N2 ) )
% 5.02/5.35 = ( Y
% 5.02/5.35 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_eq_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7446_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: num,N2: nat,Y: nat] :
% 5.02/5.35 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X2 ) @ N2 )
% 5.02/5.35 = ( semiri8010041392384452111omplex @ Y ) )
% 5.02/5.35 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 )
% 5.02/5.35 = Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_eq_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7447_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: num,N2: nat,Y: nat] :
% 5.02/5.35 ( ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 )
% 5.02/5.35 = ( semiri1314217659103216013at_int @ Y ) )
% 5.02/5.35 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 )
% 5.02/5.35 = Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_eq_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7448_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: num,N2: nat,Y: nat] :
% 5.02/5.35 ( ( ( power_power_real @ ( numeral_numeral_real @ X2 ) @ N2 )
% 5.02/5.35 = ( semiri5074537144036343181t_real @ Y ) )
% 5.02/5.35 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 )
% 5.02/5.35 = Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_eq_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7449_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: num,N2: nat,Y: nat] :
% 5.02/5.35 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 )
% 5.02/5.35 = ( semiri1316708129612266289at_nat @ Y ) )
% 5.02/5.35 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 )
% 5.02/5.35 = Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_eq_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7450_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [X2: num,N2: nat,Y: nat] :
% 5.02/5.35 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X2 ) @ N2 )
% 5.02/5.35 = ( semiri681578069525770553at_rat @ Y ) )
% 5.02/5.35 = ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 )
% 5.02/5.35 = Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_eq_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7451_of__nat__zero__less__power__iff,axiom,
% 5.02/5.35 ! [X2: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X2 ) @ N2 ) )
% 5.02/5.35 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.02/5.35 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_zero_less_power_iff
% 5.02/5.35 thf(fact_7452_of__nat__zero__less__power__iff,axiom,
% 5.02/5.35 ! [X2: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X2 ) @ N2 ) )
% 5.02/5.35 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.02/5.35 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_zero_less_power_iff
% 5.02/5.35 thf(fact_7453_of__nat__zero__less__power__iff,axiom,
% 5.02/5.35 ! [X2: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ N2 ) )
% 5.02/5.35 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.02/5.35 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_zero_less_power_iff
% 5.02/5.35 thf(fact_7454_of__nat__zero__less__power__iff,axiom,
% 5.02/5.35 ! [X2: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X2 ) @ N2 ) )
% 5.02/5.35 = ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.02/5.35 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_zero_less_power_iff
% 5.02/5.35 thf(fact_7455_cos__npi,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.02/5.35 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_npi
% 5.02/5.35 thf(fact_7456_cos__npi2,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.02/5.35 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_npi2
% 5.02/5.35 thf(fact_7457_even__of__nat,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.02/5.35 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % even_of_nat
% 5.02/5.35 thf(fact_7458_even__of__nat,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.35 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % even_of_nat
% 5.02/5.35 thf(fact_7459_even__of__nat,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.35 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % even_of_nat
% 5.02/5.35 thf(fact_7460_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,I3: num,N2: nat] :
% 5.02/5.35 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I3 ) @ N2 ) )
% 5.02/5.35 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7461_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,I3: num,N2: nat] :
% 5.02/5.35 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I3 ) @ N2 ) )
% 5.02/5.35 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7462_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,I3: num,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) )
% 5.02/5.35 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7463_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,I3: num,N2: nat] :
% 5.02/5.35 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I3 ) @ N2 ) )
% 5.02/5.35 = ( ord_less_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7464_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [I3: num,N2: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I3 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.02/5.35 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_less_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7465_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [I3: num,N2: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I3 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.02/5.35 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_less_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7466_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [I3: num,N2: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.02/5.35 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_less_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7467_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [I3: num,N2: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I3 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.02/5.35 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_less_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7468_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,I3: num,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( power_power_real @ ( numeral_numeral_real @ I3 ) @ N2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_le_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7469_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,I3: num,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I3 ) @ N2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_le_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7470_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,I3: num,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_le_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7471_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.02/5.35 ! [X2: nat,I3: num,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( power_power_int @ ( numeral_numeral_int @ I3 ) @ N2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_le_numeral_power_cancel_iff
% 5.02/5.35 thf(fact_7472_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [I3: num,N2: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I3 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_le_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7473_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [I3: num,N2: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I3 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_le_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7474_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [I3: num,N2: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_le_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7475_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.02/5.35 ! [I3: num,N2: nat,X2: nat] :
% 5.02/5.35 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I3 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I3 ) @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % numeral_power_le_of_nat_cancel_iff
% 5.02/5.35 thf(fact_7476_cos__pi__half,axiom,
% 5.02/5.35 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_pi_half
% 5.02/5.35 thf(fact_7477_cos__2npi,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_2npi
% 5.02/5.35 thf(fact_7478_cos__two__pi,axiom,
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_two_pi
% 5.02/5.35 thf(fact_7479_cos__periodic,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( cos_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.02/5.35 = ( cos_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_periodic
% 5.02/5.35 thf(fact_7480_cos__2pi__minus,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.02/5.35 = ( cos_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_2pi_minus
% 5.02/5.35 thf(fact_7481_cot__periodic,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( cot_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.02/5.35 = ( cot_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % cot_periodic
% 5.02/5.35 thf(fact_7482_cos__int__2pin,axiom,
% 5.02/5.35 ! [N2: int] :
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_int_2pin
% 5.02/5.35 thf(fact_7483_cos__3over2__pi,axiom,
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_3over2_pi
% 5.02/5.35 thf(fact_7484_cos__pi__eq__zero,axiom,
% 5.02/5.35 ! [M: nat] :
% 5.02/5.35 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_pi_eq_zero
% 5.02/5.35 thf(fact_7485_real__arch__simple,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ? [N: nat] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_arch_simple
% 5.02/5.35 thf(fact_7486_real__arch__simple,axiom,
% 5.02/5.35 ! [X2: rat] :
% 5.02/5.35 ? [N: nat] : ( ord_less_eq_rat @ X2 @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_arch_simple
% 5.02/5.35 thf(fact_7487_reals__Archimedean2,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ? [N: nat] : ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.02/5.35
% 5.02/5.35 % reals_Archimedean2
% 5.02/5.35 thf(fact_7488_reals__Archimedean2,axiom,
% 5.02/5.35 ! [X2: rat] :
% 5.02/5.35 ? [N: nat] : ( ord_less_rat @ X2 @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.02/5.35
% 5.02/5.35 % reals_Archimedean2
% 5.02/5.35 thf(fact_7489_mult__of__nat__commute,axiom,
% 5.02/5.35 ! [X2: nat,Y: int] :
% 5.02/5.35 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X2 ) @ Y )
% 5.02/5.35 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % mult_of_nat_commute
% 5.02/5.35 thf(fact_7490_mult__of__nat__commute,axiom,
% 5.02/5.35 ! [X2: nat,Y: real] :
% 5.02/5.35 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X2 ) @ Y )
% 5.02/5.35 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % mult_of_nat_commute
% 5.02/5.35 thf(fact_7491_mult__of__nat__commute,axiom,
% 5.02/5.35 ! [X2: nat,Y: nat] :
% 5.02/5.35 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ Y )
% 5.02/5.35 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % mult_of_nat_commute
% 5.02/5.35 thf(fact_7492_mult__of__nat__commute,axiom,
% 5.02/5.35 ! [X2: nat,Y: rat] :
% 5.02/5.35 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X2 ) @ Y )
% 5.02/5.35 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % mult_of_nat_commute
% 5.02/5.35 thf(fact_7493_of__nat__and__eq,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.02/5.35 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_and_eq
% 5.02/5.35 thf(fact_7494_of__nat__and__eq,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.02/5.35 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_and_eq
% 5.02/5.35 thf(fact_7495_int__cases2,axiom,
% 5.02/5.35 ! [Z: int] :
% 5.02/5.35 ( ! [N: nat] :
% 5.02/5.35 ( Z
% 5.02/5.35 != ( semiri1314217659103216013at_int @ N ) )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ( Z
% 5.02/5.35 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_cases2
% 5.02/5.35 thf(fact_7496_int__diff__cases,axiom,
% 5.02/5.35 ! [Z: int] :
% 5.02/5.35 ~ ! [M3: nat,N: nat] :
% 5.02/5.35 ( Z
% 5.02/5.35 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_diff_cases
% 5.02/5.35 thf(fact_7497_of__nat__less__of__int__iff,axiom,
% 5.02/5.35 ! [N2: nat,X2: int] :
% 5.02/5.35 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X2 ) )
% 5.02/5.35 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_of_int_iff
% 5.02/5.35 thf(fact_7498_of__nat__less__of__int__iff,axiom,
% 5.02/5.35 ! [N2: nat,X2: int] :
% 5.02/5.35 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X2 ) )
% 5.02/5.35 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_of_int_iff
% 5.02/5.35 thf(fact_7499_of__nat__less__of__int__iff,axiom,
% 5.02/5.35 ! [N2: nat,X2: int] :
% 5.02/5.35 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X2 ) )
% 5.02/5.35 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_of_int_iff
% 5.02/5.35 thf(fact_7500_of__nat__0__le__iff,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_0_le_iff
% 5.02/5.35 thf(fact_7501_of__nat__0__le__iff,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_0_le_iff
% 5.02/5.35 thf(fact_7502_of__nat__0__le__iff,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_0_le_iff
% 5.02/5.35 thf(fact_7503_of__nat__0__le__iff,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_0_le_iff
% 5.02/5.35 thf(fact_7504_of__nat__less__0__iff,axiom,
% 5.02/5.35 ! [M: nat] :
% 5.02/5.35 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_0_iff
% 5.02/5.35 thf(fact_7505_of__nat__less__0__iff,axiom,
% 5.02/5.35 ! [M: nat] :
% 5.02/5.35 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_0_iff
% 5.02/5.35 thf(fact_7506_of__nat__less__0__iff,axiom,
% 5.02/5.35 ! [M: nat] :
% 5.02/5.35 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_0_iff
% 5.02/5.35 thf(fact_7507_of__nat__less__0__iff,axiom,
% 5.02/5.35 ! [M: nat] :
% 5.02/5.35 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_0_iff
% 5.02/5.35 thf(fact_7508_of__nat__neq__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 5.02/5.35 != zero_zero_complex ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_neq_0
% 5.02/5.35 thf(fact_7509_of__nat__neq__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.02/5.35 != zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_neq_0
% 5.02/5.35 thf(fact_7510_of__nat__neq__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 5.02/5.35 != zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_neq_0
% 5.02/5.35 thf(fact_7511_of__nat__neq__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 5.02/5.35 != zero_zero_nat ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_neq_0
% 5.02/5.35 thf(fact_7512_of__nat__neq__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 5.02/5.35 != zero_zero_rat ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_neq_0
% 5.02/5.35 thf(fact_7513_div__mult2__eq_H,axiom,
% 5.02/5.35 ! [A: int,M: nat,N2: nat] :
% 5.02/5.35 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.35 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % div_mult2_eq'
% 5.02/5.35 thf(fact_7514_div__mult2__eq_H,axiom,
% 5.02/5.35 ! [A: nat,M: nat,N2: nat] :
% 5.02/5.35 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.02/5.35 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % div_mult2_eq'
% 5.02/5.35 thf(fact_7515_of__nat__less__imp__less,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.35 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_imp_less
% 5.02/5.35 thf(fact_7516_of__nat__less__imp__less,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.35 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_imp_less
% 5.02/5.35 thf(fact_7517_of__nat__less__imp__less,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.35 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_imp_less
% 5.02/5.35 thf(fact_7518_of__nat__less__imp__less,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.02/5.35 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_imp_less
% 5.02/5.35 thf(fact_7519_less__imp__of__nat__less,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % less_imp_of_nat_less
% 5.02/5.35 thf(fact_7520_less__imp__of__nat__less,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % less_imp_of_nat_less
% 5.02/5.35 thf(fact_7521_less__imp__of__nat__less,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % less_imp_of_nat_less
% 5.02/5.35 thf(fact_7522_less__imp__of__nat__less,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % less_imp_of_nat_less
% 5.02/5.35 thf(fact_7523_of__nat__mono,axiom,
% 5.02/5.35 ! [I3: nat,J: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.35 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I3 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_mono
% 5.02/5.35 thf(fact_7524_of__nat__mono,axiom,
% 5.02/5.35 ! [I3: nat,J: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.35 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I3 ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_mono
% 5.02/5.35 thf(fact_7525_of__nat__mono,axiom,
% 5.02/5.35 ! [I3: nat,J: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.35 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_mono
% 5.02/5.35 thf(fact_7526_of__nat__mono,axiom,
% 5.02/5.35 ! [I3: nat,J: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.35 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I3 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_mono
% 5.02/5.35 thf(fact_7527_cos__le__one,axiom,
% 5.02/5.35 ! [X2: real] : ( ord_less_eq_real @ ( cos_real @ X2 ) @ one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_le_one
% 5.02/5.35 thf(fact_7528_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) )
% 5.02/5.35 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.02/5.35 thf(fact_7529_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.02/5.35 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.02/5.35 thf(fact_7530_of__nat__dvd__iff,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.02/5.35 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_dvd_iff
% 5.02/5.35 thf(fact_7531_of__nat__dvd__iff,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.35 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_dvd_iff
% 5.02/5.35 thf(fact_7532_of__nat__dvd__iff,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.02/5.35 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_dvd_iff
% 5.02/5.35 thf(fact_7533_int__ops_I1_J,axiom,
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.02/5.35 = zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % int_ops(1)
% 5.02/5.35 thf(fact_7534_int__ops_I3_J,axiom,
% 5.02/5.35 ! [N2: num] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.35 = ( numeral_numeral_int @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_ops(3)
% 5.02/5.35 thf(fact_7535_nat__int__comparison_I2_J,axiom,
% 5.02/5.35 ( ord_less_nat
% 5.02/5.35 = ( ^ [A5: nat,B5: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nat_int_comparison(2)
% 5.02/5.35 thf(fact_7536_int__of__nat__induct,axiom,
% 5.02/5.35 ! [P: int > $o,Z: int] :
% 5.02/5.35 ( ! [N: nat] : ( P @ ( semiri1314217659103216013at_int @ N ) )
% 5.02/5.35 => ( ! [N: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) )
% 5.02/5.35 => ( P @ Z ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_of_nat_induct
% 5.02/5.35 thf(fact_7537_int__cases,axiom,
% 5.02/5.35 ! [Z: int] :
% 5.02/5.35 ( ! [N: nat] :
% 5.02/5.35 ( Z
% 5.02/5.35 != ( semiri1314217659103216013at_int @ N ) )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ( Z
% 5.02/5.35 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_cases
% 5.02/5.35 thf(fact_7538_nat__int__comparison_I3_J,axiom,
% 5.02/5.35 ( ord_less_eq_nat
% 5.02/5.35 = ( ^ [A5: nat,B5: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nat_int_comparison(3)
% 5.02/5.35 thf(fact_7539_zle__int,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.35 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % zle_int
% 5.02/5.35 thf(fact_7540_nonneg__int__cases,axiom,
% 5.02/5.35 ! [K: int] :
% 5.02/5.35 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ( K
% 5.02/5.35 != ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nonneg_int_cases
% 5.02/5.35 thf(fact_7541_zero__le__imp__eq__int,axiom,
% 5.02/5.35 ! [K: int] :
% 5.02/5.35 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.35 => ? [N: nat] :
% 5.02/5.35 ( K
% 5.02/5.35 = ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % zero_le_imp_eq_int
% 5.02/5.35 thf(fact_7542_of__nat__mod,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.02/5.35 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_mod
% 5.02/5.35 thf(fact_7543_of__nat__mod,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.02/5.35 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_mod
% 5.02/5.35 thf(fact_7544_int__ops_I5_J,axiom,
% 5.02/5.35 ! [A: nat,B: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.02/5.35 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_ops(5)
% 5.02/5.35 thf(fact_7545_int__plus,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 5.02/5.35 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_plus
% 5.02/5.35 thf(fact_7546_zadd__int__left,axiom,
% 5.02/5.35 ! [M: nat,N2: nat,Z: int] :
% 5.02/5.35 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 5.02/5.35 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z ) ) ).
% 5.02/5.35
% 5.02/5.35 % zadd_int_left
% 5.02/5.35 thf(fact_7547_int__ops_I7_J,axiom,
% 5.02/5.35 ! [A: nat,B: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.02/5.35 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_ops(7)
% 5.02/5.35 thf(fact_7548_int__ops_I2_J,axiom,
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.02/5.35 = one_one_int ) ).
% 5.02/5.35
% 5.02/5.35 % int_ops(2)
% 5.02/5.35 thf(fact_7549_zle__iff__zadd,axiom,
% 5.02/5.35 ( ord_less_eq_int
% 5.02/5.35 = ( ^ [W3: int,Z6: int] :
% 5.02/5.35 ? [N3: nat] :
% 5.02/5.35 ( Z6
% 5.02/5.35 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % zle_iff_zadd
% 5.02/5.35 thf(fact_7550_not__int__zless__negative,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % not_int_zless_negative
% 5.02/5.35 thf(fact_7551_int__sum,axiom,
% 5.02/5.35 ! [F: int > nat,A3: set_int] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 5.02/5.35 = ( groups4538972089207619220nt_int
% 5.02/5.35 @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 5.02/5.35 @ A3 ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_sum
% 5.02/5.35 thf(fact_7552_int__sum,axiom,
% 5.02/5.35 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.35 = ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 5.02/5.35 @ A3 ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_sum
% 5.02/5.35 thf(fact_7553_zdiv__int,axiom,
% 5.02/5.35 ! [A: nat,B: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.02/5.35 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % zdiv_int
% 5.02/5.35 thf(fact_7554_of__nat__max,axiom,
% 5.02/5.35 ! [X2: nat,Y: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X2 @ Y ) )
% 5.02/5.35 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_max
% 5.02/5.35 thf(fact_7555_of__nat__max,axiom,
% 5.02/5.35 ! [X2: nat,Y: nat] :
% 5.02/5.35 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X2 @ Y ) )
% 5.02/5.35 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_max
% 5.02/5.35 thf(fact_7556_of__nat__max,axiom,
% 5.02/5.35 ! [X2: nat,Y: nat] :
% 5.02/5.35 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X2 @ Y ) )
% 5.02/5.35 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X2 ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_max
% 5.02/5.35 thf(fact_7557_of__nat__max,axiom,
% 5.02/5.35 ! [X2: nat,Y: nat] :
% 5.02/5.35 ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X2 @ Y ) )
% 5.02/5.35 = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X2 ) @ ( semiri681578069525770553at_rat @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_max
% 5.02/5.35 thf(fact_7558_zmod__int,axiom,
% 5.02/5.35 ! [A: nat,B: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.02/5.35 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % zmod_int
% 5.02/5.35 thf(fact_7559_take__bit__of__nat,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( bit_se2923211474154528505it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 5.02/5.35 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % take_bit_of_nat
% 5.02/5.35 thf(fact_7560_take__bit__of__nat,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( bit_se2925701944663578781it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 5.02/5.35 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % take_bit_of_nat
% 5.02/5.35 thf(fact_7561_of__nat__or__eq,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( bit_se1412395901928357646or_nat @ M @ N2 ) )
% 5.02/5.35 = ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_or_eq
% 5.02/5.35 thf(fact_7562_of__nat__or__eq,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri1316708129612266289at_nat @ ( bit_se1412395901928357646or_nat @ M @ N2 ) )
% 5.02/5.35 = ( bit_se1412395901928357646or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_or_eq
% 5.02/5.35 thf(fact_7563_bit__of__nat__iff__bit,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N2 )
% 5.02/5.35 = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % bit_of_nat_iff_bit
% 5.02/5.35 thf(fact_7564_bit__of__nat__iff__bit,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 )
% 5.02/5.35 = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % bit_of_nat_iff_bit
% 5.02/5.35 thf(fact_7565_nat__less__as__int,axiom,
% 5.02/5.35 ( ord_less_nat
% 5.02/5.35 = ( ^ [A5: nat,B5: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nat_less_as_int
% 5.02/5.35 thf(fact_7566_of__nat__mask__eq,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.02/5.35 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_mask_eq
% 5.02/5.35 thf(fact_7567_of__nat__mask__eq,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.02/5.35 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_mask_eq
% 5.02/5.35 thf(fact_7568_nat__leq__as__int,axiom,
% 5.02/5.35 ( ord_less_eq_nat
% 5.02/5.35 = ( ^ [A5: nat,B5: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nat_leq_as_int
% 5.02/5.35 thf(fact_7569_ex__less__of__nat__mult,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ? [N: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % ex_less_of_nat_mult
% 5.02/5.35 thf(fact_7570_ex__less__of__nat__mult,axiom,
% 5.02/5.35 ! [X2: rat,Y: rat] :
% 5.02/5.35 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.02/5.35 => ? [N: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % ex_less_of_nat_mult
% 5.02/5.35 thf(fact_7571_cos__ge__minus__one,axiom,
% 5.02/5.35 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_ge_minus_one
% 5.02/5.35 thf(fact_7572_of__nat__diff,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.35 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_diff
% 5.02/5.35 thf(fact_7573_of__nat__diff,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.35 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_diff
% 5.02/5.35 thf(fact_7574_of__nat__diff,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.35 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_diff
% 5.02/5.35 thf(fact_7575_of__nat__diff,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 5.02/5.35 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_diff
% 5.02/5.35 thf(fact_7576_abs__cos__le__one,axiom,
% 5.02/5.35 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X2 ) ) @ one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % abs_cos_le_one
% 5.02/5.35 thf(fact_7577_exp__of__nat__mult,axiom,
% 5.02/5.35 ! [N2: nat,X2: complex] :
% 5.02/5.35 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ X2 ) )
% 5.02/5.35 = ( power_power_complex @ ( exp_complex @ X2 ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_of_nat_mult
% 5.02/5.35 thf(fact_7578_exp__of__nat__mult,axiom,
% 5.02/5.35 ! [N2: nat,X2: real] :
% 5.02/5.35 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X2 ) )
% 5.02/5.35 = ( power_power_real @ ( exp_real @ X2 ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_of_nat_mult
% 5.02/5.35 thf(fact_7579_exp__of__nat2__mult,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat] :
% 5.02/5.35 ( ( exp_complex @ ( times_times_complex @ X2 @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.02/5.35 = ( power_power_complex @ ( exp_complex @ X2 ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_of_nat2_mult
% 5.02/5.35 thf(fact_7580_exp__of__nat2__mult,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( exp_real @ ( times_times_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.02/5.35 = ( power_power_real @ ( exp_real @ X2 ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_of_nat2_mult
% 5.02/5.35 thf(fact_7581_reals__Archimedean3,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ! [Y5: real] :
% 5.02/5.35 ? [N: nat] : ( ord_less_real @ Y5 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % reals_Archimedean3
% 5.02/5.35 thf(fact_7582_int__cases4,axiom,
% 5.02/5.35 ! [M: int] :
% 5.02/5.35 ( ! [N: nat] :
% 5.02/5.35 ( M
% 5.02/5.35 != ( semiri1314217659103216013at_int @ N ) )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.02/5.35 => ( M
% 5.02/5.35 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_cases4
% 5.02/5.35 thf(fact_7583_real__of__nat__div4,axiom,
% 5.02/5.35 ! [N2: nat,X2: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X2 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_div4
% 5.02/5.35 thf(fact_7584_atLeast0__atMost__Suc,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.02/5.35 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % atLeast0_atMost_Suc
% 5.02/5.35 thf(fact_7585_int__zle__neg,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.02/5.35 = ( ( N2 = zero_zero_nat )
% 5.02/5.35 & ( M = zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_zle_neg
% 5.02/5.35 thf(fact_7586_int__Suc,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.02/5.35 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_Suc
% 5.02/5.35 thf(fact_7587_int__ops_I4_J,axiom,
% 5.02/5.35 ! [A: nat] :
% 5.02/5.35 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.02/5.35 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_ops(4)
% 5.02/5.35 thf(fact_7588_zless__iff__Suc__zadd,axiom,
% 5.02/5.35 ( ord_less_int
% 5.02/5.35 = ( ^ [W3: int,Z6: int] :
% 5.02/5.35 ? [N3: nat] :
% 5.02/5.35 ( Z6
% 5.02/5.35 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % zless_iff_Suc_zadd
% 5.02/5.35 thf(fact_7589_atLeastAtMost__insertL,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.35 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.02/5.35 = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % atLeastAtMost_insertL
% 5.02/5.35 thf(fact_7590_atLeastAtMostSuc__conv,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.35 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 5.02/5.35 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % atLeastAtMostSuc_conv
% 5.02/5.35 thf(fact_7591_Icc__eq__insert__lb__nat,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.35 => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 5.02/5.35 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % Icc_eq_insert_lb_nat
% 5.02/5.35 thf(fact_7592_negative__zle__0,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % negative_zle_0
% 5.02/5.35 thf(fact_7593_nonpos__int__cases,axiom,
% 5.02/5.35 ! [K: int] :
% 5.02/5.35 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ( K
% 5.02/5.35 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nonpos_int_cases
% 5.02/5.35 thf(fact_7594_real__of__nat__div,axiom,
% 5.02/5.35 ! [D: nat,N2: nat] :
% 5.02/5.35 ( ( dvd_dvd_nat @ D @ N2 )
% 5.02/5.35 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ D ) )
% 5.02/5.35 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_div
% 5.02/5.35 thf(fact_7595_cos__one__2pi,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 = ( ? [X: nat] :
% 5.02/5.35 ( X2
% 5.02/5.35 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.02/5.35 | ? [X: nat] :
% 5.02/5.35 ( X2
% 5.02/5.35 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_one_2pi
% 5.02/5.35 thf(fact_7596_cos__two__neq__zero,axiom,
% 5.02/5.35 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.35 != zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_two_neq_zero
% 5.02/5.35 thf(fact_7597_mod__mult2__eq_H,axiom,
% 5.02/5.35 ! [A: int,M: nat,N2: nat] :
% 5.02/5.35 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % mod_mult2_eq'
% 5.02/5.35 thf(fact_7598_mod__mult2__eq_H,axiom,
% 5.02/5.35 ! [A: nat,M: nat,N2: nat] :
% 5.02/5.35 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % mod_mult2_eq'
% 5.02/5.35 thf(fact_7599_field__char__0__class_Oof__nat__div,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N2 ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % field_char_0_class.of_nat_div
% 5.02/5.35 thf(fact_7600_field__char__0__class_Oof__nat__div,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N2 ) )
% 5.02/5.35 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % field_char_0_class.of_nat_div
% 5.02/5.35 thf(fact_7601_field__char__0__class_Oof__nat__div,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N2 ) )
% 5.02/5.35 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % field_char_0_class.of_nat_div
% 5.02/5.35 thf(fact_7602_zero__less__imp__eq__int,axiom,
% 5.02/5.35 ! [K: int] :
% 5.02/5.35 ( ( ord_less_int @ zero_zero_int @ K )
% 5.02/5.35 => ? [N: nat] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.02/5.35 & ( K
% 5.02/5.35 = ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % zero_less_imp_eq_int
% 5.02/5.35 thf(fact_7603_pos__int__cases,axiom,
% 5.02/5.35 ! [K: int] :
% 5.02/5.35 ( ( ord_less_int @ zero_zero_int @ K )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ( ( K
% 5.02/5.35 = ( semiri1314217659103216013at_int @ N ) )
% 5.02/5.35 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % pos_int_cases
% 5.02/5.35 thf(fact_7604_int__cases3,axiom,
% 5.02/5.35 ! [K: int] :
% 5.02/5.35 ( ( K != zero_zero_int )
% 5.02/5.35 => ( ! [N: nat] :
% 5.02/5.35 ( ( K
% 5.02/5.35 = ( semiri1314217659103216013at_int @ N ) )
% 5.02/5.35 => ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ( ( K
% 5.02/5.35 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.02/5.35 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_cases3
% 5.02/5.35 thf(fact_7605_nat__less__real__le,axiom,
% 5.02/5.35 ( ord_less_nat
% 5.02/5.35 = ( ^ [N3: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nat_less_real_le
% 5.02/5.35 thf(fact_7606_nat__le__real__less,axiom,
% 5.02/5.35 ( ord_less_eq_nat
% 5.02/5.35 = ( ^ [N3: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nat_le_real_less
% 5.02/5.35 thf(fact_7607_zmult__zless__mono2__lemma,axiom,
% 5.02/5.35 ! [I3: int,J: int,K: nat] :
% 5.02/5.35 ( ( ord_less_int @ I3 @ J )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.35 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I3 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % zmult_zless_mono2_lemma
% 5.02/5.35 thf(fact_7608_not__zle__0__negative,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % not_zle_0_negative
% 5.02/5.35 thf(fact_7609_negD,axiom,
% 5.02/5.35 ! [X2: int] :
% 5.02/5.35 ( ( ord_less_int @ X2 @ zero_zero_int )
% 5.02/5.35 => ? [N: nat] :
% 5.02/5.35 ( X2
% 5.02/5.35 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % negD
% 5.02/5.35 thf(fact_7610_negative__zless__0,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % negative_zless_0
% 5.02/5.35 thf(fact_7611_int__ops_I6_J,axiom,
% 5.02/5.35 ! [A: nat,B: nat] :
% 5.02/5.35 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.02/5.35 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.02/5.35 = zero_zero_int ) )
% 5.02/5.35 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.02/5.35 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.02/5.35 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_ops(6)
% 5.02/5.35 thf(fact_7612_real__of__nat__div__aux,axiom,
% 5.02/5.35 ! [X2: nat,D: nat] :
% 5.02/5.35 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X2 ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.02/5.35 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X2 @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X2 @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_div_aux
% 5.02/5.35 thf(fact_7613_nat__approx__posE,axiom,
% 5.02/5.35 ! [E2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ E2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % nat_approx_posE
% 5.02/5.35 thf(fact_7614_nat__approx__posE,axiom,
% 5.02/5.35 ! [E2: rat] :
% 5.02/5.35 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) ) @ E2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % nat_approx_posE
% 5.02/5.35 thf(fact_7615_of__nat__less__two__power,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_two_power
% 5.02/5.35 thf(fact_7616_of__nat__less__two__power,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_two_power
% 5.02/5.35 thf(fact_7617_of__nat__less__two__power,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_less_two_power
% 5.02/5.35 thf(fact_7618_cos__zero__lemma,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ( cos_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 => ? [N: nat] :
% 5.02/5.35 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_zero_lemma
% 5.02/5.35 thf(fact_7619_cos__two__less__zero,axiom,
% 5.02/5.35 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.02/5.35
% 5.02/5.35 % cos_two_less_zero
% 5.02/5.35 thf(fact_7620_cos__is__zero,axiom,
% 5.02/5.35 ? [X5: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.02/5.35 & ( ord_less_eq_real @ X5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.35 & ( ( cos_real @ X5 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 & ! [Y5: real] :
% 5.02/5.35 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.02/5.35 & ( ord_less_eq_real @ Y5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.35 & ( ( cos_real @ Y5 )
% 5.02/5.35 = zero_zero_real ) )
% 5.02/5.35 => ( Y5 = X5 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_is_zero
% 5.02/5.35 thf(fact_7621_cos__two__le__zero,axiom,
% 5.02/5.35 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.02/5.35
% 5.02/5.35 % cos_two_le_zero
% 5.02/5.35 thf(fact_7622_cos__zero__iff,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 = ( ? [N3: nat] :
% 5.02/5.35 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.35 | ? [N3: nat] :
% 5.02/5.35 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_zero_iff
% 5.02/5.35 thf(fact_7623_inverse__of__nat__le,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( ( N2 != zero_zero_nat )
% 5.02/5.35 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % inverse_of_nat_le
% 5.02/5.35 thf(fact_7624_inverse__of__nat__le,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( ( N2 != zero_zero_nat )
% 5.02/5.35 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % inverse_of_nat_le
% 5.02/5.35 thf(fact_7625_cos__total,axiom,
% 5.02/5.35 ! [Y: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.35 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.35 => ? [X5: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.02/5.35 & ( ord_less_eq_real @ X5 @ pi )
% 5.02/5.35 & ( ( cos_real @ X5 )
% 5.02/5.35 = Y )
% 5.02/5.35 & ! [Y5: real] :
% 5.02/5.35 ( ( ( ord_less_eq_real @ zero_zero_real @ Y5 )
% 5.02/5.35 & ( ord_less_eq_real @ Y5 @ pi )
% 5.02/5.35 & ( ( cos_real @ Y5 )
% 5.02/5.35 = Y ) )
% 5.02/5.35 => ( Y5 = X5 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_total
% 5.02/5.35 thf(fact_7626_exp__divide__power__eq,axiom,
% 5.02/5.35 ! [N2: nat,X2: complex] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X2 @ ( semiri8010041392384452111omplex @ N2 ) ) ) @ N2 )
% 5.02/5.35 = ( exp_complex @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_divide_power_eq
% 5.02/5.35 thf(fact_7627_exp__divide__power__eq,axiom,
% 5.02/5.35 ! [N2: nat,X2: real] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.02/5.35 = ( exp_real @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_divide_power_eq
% 5.02/5.35 thf(fact_7628_real__archimedian__rdiv__eq__0,axiom,
% 5.02/5.35 ! [X2: real,C: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.02/5.35 => ( ! [M3: nat] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ M3 )
% 5.02/5.35 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M3 ) @ X2 ) @ C ) )
% 5.02/5.35 => ( X2 = zero_zero_real ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_archimedian_rdiv_eq_0
% 5.02/5.35 thf(fact_7629_neg__int__cases,axiom,
% 5.02/5.35 ! [K: int] :
% 5.02/5.35 ( ( ord_less_int @ K @ zero_zero_int )
% 5.02/5.35 => ~ ! [N: nat] :
% 5.02/5.35 ( ( K
% 5.02/5.35 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.02/5.35 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % neg_int_cases
% 5.02/5.35 thf(fact_7630_zdiff__int__split,axiom,
% 5.02/5.35 ! [P: int > $o,X2: nat,Y: nat] :
% 5.02/5.35 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X2 @ Y ) ) )
% 5.02/5.35 = ( ( ( ord_less_eq_nat @ Y @ X2 )
% 5.02/5.35 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X2 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.02/5.35 & ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.35 => ( P @ zero_zero_int ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % zdiff_int_split
% 5.02/5.35 thf(fact_7631_real__of__nat__div2,axiom,
% 5.02/5.35 ! [N2: nat,X2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_div2
% 5.02/5.35 thf(fact_7632_ln__realpow,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ln_ln_real @ ( power_power_real @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % ln_realpow
% 5.02/5.35 thf(fact_7633_real__of__nat__div3,axiom,
% 5.02/5.35 ! [N2: nat,X2: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X2 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X2 ) ) ) @ one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % real_of_nat_div3
% 5.02/5.35 thf(fact_7634_cos__45,axiom,
% 5.02/5.35 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.02/5.35 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_45
% 5.02/5.35 thf(fact_7635_Bernoulli__inequality,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % Bernoulli_inequality
% 5.02/5.35 thf(fact_7636_cos__times__cos,axiom,
% 5.02/5.35 ! [W: complex,Z: complex] :
% 5.02/5.35 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_times_cos
% 5.02/5.35 thf(fact_7637_cos__times__cos,axiom,
% 5.02/5.35 ! [W: real,Z: real] :
% 5.02/5.35 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.02/5.35 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_times_cos
% 5.02/5.35 thf(fact_7638_cos__plus__cos,axiom,
% 5.02/5.35 ! [W: complex,Z: complex] :
% 5.02/5.35 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.02/5.35 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_plus_cos
% 5.02/5.35 thf(fact_7639_cos__plus__cos,axiom,
% 5.02/5.35 ! [W: real,Z: real] :
% 5.02/5.35 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.02/5.35 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_plus_cos
% 5.02/5.35 thf(fact_7640_set__decode__plus__power__2,axiom,
% 5.02/5.35 ! [N2: nat,Z: nat] :
% 5.02/5.35 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 5.02/5.35 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 5.02/5.35 = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % set_decode_plus_power_2
% 5.02/5.35 thf(fact_7641_cos__double__less__one,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.35 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) ) @ one_one_real ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_double_less_one
% 5.02/5.35 thf(fact_7642_cos__gt__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_gt_zero
% 5.02/5.35 thf(fact_7643_cos__60,axiom,
% 5.02/5.35 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.02/5.35 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_60
% 5.02/5.35 thf(fact_7644_cos__30,axiom,
% 5.02/5.35 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.02/5.35 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_30
% 5.02/5.35 thf(fact_7645_cos__one__2pi__int,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 = ( ? [X: int] :
% 5.02/5.35 ( X2
% 5.02/5.35 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_one_2pi_int
% 5.02/5.35 thf(fact_7646_cos__double__cos,axiom,
% 5.02/5.35 ! [W: complex] :
% 5.02/5.35 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.02/5.35 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_double_cos
% 5.02/5.35 thf(fact_7647_cos__double__cos,axiom,
% 5.02/5.35 ! [W: real] :
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.02/5.35 = ( 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 ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_double_cos
% 5.02/5.35 thf(fact_7648_cos__treble__cos,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X2 ) )
% 5.02/5.35 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_treble_cos
% 5.02/5.35 thf(fact_7649_cos__treble__cos,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X2 ) )
% 5.02/5.35 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_treble_cos
% 5.02/5.35 thf(fact_7650_cos__gt__zero__pi,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_gt_zero_pi
% 5.02/5.35 thf(fact_7651_cos__ge__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_ge_zero
% 5.02/5.35 thf(fact_7652_and__int_Opinduct,axiom,
% 5.02/5.35 ! [A0: int,A12: int,P: int > int > $o] :
% 5.02/5.35 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.02/5.35 => ( ! [K2: int,L4: int] :
% 5.02/5.35 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.02/5.35 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.02/5.35 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.02/5.35 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.02/5.35 => ( P @ K2 @ L4 ) ) )
% 5.02/5.35 => ( P @ A0 @ A12 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % and_int.pinduct
% 5.02/5.35 thf(fact_7653_double__arith__series,axiom,
% 5.02/5.35 ! [A: complex,D: complex,N2: nat] :
% 5.02/5.35 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.02/5.35 @ ( groups2073611262835488442omplex
% 5.02/5.35 @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I5 ) @ D ) )
% 5.02/5.35 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ D ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_arith_series
% 5.02/5.35 thf(fact_7654_double__arith__series,axiom,
% 5.02/5.35 ! [A: int,D: int,N2: nat] :
% 5.02/5.35 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.02/5.35 @ ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 5.02/5.35 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_arith_series
% 5.02/5.35 thf(fact_7655_double__arith__series,axiom,
% 5.02/5.35 ! [A: rat,D: rat,N2: nat] :
% 5.02/5.35 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.02/5.35 @ ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I5 ) @ D ) )
% 5.02/5.35 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_arith_series
% 5.02/5.35 thf(fact_7656_double__arith__series,axiom,
% 5.02/5.35 ! [A: nat,D: nat,N2: nat] :
% 5.02/5.35 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.02/5.35 @ ( groups3542108847815614940at_nat
% 5.02/5.35 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 5.02/5.35 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_arith_series
% 5.02/5.35 thf(fact_7657_double__arith__series,axiom,
% 5.02/5.35 ! [A: real,D: real,N2: nat] :
% 5.02/5.35 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I5 ) @ D ) )
% 5.02/5.35 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ D ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_arith_series
% 5.02/5.35 thf(fact_7658_double__gauss__sum,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum
% 5.02/5.35 thf(fact_7659_double__gauss__sum,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum
% 5.02/5.35 thf(fact_7660_double__gauss__sum,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum
% 5.02/5.35 thf(fact_7661_double__gauss__sum,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum
% 5.02/5.35 thf(fact_7662_double__gauss__sum,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.35 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum
% 5.02/5.35 thf(fact_7663_cos__arctan,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( cos_real @ ( arctan @ X2 ) )
% 5.02/5.35 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_arctan
% 5.02/5.35 thf(fact_7664_arith__series,axiom,
% 5.02/5.35 ! [A: int,D: int,N2: nat] :
% 5.02/5.35 ( ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 5.02/5.35 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.35 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % arith_series
% 5.02/5.35 thf(fact_7665_arith__series,axiom,
% 5.02/5.35 ! [A: nat,D: nat,N2: nat] :
% 5.02/5.35 ( ( groups3542108847815614940at_nat
% 5.02/5.35 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 5.02/5.35 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.35 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % arith_series
% 5.02/5.35 thf(fact_7666_gauss__sum,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.35 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % gauss_sum
% 5.02/5.35 thf(fact_7667_gauss__sum,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.35 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % gauss_sum
% 5.02/5.35 thf(fact_7668_double__gauss__sum__from__Suc__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.02/5.35 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum_from_Suc_0
% 5.02/5.35 thf(fact_7669_double__gauss__sum__from__Suc__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.02/5.35 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum_from_Suc_0
% 5.02/5.35 thf(fact_7670_double__gauss__sum__from__Suc__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.02/5.35 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum_from_Suc_0
% 5.02/5.35 thf(fact_7671_double__gauss__sum__from__Suc__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.02/5.35 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum_from_Suc_0
% 5.02/5.35 thf(fact_7672_double__gauss__sum__from__Suc__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.02/5.35 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % double_gauss_sum_from_Suc_0
% 5.02/5.35 thf(fact_7673_Bernoulli__inequality__even,axiom,
% 5.02/5.35 ! [N2: nat,X2: real] :
% 5.02/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X2 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X2 ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % Bernoulli_inequality_even
% 5.02/5.35 thf(fact_7674_sum__gp__offset,axiom,
% 5.02/5.35 ! [X2: complex,M: nat,N2: nat] :
% 5.02/5.35 ( ( ( X2 = one_one_complex )
% 5.02/5.35 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 5.02/5.35 & ( ( X2 != one_one_complex )
% 5.02/5.35 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_gp_offset
% 5.02/5.35 thf(fact_7675_sum__gp__offset,axiom,
% 5.02/5.35 ! [X2: rat,M: nat,N2: nat] :
% 5.02/5.35 ( ( ( X2 = one_one_rat )
% 5.02/5.35 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 5.02/5.35 & ( ( X2 != one_one_rat )
% 5.02/5.35 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.35 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_gp_offset
% 5.02/5.35 thf(fact_7676_sum__gp__offset,axiom,
% 5.02/5.35 ! [X2: real,M: nat,N2: nat] :
% 5.02/5.35 ( ( ( X2 = one_one_real )
% 5.02/5.35 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 5.02/5.35 & ( ( X2 != one_one_real )
% 5.02/5.35 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.35 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_gp_offset
% 5.02/5.35 thf(fact_7677_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.02/5.35 ! [N2: nat,X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_ge_one_plus_x_over_n_power_n
% 5.02/5.35 thf(fact_7678_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_ge_one_minus_x_over_n_power_n
% 5.02/5.35 thf(fact_7679_cot__gt__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cot_gt_zero
% 5.02/5.35 thf(fact_7680_cos__zero__iff__int,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 = ( ? [I5: int] :
% 5.02/5.35 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_zero_iff_int
% 5.02/5.35 thf(fact_7681_gauss__sum__from__Suc__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.02/5.35 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % gauss_sum_from_Suc_0
% 5.02/5.35 thf(fact_7682_gauss__sum__from__Suc__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.02/5.35 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % gauss_sum_from_Suc_0
% 5.02/5.35 thf(fact_7683_of__nat__code__if,axiom,
% 5.02/5.35 ( semiri8010041392384452111omplex
% 5.02/5.35 = ( ^ [N3: nat] :
% 5.02/5.35 ( if_complex @ ( N3 = zero_zero_nat ) @ zero_zero_complex
% 5.02/5.35 @ ( produc1917071388513777916omplex
% 5.02/5.35 @ ^ [M6: nat,Q4: nat] : ( if_complex @ ( Q4 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M6 ) ) @ one_one_complex ) )
% 5.02/5.35 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_code_if
% 5.02/5.35 thf(fact_7684_of__nat__code__if,axiom,
% 5.02/5.35 ( semiri1314217659103216013at_int
% 5.02/5.35 = ( ^ [N3: nat] :
% 5.02/5.35 ( if_int @ ( N3 = zero_zero_nat ) @ zero_zero_int
% 5.02/5.35 @ ( produc6840382203811409530at_int
% 5.02/5.35 @ ^ [M6: nat,Q4: nat] : ( if_int @ ( Q4 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M6 ) ) @ one_one_int ) )
% 5.02/5.35 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_code_if
% 5.02/5.35 thf(fact_7685_of__nat__code__if,axiom,
% 5.02/5.35 ( semiri5074537144036343181t_real
% 5.02/5.35 = ( ^ [N3: nat] :
% 5.02/5.35 ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 5.02/5.35 @ ( produc1703576794950452218t_real
% 5.02/5.35 @ ^ [M6: nat,Q4: nat] : ( if_real @ ( Q4 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M6 ) ) @ one_one_real ) )
% 5.02/5.35 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_code_if
% 5.02/5.35 thf(fact_7686_of__nat__code__if,axiom,
% 5.02/5.35 ( semiri1316708129612266289at_nat
% 5.02/5.35 = ( ^ [N3: nat] :
% 5.02/5.35 ( if_nat @ ( N3 = zero_zero_nat ) @ zero_zero_nat
% 5.02/5.35 @ ( produc6842872674320459806at_nat
% 5.02/5.35 @ ^ [M6: nat,Q4: nat] : ( if_nat @ ( Q4 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M6 ) ) @ one_one_nat ) )
% 5.02/5.35 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_code_if
% 5.02/5.35 thf(fact_7687_of__nat__code__if,axiom,
% 5.02/5.35 ( semiri681578069525770553at_rat
% 5.02/5.35 = ( ^ [N3: nat] :
% 5.02/5.35 ( if_rat @ ( N3 = zero_zero_nat ) @ zero_zero_rat
% 5.02/5.35 @ ( produc6207742614233964070at_rat
% 5.02/5.35 @ ^ [M6: nat,Q4: nat] : ( if_rat @ ( Q4 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M6 ) ) @ one_one_rat ) )
% 5.02/5.35 @ ( divmod_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % of_nat_code_if
% 5.02/5.35 thf(fact_7688_linear__plus__1__le__power,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X2 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X2 @ one_one_real ) @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % linear_plus_1_le_power
% 5.02/5.35 thf(fact_7689_monoseq__arctan__series,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.35 => ( topolo6980174941875973593q_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % monoseq_arctan_series
% 5.02/5.35 thf(fact_7690_lemma__termdiff3,axiom,
% 5.02/5.35 ! [H2: real,Z: real,K5: real,N2: nat] :
% 5.02/5.35 ( ( H2 != zero_zero_real )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff3
% 5.02/5.35 thf(fact_7691_lemma__termdiff3,axiom,
% 5.02/5.35 ! [H2: complex,Z: complex,K5: real,N2: nat] :
% 5.02/5.35 ( ( H2 != zero_zero_complex )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff3
% 5.02/5.35 thf(fact_7692_ln__series,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.35 => ( ( ln_ln_real @ X2 )
% 5.02/5.35 = ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % ln_series
% 5.02/5.35 thf(fact_7693_powser__zero,axiom,
% 5.02/5.35 ! [F: nat > complex] :
% 5.02/5.35 ( ( suminf_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) )
% 5.02/5.35 = ( F @ zero_zero_nat ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_zero
% 5.02/5.35 thf(fact_7694_powser__zero,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) )
% 5.02/5.35 = ( F @ zero_zero_nat ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_zero
% 5.02/5.35 thf(fact_7695_int__int__eq,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ( semiri1314217659103216013at_int @ M )
% 5.02/5.35 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.35 = ( M = N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % int_int_eq
% 5.02/5.35 thf(fact_7696_complex__mod__triangle__ineq2,axiom,
% 5.02/5.35 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.02/5.35
% 5.02/5.35 % complex_mod_triangle_ineq2
% 5.02/5.35 thf(fact_7697_monoseq__realpow,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.35 => ( topolo6980174941875973593q_real @ ( power_power_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % monoseq_realpow
% 5.02/5.35 thf(fact_7698_exp__bound__half,axiom,
% 5.02/5.35 ! [Z: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_bound_half
% 5.02/5.35 thf(fact_7699_exp__bound__half,axiom,
% 5.02/5.35 ! [Z: complex] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_bound_half
% 5.02/5.35 thf(fact_7700_exp__bound__lemma,axiom,
% 5.02/5.35 ! [Z: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_bound_lemma
% 5.02/5.35 thf(fact_7701_exp__bound__lemma,axiom,
% 5.02/5.35 ! [Z: complex] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % exp_bound_lemma
% 5.02/5.35 thf(fact_7702_pi__series,axiom,
% 5.02/5.35 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = ( suminf_real
% 5.02/5.35 @ ^ [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 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % pi_series
% 5.02/5.35 thf(fact_7703_arctan__series,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.35 => ( ( arctan @ X2 )
% 5.02/5.35 = ( suminf_real
% 5.02/5.35 @ ^ [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 @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % arctan_series
% 5.02/5.35 thf(fact_7704_norm__divide__numeral,axiom,
% 5.02/5.35 ! [A: real,W: num] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.35 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_divide_numeral
% 5.02/5.35 thf(fact_7705_norm__divide__numeral,axiom,
% 5.02/5.35 ! [A: complex,W: num] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.02/5.35 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_divide_numeral
% 5.02/5.35 thf(fact_7706_norm__mult__numeral2,axiom,
% 5.02/5.35 ! [A: real,W: num] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.35 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult_numeral2
% 5.02/5.35 thf(fact_7707_norm__mult__numeral2,axiom,
% 5.02/5.35 ! [A: complex,W: num] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.02/5.35 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult_numeral2
% 5.02/5.35 thf(fact_7708_norm__mult__numeral1,axiom,
% 5.02/5.35 ! [W: num,A: real] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.02/5.35 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult_numeral1
% 5.02/5.35 thf(fact_7709_norm__mult__numeral1,axiom,
% 5.02/5.35 ! [W: num,A: complex] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.02/5.35 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult_numeral1
% 5.02/5.35 thf(fact_7710_norm__neg__numeral,axiom,
% 5.02/5.35 ! [W: num] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.35 = ( numeral_numeral_real @ W ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_neg_numeral
% 5.02/5.35 thf(fact_7711_norm__neg__numeral,axiom,
% 5.02/5.35 ! [W: num] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.02/5.35 = ( numeral_numeral_real @ W ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_neg_numeral
% 5.02/5.35 thf(fact_7712_norm__le__zero__iff,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X2 ) @ zero_zero_real )
% 5.02/5.35 = ( X2 = zero_zero_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_le_zero_iff
% 5.02/5.35 thf(fact_7713_norm__le__zero__iff,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ zero_zero_real )
% 5.02/5.35 = ( X2 = zero_zero_complex ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_le_zero_iff
% 5.02/5.35 thf(fact_7714_norm__eq__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( real_V7735802525324610683m_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 = ( X2 = zero_zero_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_eq_zero
% 5.02/5.35 thf(fact_7715_norm__eq__zero,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( ( real_V1022390504157884413omplex @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 = ( X2 = zero_zero_complex ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_eq_zero
% 5.02/5.35 thf(fact_7716_norm__zero,axiom,
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % norm_zero
% 5.02/5.35 thf(fact_7717_norm__zero,axiom,
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % norm_zero
% 5.02/5.35 thf(fact_7718_norm__one,axiom,
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % norm_one
% 5.02/5.35 thf(fact_7719_norm__one,axiom,
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % norm_one
% 5.02/5.35 thf(fact_7720_norm__numeral,axiom,
% 5.02/5.35 ! [W: num] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.35 = ( numeral_numeral_real @ W ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_numeral
% 5.02/5.35 thf(fact_7721_norm__numeral,axiom,
% 5.02/5.35 ! [W: num] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.35 = ( numeral_numeral_real @ W ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_numeral
% 5.02/5.35 thf(fact_7722_zero__less__norm__iff,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.02/5.35 = ( X2 != zero_zero_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % zero_less_norm_iff
% 5.02/5.35 thf(fact_7723_zero__less__norm__iff,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.02/5.35 = ( X2 != zero_zero_complex ) ) ).
% 5.02/5.35
% 5.02/5.35 % zero_less_norm_iff
% 5.02/5.35 thf(fact_7724_norm__mult,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y ) )
% 5.02/5.35 = ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult
% 5.02/5.35 thf(fact_7725_norm__mult,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y ) )
% 5.02/5.35 = ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult
% 5.02/5.35 thf(fact_7726_norm__divide,axiom,
% 5.02/5.35 ! [A: real,B: real] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.35 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_divide
% 5.02/5.35 thf(fact_7727_norm__divide,axiom,
% 5.02/5.35 ! [A: complex,B: complex] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.35 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_divide
% 5.02/5.35 thf(fact_7728_norm__power,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N2 ) )
% 5.02/5.35 = ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_power
% 5.02/5.35 thf(fact_7729_norm__power,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N2 ) )
% 5.02/5.35 = ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_power
% 5.02/5.35 thf(fact_7730_norm__uminus__minus,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X2 ) @ Y ) )
% 5.02/5.35 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_uminus_minus
% 5.02/5.35 thf(fact_7731_norm__uminus__minus,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X2 ) @ Y ) )
% 5.02/5.35 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_uminus_minus
% 5.02/5.35 thf(fact_7732_nonzero__norm__divide,axiom,
% 5.02/5.35 ! [B: real,A: real] :
% 5.02/5.35 ( ( B != zero_zero_real )
% 5.02/5.35 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.35 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nonzero_norm_divide
% 5.02/5.35 thf(fact_7733_nonzero__norm__divide,axiom,
% 5.02/5.35 ! [B: complex,A: complex] :
% 5.02/5.35 ( ( B != zero_zero_complex )
% 5.02/5.35 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.35 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % nonzero_norm_divide
% 5.02/5.35 thf(fact_7734_power__eq__imp__eq__norm,axiom,
% 5.02/5.35 ! [W: real,N2: nat,Z: real] :
% 5.02/5.35 ( ( ( power_power_real @ W @ N2 )
% 5.02/5.35 = ( power_power_real @ Z @ N2 ) )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ( ( real_V7735802525324610683m_real @ W )
% 5.02/5.35 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_eq_imp_eq_norm
% 5.02/5.35 thf(fact_7735_power__eq__imp__eq__norm,axiom,
% 5.02/5.35 ! [W: complex,N2: nat,Z: complex] :
% 5.02/5.35 ( ( ( power_power_complex @ W @ N2 )
% 5.02/5.35 = ( power_power_complex @ Z @ N2 ) )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ( ( real_V1022390504157884413omplex @ W )
% 5.02/5.35 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_eq_imp_eq_norm
% 5.02/5.35 thf(fact_7736_norm__mult__less,axiom,
% 5.02/5.35 ! [X2: real,R2: real,Y: real,S2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R2 )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 5.02/5.35 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult_less
% 5.02/5.35 thf(fact_7737_norm__mult__less,axiom,
% 5.02/5.35 ! [X2: complex,R2: real,Y: complex,S2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R2 )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 5.02/5.35 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y ) ) @ ( times_times_real @ R2 @ S2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult_less
% 5.02/5.35 thf(fact_7738_norm__mult__ineq,axiom,
% 5.02/5.35 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X2 @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult_ineq
% 5.02/5.35 thf(fact_7739_norm__mult__ineq,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X2 @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_mult_ineq
% 5.02/5.35 thf(fact_7740_norm__triangle__lt,axiom,
% 5.02/5.35 ! [X2: real,Y: real,E2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 5.02/5.35 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) @ E2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_lt
% 5.02/5.35 thf(fact_7741_norm__triangle__lt,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex,E2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 5.02/5.35 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) @ E2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_lt
% 5.02/5.35 thf(fact_7742_norm__add__less,axiom,
% 5.02/5.35 ! [X2: real,R2: real,Y: real,S2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ R2 )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 5.02/5.35 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_add_less
% 5.02/5.35 thf(fact_7743_norm__add__less,axiom,
% 5.02/5.35 ! [X2: complex,R2: real,Y: complex,S2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ R2 )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 5.02/5.35 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_add_less
% 5.02/5.35 thf(fact_7744_norm__add__leD,axiom,
% 5.02/5.35 ! [A: real,B: real,C: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_add_leD
% 5.02/5.35 thf(fact_7745_norm__add__leD,axiom,
% 5.02/5.35 ! [A: complex,B: complex,C: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_add_leD
% 5.02/5.35 thf(fact_7746_norm__triangle__le,axiom,
% 5.02/5.35 ! [X2: real,Y: real,E2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) @ E2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_le
% 5.02/5.35 thf(fact_7747_norm__triangle__le,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex,E2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) @ E2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_le
% 5.02/5.35 thf(fact_7748_norm__triangle__ineq,axiom,
% 5.02/5.35 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_ineq
% 5.02/5.35 thf(fact_7749_norm__triangle__ineq,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X2 @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_ineq
% 5.02/5.35 thf(fact_7750_norm__triangle__mono,axiom,
% 5.02/5.35 ! [A: real,R2: real,B: real,S2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_mono
% 5.02/5.35 thf(fact_7751_norm__triangle__mono,axiom,
% 5.02/5.35 ! [A: complex,R2: real,B: complex,S2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R2 @ S2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_mono
% 5.02/5.35 thf(fact_7752_norm__power__ineq,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X2 @ N2 ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X2 ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_power_ineq
% 5.02/5.35 thf(fact_7753_norm__power__ineq,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X2 @ N2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X2 ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_power_ineq
% 5.02/5.35 thf(fact_7754_norm__diff__triangle__less,axiom,
% 5.02/5.35 ! [X2: real,Y: real,E1: real,Z: real,E22: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y ) ) @ E1 )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.02/5.35 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_diff_triangle_less
% 5.02/5.35 thf(fact_7755_norm__diff__triangle__less,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) @ E1 )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.02/5.35 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_diff_triangle_less
% 5.02/5.35 thf(fact_7756_norm__triangle__le__diff,axiom,
% 5.02/5.35 ! [X2: real,Y: real,E2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y ) ) @ E2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_le_diff
% 5.02/5.35 thf(fact_7757_norm__triangle__le__diff,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex,E2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) @ E2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_le_diff
% 5.02/5.35 thf(fact_7758_norm__diff__triangle__le,axiom,
% 5.02/5.35 ! [X2: real,Y: real,E1: real,Z: real,E22: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y ) ) @ E1 )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_diff_triangle_le
% 5.02/5.35 thf(fact_7759_norm__diff__triangle__le,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) @ E1 )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_diff_triangle_le
% 5.02/5.35 thf(fact_7760_norm__triangle__ineq4,axiom,
% 5.02/5.35 ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_ineq4
% 5.02/5.35 thf(fact_7761_norm__triangle__ineq4,axiom,
% 5.02/5.35 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_ineq4
% 5.02/5.35 thf(fact_7762_norm__triangle__sub,axiom,
% 5.02/5.35 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X2 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X2 @ Y ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_sub
% 5.02/5.35 thf(fact_7763_norm__triangle__sub,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X2 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X2 @ Y ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_triangle_sub
% 5.02/5.35 thf(fact_7764_norm__diff__ineq,axiom,
% 5.02/5.35 ! [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 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_diff_ineq
% 5.02/5.35 thf(fact_7765_norm__diff__ineq,axiom,
% 5.02/5.35 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_diff_ineq
% 5.02/5.35 thf(fact_7766_power__eq__1__iff,axiom,
% 5.02/5.35 ! [W: real,N2: nat] :
% 5.02/5.35 ( ( ( power_power_real @ W @ N2 )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_eq_1_iff
% 5.02/5.35 thf(fact_7767_power__eq__1__iff,axiom,
% 5.02/5.35 ! [W: complex,N2: nat] :
% 5.02/5.35 ( ( ( power_power_complex @ W @ N2 )
% 5.02/5.35 = one_one_complex )
% 5.02/5.35 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 | ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_eq_1_iff
% 5.02/5.35 thf(fact_7768_norm__diff__triangle__ineq,axiom,
% 5.02/5.35 ! [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 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_diff_triangle_ineq
% 5.02/5.35 thf(fact_7769_norm__diff__triangle__ineq,axiom,
% 5.02/5.35 ! [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 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_diff_triangle_ineq
% 5.02/5.35 thf(fact_7770_square__norm__one,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 => ( ( real_V7735802525324610683m_real @ X2 )
% 5.02/5.35 = one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % square_norm_one
% 5.02/5.35 thf(fact_7771_square__norm__one,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = one_one_complex )
% 5.02/5.35 => ( ( real_V1022390504157884413omplex @ X2 )
% 5.02/5.35 = one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % square_norm_one
% 5.02/5.35 thf(fact_7772_norm__power__diff,axiom,
% 5.02/5.35 ! [Z: real,W: real,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z @ M ) @ ( power_power_real @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z @ W ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_power_diff
% 5.02/5.35 thf(fact_7773_norm__power__diff,axiom,
% 5.02/5.35 ! [Z: complex,W: complex,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % norm_power_diff
% 5.02/5.35 thf(fact_7774_suminf__geometric,axiom,
% 5.02/5.35 ! [C: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.02/5.35 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.02/5.35 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_geometric
% 5.02/5.35 thf(fact_7775_suminf__geometric,axiom,
% 5.02/5.35 ! [C: complex] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.02/5.35 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_geometric
% 5.02/5.35 thf(fact_7776_suminf__zero,axiom,
% 5.02/5.35 ( ( suminf_complex
% 5.02/5.35 @ ^ [N3: nat] : zero_zero_complex )
% 5.02/5.35 = zero_zero_complex ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_zero
% 5.02/5.35 thf(fact_7777_suminf__zero,axiom,
% 5.02/5.35 ( ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : zero_zero_real )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_zero
% 5.02/5.35 thf(fact_7778_suminf__zero,axiom,
% 5.02/5.35 ( ( suminf_nat
% 5.02/5.35 @ ^ [N3: nat] : zero_zero_nat )
% 5.02/5.35 = zero_zero_nat ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_zero
% 5.02/5.35 thf(fact_7779_suminf__zero,axiom,
% 5.02/5.35 ( ( suminf_int
% 5.02/5.35 @ ^ [N3: nat] : zero_zero_int )
% 5.02/5.35 = zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_zero
% 5.02/5.35 thf(fact_7780_sin__cos__npi,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_npi
% 5.02/5.35 thf(fact_7781_upto_Opinduct,axiom,
% 5.02/5.35 ! [A0: int,A12: int,P: int > int > $o] :
% 5.02/5.35 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.02/5.35 => ( ! [I2: int,J2: int] :
% 5.02/5.35 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 5.02/5.35 => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 5.02/5.35 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 5.02/5.35 => ( P @ I2 @ J2 ) ) )
% 5.02/5.35 => ( P @ A0 @ A12 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % upto.pinduct
% 5.02/5.35 thf(fact_7782_lemma__termdiff2,axiom,
% 5.02/5.35 ! [H2: complex,Z: complex,N2: nat] :
% 5.02/5.35 ( ( H2 != zero_zero_complex )
% 5.02/5.35 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.02/5.35 = ( times_times_complex @ H2
% 5.02/5.35 @ ( groups2073611262835488442omplex
% 5.02/5.35 @ ^ [P6: nat] :
% 5.02/5.35 ( groups2073611262835488442omplex
% 5.02/5.35 @ ^ [Q4: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q4 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff2
% 5.02/5.35 thf(fact_7783_lemma__termdiff2,axiom,
% 5.02/5.35 ! [H2: rat,Z: rat,N2: nat] :
% 5.02/5.35 ( ( H2 != zero_zero_rat )
% 5.02/5.35 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N2 ) @ ( power_power_rat @ Z @ N2 ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.02/5.35 = ( times_times_rat @ H2
% 5.02/5.35 @ ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [P6: nat] :
% 5.02/5.35 ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [Q4: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q4 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff2
% 5.02/5.35 thf(fact_7784_lemma__termdiff2,axiom,
% 5.02/5.35 ! [H2: real,Z: real,N2: nat] :
% 5.02/5.35 ( ( H2 != zero_zero_real )
% 5.02/5.35 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.02/5.35 = ( times_times_real @ H2
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [P6: nat] :
% 5.02/5.35 ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [Q4: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q4 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q4 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P6 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff2
% 5.02/5.35 thf(fact_7785_lessThan__iff,axiom,
% 5.02/5.35 ! [I3: set_nat,K: set_nat] :
% 5.02/5.35 ( ( member_set_nat @ I3 @ ( set_or890127255671739683et_nat @ K ) )
% 5.02/5.35 = ( ord_less_set_nat @ I3 @ K ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_iff
% 5.02/5.35 thf(fact_7786_lessThan__iff,axiom,
% 5.02/5.35 ! [I3: rat,K: rat] :
% 5.02/5.35 ( ( member_rat @ I3 @ ( set_ord_lessThan_rat @ K ) )
% 5.02/5.35 = ( ord_less_rat @ I3 @ K ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_iff
% 5.02/5.35 thf(fact_7787_lessThan__iff,axiom,
% 5.02/5.35 ! [I3: num,K: num] :
% 5.02/5.35 ( ( member_num @ I3 @ ( set_ord_lessThan_num @ K ) )
% 5.02/5.35 = ( ord_less_num @ I3 @ K ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_iff
% 5.02/5.35 thf(fact_7788_lessThan__iff,axiom,
% 5.02/5.35 ! [I3: int,K: int] :
% 5.02/5.35 ( ( member_int @ I3 @ ( set_ord_lessThan_int @ K ) )
% 5.02/5.35 = ( ord_less_int @ I3 @ K ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_iff
% 5.02/5.35 thf(fact_7789_lessThan__iff,axiom,
% 5.02/5.35 ! [I3: nat,K: nat] :
% 5.02/5.35 ( ( member_nat @ I3 @ ( set_ord_lessThan_nat @ K ) )
% 5.02/5.35 = ( ord_less_nat @ I3 @ K ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_iff
% 5.02/5.35 thf(fact_7790_lessThan__iff,axiom,
% 5.02/5.35 ! [I3: real,K: real] :
% 5.02/5.35 ( ( member_real @ I3 @ ( set_or5984915006950818249n_real @ K ) )
% 5.02/5.35 = ( ord_less_real @ I3 @ K ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_iff
% 5.02/5.35 thf(fact_7791_sin__zero,axiom,
% 5.02/5.35 ( ( sin_complex @ zero_zero_complex )
% 5.02/5.35 = zero_zero_complex ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero
% 5.02/5.35 thf(fact_7792_sin__zero,axiom,
% 5.02/5.35 ( ( sin_real @ zero_zero_real )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero
% 5.02/5.35 thf(fact_7793_lessThan__subset__iff,axiom,
% 5.02/5.35 ! [X2: rat,Y: rat] :
% 5.02/5.35 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X2 ) @ ( set_ord_lessThan_rat @ Y ) )
% 5.02/5.35 = ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_subset_iff
% 5.02/5.35 thf(fact_7794_lessThan__subset__iff,axiom,
% 5.02/5.35 ! [X2: num,Y: num] :
% 5.02/5.35 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X2 ) @ ( set_ord_lessThan_num @ Y ) )
% 5.02/5.35 = ( ord_less_eq_num @ X2 @ Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_subset_iff
% 5.02/5.35 thf(fact_7795_lessThan__subset__iff,axiom,
% 5.02/5.35 ! [X2: int,Y: int] :
% 5.02/5.35 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X2 ) @ ( set_ord_lessThan_int @ Y ) )
% 5.02/5.35 = ( ord_less_eq_int @ X2 @ Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_subset_iff
% 5.02/5.35 thf(fact_7796_lessThan__subset__iff,axiom,
% 5.02/5.35 ! [X2: nat,Y: nat] :
% 5.02/5.35 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X2 ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.02/5.35 = ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_subset_iff
% 5.02/5.35 thf(fact_7797_lessThan__subset__iff,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X2 ) @ ( set_or5984915006950818249n_real @ Y ) )
% 5.02/5.35 = ( ord_less_eq_real @ X2 @ Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_subset_iff
% 5.02/5.35 thf(fact_7798_lessThan__0,axiom,
% 5.02/5.35 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.02/5.35 = bot_bot_set_nat ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_0
% 5.02/5.35 thf(fact_7799_sum_OlessThan__Suc,axiom,
% 5.02/5.35 ! [G: nat > rat,N2: nat] :
% 5.02/5.35 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.lessThan_Suc
% 5.02/5.35 thf(fact_7800_sum_OlessThan__Suc,axiom,
% 5.02/5.35 ! [G: nat > int,N2: nat] :
% 5.02/5.35 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.lessThan_Suc
% 5.02/5.35 thf(fact_7801_sum_OlessThan__Suc,axiom,
% 5.02/5.35 ! [G: nat > nat,N2: nat] :
% 5.02/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.lessThan_Suc
% 5.02/5.35 thf(fact_7802_sum_OlessThan__Suc,axiom,
% 5.02/5.35 ! [G: nat > real,N2: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.lessThan_Suc
% 5.02/5.35 thf(fact_7803_sin__periodic__pi,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( sin_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.02/5.35 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_periodic_pi
% 5.02/5.35 thf(fact_7804_sin__periodic__pi2,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( sin_real @ ( plus_plus_real @ pi @ X2 ) )
% 5.02/5.35 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_periodic_pi2
% 5.02/5.35 thf(fact_7805_sin__cos__squared__add3,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ X2 ) ) @ ( times_times_complex @ ( sin_complex @ X2 ) @ ( sin_complex @ X2 ) ) )
% 5.02/5.35 = one_one_complex ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_squared_add3
% 5.02/5.35 thf(fact_7806_sin__cos__squared__add3,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ X2 ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ X2 ) ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_squared_add3
% 5.02/5.35 thf(fact_7807_sin__npi2,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_npi2
% 5.02/5.35 thf(fact_7808_sin__npi,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_npi
% 5.02/5.35 thf(fact_7809_sin__npi__int,axiom,
% 5.02/5.35 ! [N2: int] :
% 5.02/5.35 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_npi_int
% 5.02/5.35 thf(fact_7810_sin__two__pi,axiom,
% 5.02/5.35 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_two_pi
% 5.02/5.35 thf(fact_7811_sin__pi__half,axiom,
% 5.02/5.35 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_pi_half
% 5.02/5.35 thf(fact_7812_sin__periodic,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( sin_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.02/5.35 = ( sin_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_periodic
% 5.02/5.35 thf(fact_7813_sin__cos__squared__add,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_squared_add
% 5.02/5.35 thf(fact_7814_sin__cos__squared__add,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_complex ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_squared_add
% 5.02/5.35 thf(fact_7815_sin__cos__squared__add2,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_squared_add2
% 5.02/5.35 thf(fact_7816_sin__cos__squared__add2,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_complex ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_squared_add2
% 5.02/5.35 thf(fact_7817_sin__2npi,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_2npi
% 5.02/5.35 thf(fact_7818_sin__2pi__minus,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X2 ) )
% 5.02/5.35 = ( uminus_uminus_real @ ( sin_real @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_2pi_minus
% 5.02/5.35 thf(fact_7819_sin__int__2pin,axiom,
% 5.02/5.35 ! [N2: int] :
% 5.02/5.35 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_int_2pin
% 5.02/5.35 thf(fact_7820_sin__3over2__pi,axiom,
% 5.02/5.35 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.02/5.35 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_3over2_pi
% 5.02/5.35 thf(fact_7821_lessThan__def,axiom,
% 5.02/5.35 ( set_or890127255671739683et_nat
% 5.02/5.35 = ( ^ [U2: set_nat] :
% 5.02/5.35 ( collect_set_nat
% 5.02/5.35 @ ^ [X: set_nat] : ( ord_less_set_nat @ X @ U2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_def
% 5.02/5.35 thf(fact_7822_lessThan__def,axiom,
% 5.02/5.35 ( set_ord_lessThan_rat
% 5.02/5.35 = ( ^ [U2: rat] :
% 5.02/5.35 ( collect_rat
% 5.02/5.35 @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_def
% 5.02/5.35 thf(fact_7823_lessThan__def,axiom,
% 5.02/5.35 ( set_ord_lessThan_num
% 5.02/5.35 = ( ^ [U2: num] :
% 5.02/5.35 ( collect_num
% 5.02/5.35 @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_def
% 5.02/5.35 thf(fact_7824_lessThan__def,axiom,
% 5.02/5.35 ( set_ord_lessThan_int
% 5.02/5.35 = ( ^ [U2: int] :
% 5.02/5.35 ( collect_int
% 5.02/5.35 @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_def
% 5.02/5.35 thf(fact_7825_lessThan__def,axiom,
% 5.02/5.35 ( set_ord_lessThan_nat
% 5.02/5.35 = ( ^ [U2: nat] :
% 5.02/5.35 ( collect_nat
% 5.02/5.35 @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_def
% 5.02/5.35 thf(fact_7826_lessThan__def,axiom,
% 5.02/5.35 ( set_or5984915006950818249n_real
% 5.02/5.35 = ( ^ [U2: real] :
% 5.02/5.35 ( collect_real
% 5.02/5.35 @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_def
% 5.02/5.35 thf(fact_7827_sin__le__one,axiom,
% 5.02/5.35 ! [X2: real] : ( ord_less_eq_real @ ( sin_real @ X2 ) @ one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_le_one
% 5.02/5.35 thf(fact_7828_lessThan__strict__subset__iff,axiom,
% 5.02/5.35 ! [M: rat,N2: rat] :
% 5.02/5.35 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 5.02/5.35 = ( ord_less_rat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_strict_subset_iff
% 5.02/5.35 thf(fact_7829_lessThan__strict__subset__iff,axiom,
% 5.02/5.35 ! [M: num,N2: num] :
% 5.02/5.35 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 5.02/5.35 = ( ord_less_num @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_strict_subset_iff
% 5.02/5.35 thf(fact_7830_lessThan__strict__subset__iff,axiom,
% 5.02/5.35 ! [M: int,N2: int] :
% 5.02/5.35 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 5.02/5.35 = ( ord_less_int @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_strict_subset_iff
% 5.02/5.35 thf(fact_7831_lessThan__strict__subset__iff,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_strict_subset_iff
% 5.02/5.35 thf(fact_7832_lessThan__strict__subset__iff,axiom,
% 5.02/5.35 ! [M: real,N2: real] :
% 5.02/5.35 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 5.02/5.35 = ( ord_less_real @ M @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_strict_subset_iff
% 5.02/5.35 thf(fact_7833_polar__Ex,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ? [R3: real,A4: real] :
% 5.02/5.35 ( ( X2
% 5.02/5.35 = ( times_times_real @ R3 @ ( cos_real @ A4 ) ) )
% 5.02/5.35 & ( Y
% 5.02/5.35 = ( times_times_real @ R3 @ ( sin_real @ A4 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % polar_Ex
% 5.02/5.35 thf(fact_7834_lessThan__Suc,axiom,
% 5.02/5.35 ! [K: nat] :
% 5.02/5.35 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.02/5.35 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_Suc
% 5.02/5.35 thf(fact_7835_lessThan__empty__iff,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( ( set_ord_lessThan_nat @ N2 )
% 5.02/5.35 = bot_bot_set_nat )
% 5.02/5.35 = ( N2 = zero_zero_nat ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_empty_iff
% 5.02/5.35 thf(fact_7836_cos__one__sin__zero,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( ( cos_complex @ X2 )
% 5.02/5.35 = one_one_complex )
% 5.02/5.35 => ( ( sin_complex @ X2 )
% 5.02/5.35 = zero_zero_complex ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_one_sin_zero
% 5.02/5.35 thf(fact_7837_cos__one__sin__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 => ( ( sin_real @ X2 )
% 5.02/5.35 = zero_zero_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_one_sin_zero
% 5.02/5.35 thf(fact_7838_sin__add,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( sin_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.02/5.35 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_add
% 5.02/5.35 thf(fact_7839_sin__diff,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( sin_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.02/5.35 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_diff
% 5.02/5.35 thf(fact_7840_sin__ge__minus__one,axiom,
% 5.02/5.35 ! [X2: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_ge_minus_one
% 5.02/5.35 thf(fact_7841_abs__sin__le__one,axiom,
% 5.02/5.35 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X2 ) ) @ one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % abs_sin_le_one
% 5.02/5.35 thf(fact_7842_cot__def,axiom,
% 5.02/5.35 ( cot_complex
% 5.02/5.35 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X ) @ ( sin_complex @ X ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cot_def
% 5.02/5.35 thf(fact_7843_cot__def,axiom,
% 5.02/5.35 ( cot_real
% 5.02/5.35 = ( ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cot_def
% 5.02/5.35 thf(fact_7844_lessThan__nat__numeral,axiom,
% 5.02/5.35 ! [K: num] :
% 5.02/5.35 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.02/5.35 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lessThan_nat_numeral
% 5.02/5.35 thf(fact_7845_sum_Onat__diff__reindex,axiom,
% 5.02/5.35 ! [G: nat > nat,N2: nat] :
% 5.02/5.35 ( ( groups3542108847815614940at_nat
% 5.02/5.35 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.nat_diff_reindex
% 5.02/5.35 thf(fact_7846_sum_Onat__diff__reindex,axiom,
% 5.02/5.35 ! [G: nat > real,N2: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.nat_diff_reindex
% 5.02/5.35 thf(fact_7847_sum__diff__distrib,axiom,
% 5.02/5.35 ! [Q: real > nat,P: real > nat,N2: real] :
% 5.02/5.35 ( ! [X5: real] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.02/5.35 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 5.02/5.35 = ( groups1935376822645274424al_nat
% 5.02/5.35 @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.02/5.35 @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_diff_distrib
% 5.02/5.35 thf(fact_7848_sum__diff__distrib,axiom,
% 5.02/5.35 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 5.02/5.35 ( ! [X5: nat] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.02/5.35 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.02/5.35 = ( groups3542108847815614940at_nat
% 5.02/5.35 @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_diff_distrib
% 5.02/5.35 thf(fact_7849_cos__diff,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( cos_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.02/5.35 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_diff
% 5.02/5.35 thf(fact_7850_cos__add,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( cos_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.02/5.35 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_add
% 5.02/5.35 thf(fact_7851_sin__zero__norm__cos__one,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( sin_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X2 ) )
% 5.02/5.35 = one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero_norm_cos_one
% 5.02/5.35 thf(fact_7852_sin__zero__norm__cos__one,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( ( sin_complex @ X2 )
% 5.02/5.35 = zero_zero_complex )
% 5.02/5.35 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X2 ) )
% 5.02/5.35 = one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero_norm_cos_one
% 5.02/5.35 thf(fact_7853_sin__zero__abs__cos__one,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( sin_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 => ( ( abs_abs_real @ ( cos_real @ X2 ) )
% 5.02/5.35 = one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero_abs_cos_one
% 5.02/5.35 thf(fact_7854_sin__zero__iff__int2,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( sin_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 = ( ? [I5: int] :
% 5.02/5.35 ( X2
% 5.02/5.35 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ pi ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero_iff_int2
% 5.02/5.35 thf(fact_7855_sum_OlessThan__Suc__shift,axiom,
% 5.02/5.35 ! [G: nat > rat,N2: nat] :
% 5.02/5.35 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.02/5.35 @ ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.lessThan_Suc_shift
% 5.02/5.35 thf(fact_7856_sum_OlessThan__Suc__shift,axiom,
% 5.02/5.35 ! [G: nat > int,N2: nat] :
% 5.02/5.35 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.02/5.35 @ ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.lessThan_Suc_shift
% 5.02/5.35 thf(fact_7857_sum_OlessThan__Suc__shift,axiom,
% 5.02/5.35 ! [G: nat > nat,N2: nat] :
% 5.02/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.02/5.35 @ ( groups3542108847815614940at_nat
% 5.02/5.35 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.lessThan_Suc_shift
% 5.02/5.35 thf(fact_7858_sum_OlessThan__Suc__shift,axiom,
% 5.02/5.35 ! [G: nat > real,N2: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.lessThan_Suc_shift
% 5.02/5.35 thf(fact_7859_sumr__diff__mult__const2,axiom,
% 5.02/5.35 ! [F: nat > int,N2: nat,R2: int] :
% 5.02/5.35 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ R2 ) )
% 5.02/5.35 = ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ R2 )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sumr_diff_mult_const2
% 5.02/5.35 thf(fact_7860_sumr__diff__mult__const2,axiom,
% 5.02/5.35 ! [F: nat > rat,N2: nat,R2: rat] :
% 5.02/5.35 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ R2 ) )
% 5.02/5.35 = ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ R2 )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sumr_diff_mult_const2
% 5.02/5.35 thf(fact_7861_sumr__diff__mult__const2,axiom,
% 5.02/5.35 ! [F: nat > real,N2: nat,R2: real] :
% 5.02/5.35 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ R2 ) )
% 5.02/5.35 = ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ R2 )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sumr_diff_mult_const2
% 5.02/5.35 thf(fact_7862_sum__lessThan__telescope,axiom,
% 5.02/5.35 ! [F: nat > rat,M: nat] :
% 5.02/5.35 ( ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [N3: nat] : ( minus_minus_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_lessThan_telescope
% 5.02/5.35 thf(fact_7863_sum__lessThan__telescope,axiom,
% 5.02/5.35 ! [F: nat > int,M: nat] :
% 5.02/5.35 ( ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [N3: nat] : ( minus_minus_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_lessThan_telescope
% 5.02/5.35 thf(fact_7864_sum__lessThan__telescope,axiom,
% 5.02/5.35 ! [F: nat > real,M: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_lessThan_telescope
% 5.02/5.35 thf(fact_7865_sum__lessThan__telescope_H,axiom,
% 5.02/5.35 ! [F: nat > rat,M: nat] :
% 5.02/5.35 ( ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [N3: nat] : ( minus_minus_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_lessThan_telescope'
% 5.02/5.35 thf(fact_7866_sum__lessThan__telescope_H,axiom,
% 5.02/5.35 ! [F: nat > int,M: nat] :
% 5.02/5.35 ( ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [N3: nat] : ( minus_minus_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_lessThan_telescope'
% 5.02/5.35 thf(fact_7867_sum__lessThan__telescope_H,axiom,
% 5.02/5.35 ! [F: nat > real,M: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_lessThan_telescope'
% 5.02/5.35 thf(fact_7868_sum_OatLeast1__atMost__eq,axiom,
% 5.02/5.35 ! [G: nat > nat,N2: nat] :
% 5.02/5.35 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.02/5.35 = ( groups3542108847815614940at_nat
% 5.02/5.35 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.atLeast1_atMost_eq
% 5.02/5.35 thf(fact_7869_sum_OatLeast1__atMost__eq,axiom,
% 5.02/5.35 ! [G: nat > real,N2: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.02/5.35 = ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum.atLeast1_atMost_eq
% 5.02/5.35 thf(fact_7870_sin__gt__zero__02,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_gt_zero_02
% 5.02/5.35 thf(fact_7871_sin__double,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.02/5.35 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X2 ) ) @ ( cos_complex @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_double
% 5.02/5.35 thf(fact_7872_sin__double,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.02/5.35 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X2 ) ) @ ( cos_real @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_double
% 5.02/5.35 thf(fact_7873_power__diff__1__eq,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat] :
% 5.02/5.35 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N2 ) @ one_one_complex )
% 5.02/5.35 = ( times_times_complex @ ( minus_minus_complex @ X2 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_diff_1_eq
% 5.02/5.35 thf(fact_7874_power__diff__1__eq,axiom,
% 5.02/5.35 ! [X2: rat,N2: nat] :
% 5.02/5.35 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N2 ) @ one_one_rat )
% 5.02/5.35 = ( times_times_rat @ ( minus_minus_rat @ X2 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_diff_1_eq
% 5.02/5.35 thf(fact_7875_power__diff__1__eq,axiom,
% 5.02/5.35 ! [X2: int,N2: nat] :
% 5.02/5.35 ( ( minus_minus_int @ ( power_power_int @ X2 @ N2 ) @ one_one_int )
% 5.02/5.35 = ( times_times_int @ ( minus_minus_int @ X2 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_diff_1_eq
% 5.02/5.35 thf(fact_7876_power__diff__1__eq,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( minus_minus_real @ ( power_power_real @ X2 @ N2 ) @ one_one_real )
% 5.02/5.35 = ( times_times_real @ ( minus_minus_real @ X2 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_diff_1_eq
% 5.02/5.35 thf(fact_7877_one__diff__power__eq,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat] :
% 5.02/5.35 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % one_diff_power_eq
% 5.02/5.35 thf(fact_7878_one__diff__power__eq,axiom,
% 5.02/5.35 ! [X2: rat,N2: nat] :
% 5.02/5.35 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % one_diff_power_eq
% 5.02/5.35 thf(fact_7879_one__diff__power__eq,axiom,
% 5.02/5.35 ! [X2: int,N2: nat] :
% 5.02/5.35 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % one_diff_power_eq
% 5.02/5.35 thf(fact_7880_one__diff__power__eq,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % one_diff_power_eq
% 5.02/5.35 thf(fact_7881_geometric__sum,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat] :
% 5.02/5.35 ( ( X2 != one_one_complex )
% 5.02/5.35 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X2 @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X2 @ one_one_complex ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % geometric_sum
% 5.02/5.35 thf(fact_7882_geometric__sum,axiom,
% 5.02/5.35 ! [X2: rat,N2: nat] :
% 5.02/5.35 ( ( X2 != one_one_rat )
% 5.02/5.35 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X2 @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X2 @ one_one_rat ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % geometric_sum
% 5.02/5.35 thf(fact_7883_geometric__sum,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( X2 != one_one_real )
% 5.02/5.35 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X2 @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X2 @ one_one_real ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % geometric_sum
% 5.02/5.35 thf(fact_7884_sin__pi__divide__n__ge__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( N2 != zero_zero_nat )
% 5.02/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_pi_divide_n_ge_0
% 5.02/5.35 thf(fact_7885_sin__45,axiom,
% 5.02/5.35 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.02/5.35 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_45
% 5.02/5.35 thf(fact_7886_sin__cos__le1,axiom,
% 5.02/5.35 ! [X2: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_le1
% 5.02/5.35 thf(fact_7887_sum__gp__strict,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat] :
% 5.02/5.35 ( ( ( X2 = one_one_complex )
% 5.02/5.35 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.02/5.35 & ( ( X2 != one_one_complex )
% 5.02/5.35 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_gp_strict
% 5.02/5.35 thf(fact_7888_sum__gp__strict,axiom,
% 5.02/5.35 ! [X2: rat,N2: nat] :
% 5.02/5.35 ( ( ( X2 = one_one_rat )
% 5.02/5.35 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( semiri681578069525770553at_rat @ N2 ) ) )
% 5.02/5.35 & ( ( X2 != one_one_rat )
% 5.02/5.35 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_gp_strict
% 5.02/5.35 thf(fact_7889_sum__gp__strict,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( ( X2 = one_one_real )
% 5.02/5.35 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.02/5.35 & ( ( X2 != one_one_real )
% 5.02/5.35 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_gp_strict
% 5.02/5.35 thf(fact_7890_lemma__termdiff1,axiom,
% 5.02/5.35 ! [Z: complex,H2: complex,M: nat] :
% 5.02/5.35 ( ( groups2073611262835488442omplex
% 5.02/5.35 @ ^ [P6: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_complex @ Z @ P6 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( groups2073611262835488442omplex
% 5.02/5.35 @ ^ [P6: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P6 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff1
% 5.02/5.35 thf(fact_7891_lemma__termdiff1,axiom,
% 5.02/5.35 ! [Z: rat,H2: rat,M: nat] :
% 5.02/5.35 ( ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [P6: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_rat @ Z @ P6 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P6 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff1
% 5.02/5.35 thf(fact_7892_lemma__termdiff1,axiom,
% 5.02/5.35 ! [Z: int,H2: int,M: nat] :
% 5.02/5.35 ( ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [P6: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_int @ Z @ P6 ) ) @ ( power_power_int @ Z @ M ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ Z @ P6 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff1
% 5.02/5.35 thf(fact_7893_lemma__termdiff1,axiom,
% 5.02/5.35 ! [Z: real,H2: real,M: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [P6: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_real @ Z @ P6 ) ) @ ( power_power_real @ Z @ M ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) )
% 5.02/5.35 = ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [P6: nat] : ( times_times_real @ ( power_power_real @ Z @ P6 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P6 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P6 ) ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_termdiff1
% 5.02/5.35 thf(fact_7894_power__diff__sumr2,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat,Y: complex] :
% 5.02/5.35 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.02/5.35 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y )
% 5.02/5.35 @ ( groups2073611262835488442omplex
% 5.02/5.35 @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_diff_sumr2
% 5.02/5.35 thf(fact_7895_power__diff__sumr2,axiom,
% 5.02/5.35 ! [X2: rat,N2: nat,Y: rat] :
% 5.02/5.35 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.02/5.35 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y )
% 5.02/5.35 @ ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_rat @ X2 @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_diff_sumr2
% 5.02/5.35 thf(fact_7896_power__diff__sumr2,axiom,
% 5.02/5.35 ! [X2: int,N2: nat,Y: int] :
% 5.02/5.35 ( ( minus_minus_int @ ( power_power_int @ X2 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.02/5.35 = ( times_times_int @ ( minus_minus_int @ X2 @ Y )
% 5.02/5.35 @ ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_int @ X2 @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_diff_sumr2
% 5.02/5.35 thf(fact_7897_power__diff__sumr2,axiom,
% 5.02/5.35 ! [X2: real,N2: nat,Y: real] :
% 5.02/5.35 ( ( minus_minus_real @ ( power_power_real @ X2 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.02/5.35 = ( times_times_real @ ( minus_minus_real @ X2 @ Y )
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) ) @ ( power_power_real @ X2 @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % power_diff_sumr2
% 5.02/5.35 thf(fact_7898_diff__power__eq__sum,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat,Y: complex] :
% 5.02/5.35 ( ( minus_minus_complex @ ( power_power_complex @ X2 @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( times_times_complex @ ( minus_minus_complex @ X2 @ Y )
% 5.02/5.35 @ ( groups2073611262835488442omplex
% 5.02/5.35 @ ^ [P6: nat] : ( times_times_complex @ ( power_power_complex @ X2 @ P6 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % diff_power_eq_sum
% 5.02/5.35 thf(fact_7899_diff__power__eq__sum,axiom,
% 5.02/5.35 ! [X2: rat,N2: nat,Y: rat] :
% 5.02/5.35 ( ( minus_minus_rat @ ( power_power_rat @ X2 @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( times_times_rat @ ( minus_minus_rat @ X2 @ Y )
% 5.02/5.35 @ ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ X2 @ P6 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % diff_power_eq_sum
% 5.02/5.35 thf(fact_7900_diff__power__eq__sum,axiom,
% 5.02/5.35 ! [X2: int,N2: nat,Y: int] :
% 5.02/5.35 ( ( minus_minus_int @ ( power_power_int @ X2 @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( times_times_int @ ( minus_minus_int @ X2 @ Y )
% 5.02/5.35 @ ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ X2 @ P6 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % diff_power_eq_sum
% 5.02/5.35 thf(fact_7901_diff__power__eq__sum,axiom,
% 5.02/5.35 ! [X2: real,N2: nat,Y: real] :
% 5.02/5.35 ( ( minus_minus_real @ ( power_power_real @ X2 @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 5.02/5.35 = ( times_times_real @ ( minus_minus_real @ X2 @ Y )
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [P6: nat] : ( times_times_real @ ( power_power_real @ X2 @ P6 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P6 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % diff_power_eq_sum
% 5.02/5.35 thf(fact_7902_real__sum__nat__ivl__bounded2,axiom,
% 5.02/5.35 ! [N2: nat,F: nat > rat,K5: rat,K: nat] :
% 5.02/5.35 ( ! [P7: nat] :
% 5.02/5.35 ( ( ord_less_nat @ P7 @ N2 )
% 5.02/5.35 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.02/5.35 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.02/5.35 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_sum_nat_ivl_bounded2
% 5.02/5.35 thf(fact_7903_real__sum__nat__ivl__bounded2,axiom,
% 5.02/5.35 ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 5.02/5.35 ( ! [P7: nat] :
% 5.02/5.35 ( ( ord_less_nat @ P7 @ N2 )
% 5.02/5.35 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.02/5.35 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.02/5.35 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_sum_nat_ivl_bounded2
% 5.02/5.35 thf(fact_7904_real__sum__nat__ivl__bounded2,axiom,
% 5.02/5.35 ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 5.02/5.35 ( ! [P7: nat] :
% 5.02/5.35 ( ( ord_less_nat @ P7 @ N2 )
% 5.02/5.35 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.02/5.35 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.02/5.35 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_sum_nat_ivl_bounded2
% 5.02/5.35 thf(fact_7905_real__sum__nat__ivl__bounded2,axiom,
% 5.02/5.35 ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 5.02/5.35 ( ! [P7: nat] :
% 5.02/5.35 ( ( ord_less_nat @ P7 @ N2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.02/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.02/5.35 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % real_sum_nat_ivl_bounded2
% 5.02/5.35 thf(fact_7906_sin__gt__zero2,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_gt_zero2
% 5.02/5.35 thf(fact_7907_cos__squared__eq,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_squared_eq
% 5.02/5.35 thf(fact_7908_cos__squared__eq,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_squared_eq
% 5.02/5.35 thf(fact_7909_sin__squared__eq,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_squared_eq
% 5.02/5.35 thf(fact_7910_sin__squared__eq,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_squared_eq
% 5.02/5.35 thf(fact_7911_sin__lt__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ pi @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.02/5.35 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_lt_zero
% 5.02/5.35 thf(fact_7912_sin__30,axiom,
% 5.02/5.35 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.02/5.35 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_30
% 5.02/5.35 thf(fact_7913_sin__inj__pi,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ( sin_real @ X2 )
% 5.02/5.35 = ( sin_real @ Y ) )
% 5.02/5.35 => ( X2 = Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_inj_pi
% 5.02/5.35 thf(fact_7914_sin__mono__le__eq,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) )
% 5.02/5.35 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_mono_le_eq
% 5.02/5.35 thf(fact_7915_sin__monotone__2pi__le,axiom,
% 5.02/5.35 ! [Y: real,X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_eq_real @ Y @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_monotone_2pi_le
% 5.02/5.35 thf(fact_7916_sin__60,axiom,
% 5.02/5.35 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.02/5.35 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_60
% 5.02/5.35 thf(fact_7917_one__diff__power__eq_H,axiom,
% 5.02/5.35 ! [X2: complex,N2: nat] :
% 5.02/5.35 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 )
% 5.02/5.35 @ ( groups2073611262835488442omplex
% 5.02/5.35 @ ^ [I5: nat] : ( power_power_complex @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % one_diff_power_eq'
% 5.02/5.35 thf(fact_7918_one__diff__power__eq_H,axiom,
% 5.02/5.35 ! [X2: rat,N2: nat] :
% 5.02/5.35 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 )
% 5.02/5.35 @ ( groups2906978787729119204at_rat
% 5.02/5.35 @ ^ [I5: nat] : ( power_power_rat @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % one_diff_power_eq'
% 5.02/5.35 thf(fact_7919_one__diff__power__eq_H,axiom,
% 5.02/5.35 ! [X2: int,N2: nat] :
% 5.02/5.35 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 )
% 5.02/5.35 @ ( groups3539618377306564664at_int
% 5.02/5.35 @ ^ [I5: nat] : ( power_power_int @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % one_diff_power_eq'
% 5.02/5.35 thf(fact_7920_one__diff__power__eq_H,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ N2 ) )
% 5.02/5.35 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 )
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( power_power_real @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % one_diff_power_eq'
% 5.02/5.35 thf(fact_7921_cos__diff__cos,axiom,
% 5.02/5.35 ! [W: complex,Z: complex] :
% 5.02/5.35 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.02/5.35 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z @ W ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_diff_cos
% 5.02/5.35 thf(fact_7922_cos__diff__cos,axiom,
% 5.02/5.35 ! [W: real,Z: real] :
% 5.02/5.35 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.02/5.35 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z @ W ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_diff_cos
% 5.02/5.35 thf(fact_7923_sin__diff__sin,axiom,
% 5.02/5.35 ! [W: complex,Z: complex] :
% 5.02/5.35 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.02/5.35 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_diff_sin
% 5.02/5.35 thf(fact_7924_sin__diff__sin,axiom,
% 5.02/5.35 ! [W: real,Z: real] :
% 5.02/5.35 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.02/5.35 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_diff_sin
% 5.02/5.35 thf(fact_7925_sin__plus__sin,axiom,
% 5.02/5.35 ! [W: complex,Z: complex] :
% 5.02/5.35 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.02/5.35 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W @ Z ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_plus_sin
% 5.02/5.35 thf(fact_7926_sin__plus__sin,axiom,
% 5.02/5.35 ! [W: real,Z: real] :
% 5.02/5.35 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.02/5.35 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W @ Z ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_plus_sin
% 5.02/5.35 thf(fact_7927_cos__times__sin,axiom,
% 5.02/5.35 ! [W: complex,Z: complex] :
% 5.02/5.35 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_times_sin
% 5.02/5.35 thf(fact_7928_cos__times__sin,axiom,
% 5.02/5.35 ! [W: real,Z: real] :
% 5.02/5.35 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.02/5.35 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_times_sin
% 5.02/5.35 thf(fact_7929_sin__times__cos,axiom,
% 5.02/5.35 ! [W: complex,Z: complex] :
% 5.02/5.35 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_times_cos
% 5.02/5.35 thf(fact_7930_sin__times__cos,axiom,
% 5.02/5.35 ! [W: real,Z: real] :
% 5.02/5.35 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.02/5.35 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W @ Z ) ) @ ( sin_real @ ( minus_minus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_times_cos
% 5.02/5.35 thf(fact_7931_sin__times__sin,axiom,
% 5.02/5.35 ! [W: complex,Z: complex] :
% 5.02/5.35 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_times_sin
% 5.02/5.35 thf(fact_7932_sin__times__sin,axiom,
% 5.02/5.35 ! [W: real,Z: real] :
% 5.02/5.35 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.02/5.35 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W @ Z ) ) @ ( cos_real @ ( plus_plus_real @ W @ Z ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_times_sin
% 5.02/5.35 thf(fact_7933_cos__double,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.02/5.35 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_double
% 5.02/5.35 thf(fact_7934_cos__double,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.02/5.35 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_double
% 5.02/5.35 thf(fact_7935_sin__le__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ pi @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.02/5.35 => ( ord_less_eq_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_le_zero
% 5.02/5.35 thf(fact_7936_sin__less__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.02/5.35 => ( ord_less_real @ ( sin_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_less_zero
% 5.02/5.35 thf(fact_7937_sin__mono__less__eq,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( sin_real @ X2 ) @ ( sin_real @ Y ) )
% 5.02/5.35 = ( ord_less_real @ X2 @ Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_mono_less_eq
% 5.02/5.35 thf(fact_7938_sin__monotone__2pi,axiom,
% 5.02/5.35 ! [Y: real,X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_real @ Y @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_monotone_2pi
% 5.02/5.35 thf(fact_7939_sin__total,axiom,
% 5.02/5.35 ! [Y: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.35 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.35 => ? [X5: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.02/5.35 & ( ord_less_eq_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( ( sin_real @ X5 )
% 5.02/5.35 = Y )
% 5.02/5.35 & ! [Y5: real] :
% 5.02/5.35 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.02/5.35 & ( ord_less_eq_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( ( sin_real @ Y5 )
% 5.02/5.35 = Y ) )
% 5.02/5.35 => ( Y5 = X5 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_total
% 5.02/5.35 thf(fact_7940_sum__split__even__odd,axiom,
% 5.02/5.35 ! [F: nat > real,G: nat > real,N2: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( F @ I5 ) @ ( G @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.35 = ( plus_plus_real
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ one_one_nat ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_split_even_odd
% 5.02/5.35 thf(fact_7941_cos__double__sin,axiom,
% 5.02/5.35 ! [W: complex] :
% 5.02/5.35 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.02/5.35 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_double_sin
% 5.02/5.35 thf(fact_7942_cos__double__sin,axiom,
% 5.02/5.35 ! [W: real] :
% 5.02/5.35 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.02/5.35 = ( 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 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_double_sin
% 5.02/5.35 thf(fact_7943_sin__pi__divide__n__gt__0,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_pi_divide_n_gt_0
% 5.02/5.35 thf(fact_7944_sin__arctan,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( sin_real @ ( arctan @ X2 ) )
% 5.02/5.35 = ( divide_divide_real @ X2 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_arctan
% 5.02/5.35 thf(fact_7945_sincos__total__pi,axiom,
% 5.02/5.35 ! [Y: real,X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.35 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 => ? [T3: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.02/5.35 & ( ord_less_eq_real @ T3 @ pi )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( cos_real @ T3 ) )
% 5.02/5.35 & ( Y
% 5.02/5.35 = ( sin_real @ T3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sincos_total_pi
% 5.02/5.35 thf(fact_7946_sin__cos__sqrt,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X2 ) )
% 5.02/5.35 => ( ( sin_real @ X2 )
% 5.02/5.35 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_cos_sqrt
% 5.02/5.35 thf(fact_7947_sin__expansion__lemma,axiom,
% 5.02/5.35 ! [X2: real,M: nat] :
% 5.02/5.35 ( ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.02/5.35 = ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_expansion_lemma
% 5.02/5.35 thf(fact_7948_sin__zero__iff__int,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( sin_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 = ( ? [I5: int] :
% 5.02/5.35 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero_iff_int
% 5.02/5.35 thf(fact_7949_sin__zero__lemma,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ( sin_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 => ? [N: nat] :
% 5.02/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero_lemma
% 5.02/5.35 thf(fact_7950_sin__zero__iff,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( sin_real @ X2 )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 = ( ? [N3: nat] :
% 5.02/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.35 | ? [N3: nat] :
% 5.02/5.35 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_zero_iff
% 5.02/5.35 thf(fact_7951_cos__expansion__lemma,axiom,
% 5.02/5.35 ! [X2: real,M: nat] :
% 5.02/5.35 ( ( cos_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.02/5.35 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X2 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_expansion_lemma
% 5.02/5.35 thf(fact_7952_sincos__total__pi__half,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.35 => ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 => ? [T3: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.02/5.35 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( cos_real @ T3 ) )
% 5.02/5.35 & ( Y
% 5.02/5.35 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sincos_total_pi_half
% 5.02/5.35 thf(fact_7953_sincos__total__2pi__le,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 => ? [T3: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.02/5.35 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.02/5.35 & ( X2
% 5.02/5.35 = ( cos_real @ T3 ) )
% 5.02/5.35 & ( Y
% 5.02/5.35 = ( sin_real @ T3 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sincos_total_2pi_le
% 5.02/5.35 thf(fact_7954_sincos__total__2pi,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 => ~ ! [T3: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.02/5.35 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.02/5.35 => ( ( X2
% 5.02/5.35 = ( cos_real @ T3 ) )
% 5.02/5.35 => ( Y
% 5.02/5.35 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sincos_total_2pi
% 5.02/5.35 thf(fact_7955_sum__bounds__lt__plus1,axiom,
% 5.02/5.35 ! [F: nat > nat,Mm: nat] :
% 5.02/5.35 ( ( groups3542108847815614940at_nat
% 5.02/5.35 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.02/5.35 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_bounds_lt_plus1
% 5.02/5.35 thf(fact_7956_sum__bounds__lt__plus1,axiom,
% 5.02/5.35 ! [F: nat > real,Mm: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.02/5.35 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_bounds_lt_plus1
% 5.02/5.35 thf(fact_7957_sumr__cos__zero__one,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % sumr_cos_zero_one
% 5.02/5.35 thf(fact_7958_summable__arctan__series,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [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 @ X2 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_arctan_series
% 5.02/5.35 thf(fact_7959_tan__double,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( ( cos_complex @ X2 )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X2 ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X2 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_double
% 5.02/5.35 thf(fact_7960_tan__double,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X2 ) )
% 5.02/5.35 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X2 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_double
% 5.02/5.35 thf(fact_7961_sin__tan,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( sin_real @ X2 )
% 5.02/5.35 = ( divide_divide_real @ ( tan_real @ X2 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sin_tan
% 5.02/5.35 thf(fact_7962_tan__zero,axiom,
% 5.02/5.35 ( ( tan_complex @ zero_zero_complex )
% 5.02/5.35 = zero_zero_complex ) ).
% 5.02/5.35
% 5.02/5.35 % tan_zero
% 5.02/5.35 thf(fact_7963_tan__zero,axiom,
% 5.02/5.35 ( ( tan_real @ zero_zero_real )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % tan_zero
% 5.02/5.35 thf(fact_7964_summable__single,axiom,
% 5.02/5.35 ! [I3: nat,F: nat > complex] :
% 5.02/5.35 ( summable_complex
% 5.02/5.35 @ ^ [R5: nat] : ( if_complex @ ( R5 = I3 ) @ ( F @ R5 ) @ zero_zero_complex ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_single
% 5.02/5.35 thf(fact_7965_summable__single,axiom,
% 5.02/5.35 ! [I3: nat,F: nat > real] :
% 5.02/5.35 ( summable_real
% 5.02/5.35 @ ^ [R5: nat] : ( if_real @ ( R5 = I3 ) @ ( F @ R5 ) @ zero_zero_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_single
% 5.02/5.35 thf(fact_7966_summable__single,axiom,
% 5.02/5.35 ! [I3: nat,F: nat > nat] :
% 5.02/5.35 ( summable_nat
% 5.02/5.35 @ ^ [R5: nat] : ( if_nat @ ( R5 = I3 ) @ ( F @ R5 ) @ zero_zero_nat ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_single
% 5.02/5.35 thf(fact_7967_summable__single,axiom,
% 5.02/5.35 ! [I3: nat,F: nat > int] :
% 5.02/5.35 ( summable_int
% 5.02/5.35 @ ^ [R5: nat] : ( if_int @ ( R5 = I3 ) @ ( F @ R5 ) @ zero_zero_int ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_single
% 5.02/5.35 thf(fact_7968_summable__zero,axiom,
% 5.02/5.35 ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : zero_zero_complex ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero
% 5.02/5.35 thf(fact_7969_summable__zero,axiom,
% 5.02/5.35 ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero
% 5.02/5.35 thf(fact_7970_summable__zero,axiom,
% 5.02/5.35 ( summable_nat
% 5.02/5.35 @ ^ [N3: nat] : zero_zero_nat ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero
% 5.02/5.35 thf(fact_7971_summable__zero,axiom,
% 5.02/5.35 ( summable_int
% 5.02/5.35 @ ^ [N3: nat] : zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero
% 5.02/5.35 thf(fact_7972_summable__iff__shift,axiom,
% 5.02/5.35 ! [F: nat > real,K: nat] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.02/5.35 = ( summable_real @ F ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_iff_shift
% 5.02/5.35 thf(fact_7973_tan__periodic__pi,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( tan_real @ ( plus_plus_real @ X2 @ pi ) )
% 5.02/5.35 = ( tan_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_periodic_pi
% 5.02/5.35 thf(fact_7974_cos__coeff__0,axiom,
% 5.02/5.35 ( ( cos_coeff @ zero_zero_nat )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % cos_coeff_0
% 5.02/5.35 thf(fact_7975_summable__cmult__iff,axiom,
% 5.02/5.35 ! [C: complex,F: nat > complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) ) )
% 5.02/5.35 = ( ( C = zero_zero_complex )
% 5.02/5.35 | ( summable_complex @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_cmult_iff
% 5.02/5.35 thf(fact_7976_summable__cmult__iff,axiom,
% 5.02/5.35 ! [C: real,F: nat > real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.02/5.35 = ( ( C = zero_zero_real )
% 5.02/5.35 | ( summable_real @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_cmult_iff
% 5.02/5.35 thf(fact_7977_summable__divide__iff,axiom,
% 5.02/5.35 ! [F: nat > complex,C: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) )
% 5.02/5.35 = ( ( C = zero_zero_complex )
% 5.02/5.35 | ( summable_complex @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_divide_iff
% 5.02/5.35 thf(fact_7978_summable__divide__iff,axiom,
% 5.02/5.35 ! [F: nat > real,C: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) )
% 5.02/5.35 = ( ( C = zero_zero_real )
% 5.02/5.35 | ( summable_real @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_divide_iff
% 5.02/5.35 thf(fact_7979_tan__npi,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.02/5.35 = zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % tan_npi
% 5.02/5.35 thf(fact_7980_tan__periodic__n,axiom,
% 5.02/5.35 ! [X2: real,N2: num] :
% 5.02/5.35 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ N2 ) @ pi ) ) )
% 5.02/5.35 = ( tan_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_periodic_n
% 5.02/5.35 thf(fact_7981_tan__periodic__nat,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) ) )
% 5.02/5.35 = ( tan_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_periodic_nat
% 5.02/5.35 thf(fact_7982_tan__periodic__int,axiom,
% 5.02/5.35 ! [X2: real,I3: int] :
% 5.02/5.35 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ pi ) ) )
% 5.02/5.35 = ( tan_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_periodic_int
% 5.02/5.35 thf(fact_7983_summable__geometric__iff,axiom,
% 5.02/5.35 ! [C: real] :
% 5.02/5.35 ( ( summable_real @ ( power_power_real @ C ) )
% 5.02/5.35 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_geometric_iff
% 5.02/5.35 thf(fact_7984_summable__geometric__iff,axiom,
% 5.02/5.35 ! [C: complex] :
% 5.02/5.35 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.02/5.35 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_geometric_iff
% 5.02/5.35 thf(fact_7985_tan__periodic,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( tan_real @ ( plus_plus_real @ X2 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.02/5.35 = ( tan_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_periodic
% 5.02/5.35 thf(fact_7986_summable__const__iff,axiom,
% 5.02/5.35 ! [C: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [Uu3: nat] : C )
% 5.02/5.35 = ( C = zero_zero_complex ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_const_iff
% 5.02/5.35 thf(fact_7987_summable__const__iff,axiom,
% 5.02/5.35 ! [C: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [Uu3: nat] : C )
% 5.02/5.35 = ( C = zero_zero_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_const_iff
% 5.02/5.35 thf(fact_7988_summable__comparison__test_H,axiom,
% 5.02/5.35 ! [G: nat > real,N4: nat,F: nat > real] :
% 5.02/5.35 ( ( summable_real @ G )
% 5.02/5.35 => ( ! [N: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N4 @ N )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.02/5.35 => ( summable_real @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_comparison_test'
% 5.02/5.35 thf(fact_7989_summable__comparison__test_H,axiom,
% 5.02/5.35 ! [G: nat > real,N4: nat,F: nat > complex] :
% 5.02/5.35 ( ( summable_real @ G )
% 5.02/5.35 => ( ! [N: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N4 @ N )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.02/5.35 => ( summable_complex @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_comparison_test'
% 5.02/5.35 thf(fact_7990_summable__comparison__test,axiom,
% 5.02/5.35 ! [F: nat > real,G: nat > real] :
% 5.02/5.35 ( ? [N6: nat] :
% 5.02/5.35 ! [N: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N6 @ N )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.02/5.35 => ( ( summable_real @ G )
% 5.02/5.35 => ( summable_real @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_comparison_test
% 5.02/5.35 thf(fact_7991_summable__comparison__test,axiom,
% 5.02/5.35 ! [F: nat > complex,G: nat > real] :
% 5.02/5.35 ( ? [N6: nat] :
% 5.02/5.35 ! [N: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N6 @ N )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.02/5.35 => ( ( summable_real @ G )
% 5.02/5.35 => ( summable_complex @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_comparison_test
% 5.02/5.35 thf(fact_7992_summable__mult2,axiom,
% 5.02/5.35 ! [F: nat > real,C: real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_mult2
% 5.02/5.35 thf(fact_7993_summable__mult,axiom,
% 5.02/5.35 ! [F: nat > real,C: real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_mult
% 5.02/5.35 thf(fact_7994_summable__add,axiom,
% 5.02/5.35 ! [F: nat > real,G: nat > real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( summable_real @ G )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_add
% 5.02/5.35 thf(fact_7995_summable__add,axiom,
% 5.02/5.35 ! [F: nat > nat,G: nat > nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ( summable_nat @ G )
% 5.02/5.35 => ( summable_nat
% 5.02/5.35 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_add
% 5.02/5.35 thf(fact_7996_summable__add,axiom,
% 5.02/5.35 ! [F: nat > int,G: nat > int] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ( summable_int @ G )
% 5.02/5.35 => ( summable_int
% 5.02/5.35 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_add
% 5.02/5.35 thf(fact_7997_summable__divide,axiom,
% 5.02/5.35 ! [F: nat > complex,C: complex] :
% 5.02/5.35 ( ( summable_complex @ F )
% 5.02/5.35 => ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_divide
% 5.02/5.35 thf(fact_7998_summable__divide,axiom,
% 5.02/5.35 ! [F: nat > real,C: real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_divide
% 5.02/5.35 thf(fact_7999_summable__Suc__iff,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 5.02/5.35 = ( summable_real @ F ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_Suc_iff
% 5.02/5.35 thf(fact_8000_summable__ignore__initial__segment,axiom,
% 5.02/5.35 ! [F: nat > real,K: nat] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_ignore_initial_segment
% 5.02/5.35 thf(fact_8001_powser__insidea,axiom,
% 5.02/5.35 ! [F: nat > real,X2: real,Z: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_insidea
% 5.02/5.35 thf(fact_8002_powser__insidea,axiom,
% 5.02/5.35 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_insidea
% 5.02/5.35 thf(fact_8003_suminf__le,axiom,
% 5.02/5.35 ! [F: nat > real,G: nat > real] :
% 5.02/5.35 ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( G @ N ) )
% 5.02/5.35 => ( ( summable_real @ F )
% 5.02/5.35 => ( ( summable_real @ G )
% 5.02/5.35 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_le
% 5.02/5.35 thf(fact_8004_suminf__le,axiom,
% 5.02/5.35 ! [F: nat > nat,G: nat > nat] :
% 5.02/5.35 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ ( G @ N ) )
% 5.02/5.35 => ( ( summable_nat @ F )
% 5.02/5.35 => ( ( summable_nat @ G )
% 5.02/5.35 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_le
% 5.02/5.35 thf(fact_8005_suminf__le,axiom,
% 5.02/5.35 ! [F: nat > int,G: nat > int] :
% 5.02/5.35 ( ! [N: nat] : ( ord_less_eq_int @ ( F @ N ) @ ( G @ N ) )
% 5.02/5.35 => ( ( summable_int @ F )
% 5.02/5.35 => ( ( summable_int @ G )
% 5.02/5.35 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_le
% 5.02/5.35 thf(fact_8006_summable__mult__D,axiom,
% 5.02/5.35 ! [C: complex,F: nat > complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) ) )
% 5.02/5.35 => ( ( C != zero_zero_complex )
% 5.02/5.35 => ( summable_complex @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_mult_D
% 5.02/5.35 thf(fact_8007_summable__mult__D,axiom,
% 5.02/5.35 ! [C: real,F: nat > real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.02/5.35 => ( ( C != zero_zero_real )
% 5.02/5.35 => ( summable_real @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_mult_D
% 5.02/5.35 thf(fact_8008_summable__zero__power,axiom,
% 5.02/5.35 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero_power
% 5.02/5.35 thf(fact_8009_summable__zero__power,axiom,
% 5.02/5.35 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero_power
% 5.02/5.35 thf(fact_8010_summable__zero__power,axiom,
% 5.02/5.35 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero_power
% 5.02/5.35 thf(fact_8011_suminf__mult2,axiom,
% 5.02/5.35 ! [F: nat > real,C: real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( times_times_real @ ( suminf_real @ F ) @ C )
% 5.02/5.35 = ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_mult2
% 5.02/5.35 thf(fact_8012_suminf__mult,axiom,
% 5.02/5.35 ! [F: nat > real,C: real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) ) )
% 5.02/5.35 = ( times_times_real @ C @ ( suminf_real @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_mult
% 5.02/5.35 thf(fact_8013_suminf__add,axiom,
% 5.02/5.35 ! [F: nat > real,G: nat > real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( summable_real @ G )
% 5.02/5.35 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.02/5.35 = ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_add
% 5.02/5.35 thf(fact_8014_suminf__add,axiom,
% 5.02/5.35 ! [F: nat > nat,G: nat > nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ( summable_nat @ G )
% 5.02/5.35 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.02/5.35 = ( suminf_nat
% 5.02/5.35 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_add
% 5.02/5.35 thf(fact_8015_suminf__add,axiom,
% 5.02/5.35 ! [F: nat > int,G: nat > int] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ( summable_int @ G )
% 5.02/5.35 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.02/5.35 = ( suminf_int
% 5.02/5.35 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_add
% 5.02/5.35 thf(fact_8016_suminf__divide,axiom,
% 5.02/5.35 ! [F: nat > complex,C: complex] :
% 5.02/5.35 ( ( summable_complex @ F )
% 5.02/5.35 => ( ( suminf_complex
% 5.02/5.35 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_divide
% 5.02/5.35 thf(fact_8017_suminf__divide,axiom,
% 5.02/5.35 ! [F: nat > real,C: real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C ) )
% 5.02/5.35 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_divide
% 5.02/5.35 thf(fact_8018_suminf__eq__zero__iff,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.02/5.35 => ( ( ( suminf_real @ F )
% 5.02/5.35 = zero_zero_real )
% 5.02/5.35 = ( ! [N3: nat] :
% 5.02/5.35 ( ( F @ N3 )
% 5.02/5.35 = zero_zero_real ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_eq_zero_iff
% 5.02/5.35 thf(fact_8019_suminf__eq__zero__iff,axiom,
% 5.02/5.35 ! [F: nat > nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.02/5.35 => ( ( ( suminf_nat @ F )
% 5.02/5.35 = zero_zero_nat )
% 5.02/5.35 = ( ! [N3: nat] :
% 5.02/5.35 ( ( F @ N3 )
% 5.02/5.35 = zero_zero_nat ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_eq_zero_iff
% 5.02/5.35 thf(fact_8020_suminf__eq__zero__iff,axiom,
% 5.02/5.35 ! [F: nat > int] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.02/5.35 => ( ( ( suminf_int @ F )
% 5.02/5.35 = zero_zero_int )
% 5.02/5.35 = ( ! [N3: nat] :
% 5.02/5.35 ( ( F @ N3 )
% 5.02/5.35 = zero_zero_int ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_eq_zero_iff
% 5.02/5.35 thf(fact_8021_suminf__nonneg,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.02/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_nonneg
% 5.02/5.35 thf(fact_8022_suminf__nonneg,axiom,
% 5.02/5.35 ! [F: nat > nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.02/5.35 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_nonneg
% 5.02/5.35 thf(fact_8023_suminf__nonneg,axiom,
% 5.02/5.35 ! [F: nat > int] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.02/5.35 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_nonneg
% 5.02/5.35 thf(fact_8024_suminf__pos,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N ) )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos
% 5.02/5.35 thf(fact_8025_suminf__pos,axiom,
% 5.02/5.35 ! [F: nat > nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N ) )
% 5.02/5.35 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos
% 5.02/5.35 thf(fact_8026_suminf__pos,axiom,
% 5.02/5.35 ! [F: nat > int] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N ) )
% 5.02/5.35 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos
% 5.02/5.35 thf(fact_8027_summable__zero__power_H,axiom,
% 5.02/5.35 ! [F: nat > complex] :
% 5.02/5.35 ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero_power'
% 5.02/5.35 thf(fact_8028_summable__zero__power_H,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero_power'
% 5.02/5.35 thf(fact_8029_summable__zero__power_H,axiom,
% 5.02/5.35 ! [F: nat > int] :
% 5.02/5.35 ( summable_int
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_int @ ( F @ N3 ) @ ( power_power_int @ zero_zero_int @ N3 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_zero_power'
% 5.02/5.35 thf(fact_8030_summable__0__powser,axiom,
% 5.02/5.35 ! [F: nat > complex] :
% 5.02/5.35 ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_0_powser
% 5.02/5.35 thf(fact_8031_summable__0__powser,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_0_powser
% 5.02/5.35 thf(fact_8032_summable__powser__split__head,axiom,
% 5.02/5.35 ! [F: nat > complex,Z: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 = ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_powser_split_head
% 5.02/5.35 thf(fact_8033_summable__powser__split__head,axiom,
% 5.02/5.35 ! [F: nat > real,Z: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 = ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_powser_split_head
% 5.02/5.35 thf(fact_8034_powser__split__head_I3_J,axiom,
% 5.02/5.35 ! [F: nat > complex,Z: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 => ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_split_head(3)
% 5.02/5.35 thf(fact_8035_powser__split__head_I3_J,axiom,
% 5.02/5.35 ! [F: nat > real,Z: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_split_head(3)
% 5.02/5.35 thf(fact_8036_summable__powser__ignore__initial__segment,axiom,
% 5.02/5.35 ! [F: nat > complex,M: nat,Z: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 = ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_powser_ignore_initial_segment
% 5.02/5.35 thf(fact_8037_summable__powser__ignore__initial__segment,axiom,
% 5.02/5.35 ! [F: nat > real,M: nat,Z: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N3 @ M ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 = ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_powser_ignore_initial_segment
% 5.02/5.35 thf(fact_8038_summable__norm__comparison__test,axiom,
% 5.02/5.35 ! [F: nat > complex,G: nat > real] :
% 5.02/5.35 ( ? [N6: nat] :
% 5.02/5.35 ! [N: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N6 @ N )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.02/5.35 => ( ( summable_real @ G )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_norm_comparison_test
% 5.02/5.35 thf(fact_8039_summable__rabs__comparison__test,axiom,
% 5.02/5.35 ! [F: nat > real,G: nat > real] :
% 5.02/5.35 ( ? [N6: nat] :
% 5.02/5.35 ! [N: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N6 @ N )
% 5.02/5.35 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N ) ) @ ( G @ N ) ) )
% 5.02/5.35 => ( ( summable_real @ G )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( abs_abs_real @ ( F @ N3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_rabs_comparison_test
% 5.02/5.35 thf(fact_8040_suminf__pos2,axiom,
% 5.02/5.35 ! [F: nat > real,I3: nat] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.02/5.35 => ( ( ord_less_real @ zero_zero_real @ ( F @ I3 ) )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos2
% 5.02/5.35 thf(fact_8041_suminf__pos2,axiom,
% 5.02/5.35 ! [F: nat > nat,I3: nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.02/5.35 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos2
% 5.02/5.35 thf(fact_8042_suminf__pos2,axiom,
% 5.02/5.35 ! [F: nat > int,I3: nat] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.02/5.35 => ( ( ord_less_int @ zero_zero_int @ ( F @ I3 ) )
% 5.02/5.35 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos2
% 5.02/5.35 thf(fact_8043_suminf__pos__iff,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.02/5.35 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.02/5.35 = ( ? [I5: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I5 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos_iff
% 5.02/5.35 thf(fact_8044_suminf__pos__iff,axiom,
% 5.02/5.35 ! [F: nat > nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.02/5.35 = ( ? [I5: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I5 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos_iff
% 5.02/5.35 thf(fact_8045_suminf__pos__iff,axiom,
% 5.02/5.35 ! [F: nat > int] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.02/5.35 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.02/5.35 = ( ? [I5: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I5 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_pos_iff
% 5.02/5.35 thf(fact_8046_suminf__le__const,axiom,
% 5.02/5.35 ! [F: nat > int,X2: int] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ X2 )
% 5.02/5.35 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_le_const
% 5.02/5.35 thf(fact_8047_suminf__le__const,axiom,
% 5.02/5.35 ! [F: nat > nat,X2: nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ X2 )
% 5.02/5.35 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_le_const
% 5.02/5.35 thf(fact_8048_suminf__le__const,axiom,
% 5.02/5.35 ! [F: nat > real,X2: real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ X2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_le_const
% 5.02/5.35 thf(fact_8049_tan__def,axiom,
% 5.02/5.35 ( tan_complex
% 5.02/5.35 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X ) @ ( cos_complex @ X ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_def
% 5.02/5.35 thf(fact_8050_tan__def,axiom,
% 5.02/5.35 ( tan_real
% 5.02/5.35 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ X ) @ ( cos_real @ X ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_def
% 5.02/5.35 thf(fact_8051_powser__inside,axiom,
% 5.02/5.35 ! [F: nat > real,X2: real,Z: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X2 ) )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_inside
% 5.02/5.35 thf(fact_8052_powser__inside,axiom,
% 5.02/5.35 ! [F: nat > complex,X2: complex,Z: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X2 ) )
% 5.02/5.35 => ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_inside
% 5.02/5.35 thf(fact_8053_summableI__nonneg__bounded,axiom,
% 5.02/5.35 ! [F: nat > int,X2: int] :
% 5.02/5.35 ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N ) )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ X2 )
% 5.02/5.35 => ( summable_int @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summableI_nonneg_bounded
% 5.02/5.35 thf(fact_8054_summableI__nonneg__bounded,axiom,
% 5.02/5.35 ! [F: nat > nat,X2: nat] :
% 5.02/5.35 ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N ) )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N ) ) @ X2 )
% 5.02/5.35 => ( summable_nat @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summableI_nonneg_bounded
% 5.02/5.35 thf(fact_8055_summableI__nonneg__bounded,axiom,
% 5.02/5.35 ! [F: nat > real,X2: real] :
% 5.02/5.35 ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N ) )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ X2 )
% 5.02/5.35 => ( summable_real @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summableI_nonneg_bounded
% 5.02/5.35 thf(fact_8056_complete__algebra__summable__geometric,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ one_one_real )
% 5.02/5.35 => ( summable_real @ ( power_power_real @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % complete_algebra_summable_geometric
% 5.02/5.35 thf(fact_8057_complete__algebra__summable__geometric,axiom,
% 5.02/5.35 ! [X2: complex] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ one_one_real )
% 5.02/5.35 => ( summable_complex @ ( power_power_complex @ X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % complete_algebra_summable_geometric
% 5.02/5.35 thf(fact_8058_summable__geometric,axiom,
% 5.02/5.35 ! [C: real] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.02/5.35 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_geometric
% 5.02/5.35 thf(fact_8059_summable__geometric,axiom,
% 5.02/5.35 ! [C: complex] :
% 5.02/5.35 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.02/5.35 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_geometric
% 5.02/5.35 thf(fact_8060_suminf__split__head,axiom,
% 5.02/5.35 ! [F: nat > real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) ) )
% 5.02/5.35 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_split_head
% 5.02/5.35 thf(fact_8061_suminf__split__initial__segment,axiom,
% 5.02/5.35 ! [F: nat > real,K: nat] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( suminf_real @ F )
% 5.02/5.35 = ( plus_plus_real
% 5.02/5.35 @ ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.02/5.35 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_split_initial_segment
% 5.02/5.35 thf(fact_8062_suminf__minus__initial__segment,axiom,
% 5.02/5.35 ! [F: nat > real,K: nat] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( F @ ( plus_plus_nat @ N3 @ K ) ) )
% 5.02/5.35 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_minus_initial_segment
% 5.02/5.35 thf(fact_8063_sum__less__suminf,axiom,
% 5.02/5.35 ! [F: nat > int,N2: nat] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ! [M3: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.02/5.35 => ( ord_less_int @ zero_zero_int @ ( F @ M3 ) ) )
% 5.02/5.35 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_less_suminf
% 5.02/5.35 thf(fact_8064_sum__less__suminf,axiom,
% 5.02/5.35 ! [F: nat > nat,N2: nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ! [M3: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.02/5.35 => ( ord_less_nat @ zero_zero_nat @ ( F @ M3 ) ) )
% 5.02/5.35 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_less_suminf
% 5.02/5.35 thf(fact_8065_sum__less__suminf,axiom,
% 5.02/5.35 ! [F: nat > real,N2: nat] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [M3: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( F @ M3 ) ) )
% 5.02/5.35 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_less_suminf
% 5.02/5.35 thf(fact_8066_powser__split__head_I1_J,axiom,
% 5.02/5.35 ! [F: nat > complex,Z: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 => ( ( suminf_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.02/5.35 @ ( times_times_complex
% 5.02/5.35 @ ( suminf_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 @ Z ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_split_head(1)
% 5.02/5.35 thf(fact_8067_powser__split__head_I1_J,axiom,
% 5.02/5.35 ! [F: nat > real,Z: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 => ( ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.02/5.35 @ ( times_times_real
% 5.02/5.35 @ ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 @ Z ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_split_head(1)
% 5.02/5.35 thf(fact_8068_powser__split__head_I2_J,axiom,
% 5.02/5.35 ! [F: nat > complex,Z: complex] :
% 5.02/5.35 ( ( summable_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 => ( ( times_times_complex
% 5.02/5.35 @ ( suminf_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 @ Z )
% 5.02/5.35 = ( minus_minus_complex
% 5.02/5.35 @ ( suminf_complex
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ ( power_power_complex @ Z @ N3 ) ) )
% 5.02/5.35 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_split_head(2)
% 5.02/5.35 thf(fact_8069_powser__split__head_I2_J,axiom,
% 5.02/5.35 ! [F: nat > real,Z: real] :
% 5.02/5.35 ( ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 => ( ( times_times_real
% 5.02/5.35 @ ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 @ Z )
% 5.02/5.35 = ( minus_minus_real
% 5.02/5.35 @ ( suminf_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ Z @ N3 ) ) )
% 5.02/5.35 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % powser_split_head(2)
% 5.02/5.35 thf(fact_8070_tan__45,axiom,
% 5.02/5.35 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % tan_45
% 5.02/5.35 thf(fact_8071_summable__partial__sum__bound,axiom,
% 5.02/5.35 ! [F: nat > complex,E2: real] :
% 5.02/5.35 ( ( summable_complex @ F )
% 5.02/5.35 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.02/5.35 => ~ ! [N7: nat] :
% 5.02/5.35 ~ ! [M2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N7 @ M2 )
% 5.02/5.35 => ! [N8: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N8 ) ) ) @ E2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_partial_sum_bound
% 5.02/5.35 thf(fact_8072_summable__partial__sum__bound,axiom,
% 5.02/5.35 ! [F: nat > real,E2: real] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.02/5.35 => ~ ! [N7: nat] :
% 5.02/5.35 ~ ! [M2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N7 @ M2 )
% 5.02/5.35 => ! [N8: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N8 ) ) ) @ E2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_partial_sum_bound
% 5.02/5.35 thf(fact_8073_suminf__exist__split,axiom,
% 5.02/5.35 ! [R2: real,F: nat > real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.02/5.35 => ( ( summable_real @ F )
% 5.02/5.35 => ? [N7: nat] :
% 5.02/5.35 ! [N8: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N7 @ N8 )
% 5.02/5.35 => ( ord_less_real
% 5.02/5.35 @ ( real_V7735802525324610683m_real
% 5.02/5.35 @ ( suminf_real
% 5.02/5.35 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N8 ) ) ) )
% 5.02/5.35 @ R2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_exist_split
% 5.02/5.35 thf(fact_8074_suminf__exist__split,axiom,
% 5.02/5.35 ! [R2: real,F: nat > complex] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.02/5.35 => ( ( summable_complex @ F )
% 5.02/5.35 => ? [N7: nat] :
% 5.02/5.35 ! [N8: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N7 @ N8 )
% 5.02/5.35 => ( ord_less_real
% 5.02/5.35 @ ( real_V1022390504157884413omplex
% 5.02/5.35 @ ( suminf_complex
% 5.02/5.35 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N8 ) ) ) )
% 5.02/5.35 @ R2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % suminf_exist_split
% 5.02/5.35 thf(fact_8075_tan__60,axiom,
% 5.02/5.35 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.02/5.35 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_60
% 5.02/5.35 thf(fact_8076_summable__power__series,axiom,
% 5.02/5.35 ! [F: nat > real,Z: real] :
% 5.02/5.35 ( ! [I2: nat] : ( ord_less_eq_real @ ( F @ I2 ) @ one_one_real )
% 5.02/5.35 => ( ! [I2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.02/5.35 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.02/5.35 => ( ( ord_less_real @ Z @ one_one_real )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [I5: nat] : ( times_times_real @ ( F @ I5 ) @ ( power_power_real @ Z @ I5 ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_power_series
% 5.02/5.35 thf(fact_8077_Abel__lemma,axiom,
% 5.02/5.35 ! [R2: real,R0: real,A: nat > complex,M7: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ R2 )
% 5.02/5.35 => ( ( ord_less_real @ R2 @ R0 )
% 5.02/5.35 => ( ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R0 @ N ) ) @ M7 )
% 5.02/5.35 => ( summable_real
% 5.02/5.35 @ ^ [N3: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R2 @ N3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % Abel_lemma
% 5.02/5.35 thf(fact_8078_summable__ratio__test,axiom,
% 5.02/5.35 ! [C: real,N4: nat,F: nat > real] :
% 5.02/5.35 ( ( ord_less_real @ C @ one_one_real )
% 5.02/5.35 => ( ! [N: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N4 @ N )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N ) ) ) ) )
% 5.02/5.35 => ( summable_real @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_ratio_test
% 5.02/5.35 thf(fact_8079_summable__ratio__test,axiom,
% 5.02/5.35 ! [C: real,N4: nat,F: nat > complex] :
% 5.02/5.35 ( ( ord_less_real @ C @ one_one_real )
% 5.02/5.35 => ( ! [N: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N4 @ N )
% 5.02/5.35 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) )
% 5.02/5.35 => ( summable_complex @ F ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % summable_ratio_test
% 5.02/5.35 thf(fact_8080_sum__less__suminf2,axiom,
% 5.02/5.35 ! [F: nat > int,N2: nat,I3: nat] :
% 5.02/5.35 ( ( summable_int @ F )
% 5.02/5.35 => ( ! [M3: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.02/5.35 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M3 ) ) )
% 5.02/5.35 => ( ( ord_less_eq_nat @ N2 @ I3 )
% 5.02/5.35 => ( ( ord_less_int @ zero_zero_int @ ( F @ I3 ) )
% 5.02/5.35 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_less_suminf2
% 5.02/5.35 thf(fact_8081_sum__less__suminf2,axiom,
% 5.02/5.35 ! [F: nat > nat,N2: nat,I3: nat] :
% 5.02/5.35 ( ( summable_nat @ F )
% 5.02/5.35 => ( ! [M3: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.02/5.35 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M3 ) ) )
% 5.02/5.35 => ( ( ord_less_eq_nat @ N2 @ I3 )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.02/5.35 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_less_suminf2
% 5.02/5.35 thf(fact_8082_sum__less__suminf2,axiom,
% 5.02/5.35 ! [F: nat > real,N2: nat,I3: nat] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [M3: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M3 )
% 5.02/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M3 ) ) )
% 5.02/5.35 => ( ( ord_less_eq_nat @ N2 @ I3 )
% 5.02/5.35 => ( ( ord_less_real @ zero_zero_real @ ( F @ I3 ) )
% 5.02/5.35 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_less_suminf2
% 5.02/5.35 thf(fact_8083_lemma__tan__total,axiom,
% 5.02/5.35 ! [Y: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.02/5.35 => ? [X5: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.02/5.35 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( ord_less_real @ Y @ ( tan_real @ X5 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_tan_total
% 5.02/5.35 thf(fact_8084_tan__gt__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_gt_zero
% 5.02/5.35 thf(fact_8085_lemma__tan__total1,axiom,
% 5.02/5.35 ! [Y: real] :
% 5.02/5.35 ? [X5: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.02/5.35 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( ( tan_real @ X5 )
% 5.02/5.35 = Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_tan_total1
% 5.02/5.35 thf(fact_8086_tan__mono__lt__eq,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) )
% 5.02/5.35 = ( ord_less_real @ X2 @ Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_mono_lt_eq
% 5.02/5.35 thf(fact_8087_tan__monotone_H,axiom,
% 5.02/5.35 ! [Y: real,X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_real @ Y @ X2 )
% 5.02/5.35 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X2 ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_monotone'
% 5.02/5.35 thf(fact_8088_tan__monotone,axiom,
% 5.02/5.35 ! [Y: real,X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_real @ Y @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_monotone
% 5.02/5.35 thf(fact_8089_tan__total,axiom,
% 5.02/5.35 ! [Y: real] :
% 5.02/5.35 ? [X5: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.02/5.35 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( ( tan_real @ X5 )
% 5.02/5.35 = Y )
% 5.02/5.35 & ! [Y5: real] :
% 5.02/5.35 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y5 )
% 5.02/5.35 & ( ord_less_real @ Y5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( ( tan_real @ Y5 )
% 5.02/5.35 = Y ) )
% 5.02/5.35 => ( Y5 = X5 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_total
% 5.02/5.35 thf(fact_8090_tan__minus__45,axiom,
% 5.02/5.35 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.35 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_minus_45
% 5.02/5.35 thf(fact_8091_tan__inverse,axiom,
% 5.02/5.35 ! [Y: real] :
% 5.02/5.35 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.02/5.35 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_inverse
% 5.02/5.35 thf(fact_8092_add__tan__eq,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] :
% 5.02/5.35 ( ( ( cos_complex @ X2 )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( ( cos_complex @ Y )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X2 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % add_tan_eq
% 5.02/5.35 thf(fact_8093_add__tan__eq,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( ( cos_real @ Y )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) )
% 5.02/5.35 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % add_tan_eq
% 5.02/5.35 thf(fact_8094_tan__cot_H,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.02/5.35 = ( cot_real @ X2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_cot'
% 5.02/5.35 thf(fact_8095_tan__pos__pi2__le,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_pos_pi2_le
% 5.02/5.35 thf(fact_8096_tan__total__pos,axiom,
% 5.02/5.35 ! [Y: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.35 => ? [X5: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.02/5.35 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( ( tan_real @ X5 )
% 5.02/5.35 = Y ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_total_pos
% 5.02/5.35 thf(fact_8097_tan__less__zero,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.02/5.35 => ( ord_less_real @ ( tan_real @ X2 ) @ zero_zero_real ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_less_zero
% 5.02/5.35 thf(fact_8098_tan__mono__le__eq,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.02/5.35 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) )
% 5.02/5.35 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_mono_le_eq
% 5.02/5.35 thf(fact_8099_tan__mono__le,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.35 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ord_less_eq_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_mono_le
% 5.02/5.35 thf(fact_8100_tan__bound__pi2,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.02/5.35 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X2 ) ) @ one_one_real ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_bound_pi2
% 5.02/5.35 thf(fact_8101_tan__30,axiom,
% 5.02/5.35 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.02/5.35 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_30
% 5.02/5.35 thf(fact_8102_arctan,axiom,
% 5.02/5.35 ! [Y: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.02/5.35 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 & ( ( tan_real @ ( arctan @ Y ) )
% 5.02/5.35 = Y ) ) ).
% 5.02/5.35
% 5.02/5.35 % arctan
% 5.02/5.35 thf(fact_8103_arctan__tan,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( arctan @ ( tan_real @ X2 ) )
% 5.02/5.35 = X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % arctan_tan
% 5.02/5.35 thf(fact_8104_arctan__unique,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( ( tan_real @ X2 )
% 5.02/5.35 = Y )
% 5.02/5.35 => ( ( arctan @ Y )
% 5.02/5.35 = X2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % arctan_unique
% 5.02/5.35 thf(fact_8105_tan__add,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] :
% 5.02/5.35 ( ( ( cos_complex @ X2 )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( ( cos_complex @ Y )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( ( cos_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( tan_complex @ ( plus_plus_complex @ X2 @ Y ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_add
% 5.02/5.35 thf(fact_8106_tan__add,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( ( cos_real @ Y )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( ( cos_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( tan_real @ ( plus_plus_real @ X2 @ Y ) )
% 5.02/5.35 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_add
% 5.02/5.35 thf(fact_8107_tan__diff,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] :
% 5.02/5.35 ( ( ( cos_complex @ X2 )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( ( cos_complex @ Y )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( ( cos_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( tan_complex @ ( minus_minus_complex @ X2 @ Y ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_diff
% 5.02/5.35 thf(fact_8108_tan__diff,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( ( cos_real @ Y )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( ( cos_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( tan_real @ ( minus_minus_real @ X2 @ Y ) )
% 5.02/5.35 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_diff
% 5.02/5.35 thf(fact_8109_lemma__tan__add1,axiom,
% 5.02/5.35 ! [X2: complex,Y: complex] :
% 5.02/5.35 ( ( ( cos_complex @ X2 )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( ( cos_complex @ Y )
% 5.02/5.35 != zero_zero_complex )
% 5.02/5.35 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X2 ) @ ( tan_complex @ Y ) ) )
% 5.02/5.35 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X2 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X2 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_tan_add1
% 5.02/5.35 thf(fact_8110_lemma__tan__add1,axiom,
% 5.02/5.35 ! [X2: real,Y: real] :
% 5.02/5.35 ( ( ( cos_real @ X2 )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( ( cos_real @ Y )
% 5.02/5.35 != zero_zero_real )
% 5.02/5.35 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X2 ) @ ( tan_real @ Y ) ) )
% 5.02/5.35 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X2 @ Y ) ) @ ( times_times_real @ ( cos_real @ X2 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % lemma_tan_add1
% 5.02/5.35 thf(fact_8111_tan__total__pi4,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.35 => ? [Z3: real] :
% 5.02/5.35 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z3 )
% 5.02/5.35 & ( ord_less_real @ Z3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.02/5.35 & ( ( tan_real @ Z3 )
% 5.02/5.35 = X2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_total_pi4
% 5.02/5.35 thf(fact_8112_sum__pos__lt__pair,axiom,
% 5.02/5.35 ! [F: nat > real,K: nat] :
% 5.02/5.35 ( ( summable_real @ F )
% 5.02/5.35 => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 5.02/5.35 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % sum_pos_lt_pair
% 5.02/5.35 thf(fact_8113_tan__half,axiom,
% 5.02/5.35 ( tan_complex
% 5.02/5.35 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_half
% 5.02/5.35 thf(fact_8114_tan__half,axiom,
% 5.02/5.35 ( tan_real
% 5.02/5.35 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % tan_half
% 5.02/5.35 thf(fact_8115_cos__tan,axiom,
% 5.02/5.35 ! [X2: real] :
% 5.02/5.35 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.35 => ( ( cos_real @ X2 )
% 5.02/5.35 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % cos_tan
% 5.02/5.35 thf(fact_8116_Maclaurin__minus__cos__expansion,axiom,
% 5.02/5.35 ! [N2: nat,X2: real] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.02/5.35 => ? [T3: real] :
% 5.02/5.35 ( ( ord_less_real @ X2 @ T3 )
% 5.02/5.35 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.02/5.35 & ( ( cos_real @ X2 )
% 5.02/5.35 = ( plus_plus_real
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % Maclaurin_minus_cos_expansion
% 5.02/5.35 thf(fact_8117_Maclaurin__cos__expansion2,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ? [T3: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.02/5.35 & ( ord_less_real @ T3 @ X2 )
% 5.02/5.35 & ( ( cos_real @ X2 )
% 5.02/5.35 = ( plus_plus_real
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % Maclaurin_cos_expansion2
% 5.02/5.35 thf(fact_8118_Maclaurin__cos__expansion,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ? [T3: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.02/5.35 & ( ( cos_real @ X2 )
% 5.02/5.35 = ( plus_plus_real
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % Maclaurin_cos_expansion
% 5.02/5.35 thf(fact_8119_complex__unimodular__polar,axiom,
% 5.02/5.35 ! [Z: complex] :
% 5.02/5.35 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.02/5.35 = one_one_real )
% 5.02/5.35 => ~ ! [T3: real] :
% 5.02/5.35 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.02/5.35 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.02/5.35 => ( Z
% 5.02/5.35 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % complex_unimodular_polar
% 5.02/5.35 thf(fact_8120_Maclaurin__exp__lt,axiom,
% 5.02/5.35 ! [X2: real,N2: nat] :
% 5.02/5.35 ( ( X2 != zero_zero_real )
% 5.02/5.35 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.35 => ? [T3: real] :
% 5.02/5.35 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.02/5.35 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.02/5.35 & ( ( exp_real @ X2 )
% 5.02/5.35 = ( plus_plus_real
% 5.02/5.35 @ ( groups6591440286371151544t_real
% 5.02/5.35 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.02/5.35 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.35 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % Maclaurin_exp_lt
% 5.02/5.35 thf(fact_8121_fact__0,axiom,
% 5.02/5.35 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.02/5.35 = one_one_complex ) ).
% 5.02/5.35
% 5.02/5.35 % fact_0
% 5.02/5.35 thf(fact_8122_fact__0,axiom,
% 5.02/5.35 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.02/5.35 = one_one_rat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_0
% 5.02/5.35 thf(fact_8123_fact__0,axiom,
% 5.02/5.35 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.02/5.35 = one_one_int ) ).
% 5.02/5.35
% 5.02/5.35 % fact_0
% 5.02/5.35 thf(fact_8124_fact__0,axiom,
% 5.02/5.35 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % fact_0
% 5.02/5.35 thf(fact_8125_fact__0,axiom,
% 5.02/5.35 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.02/5.35 = one_one_nat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_0
% 5.02/5.35 thf(fact_8126_fact__1,axiom,
% 5.02/5.35 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.02/5.35 = one_one_complex ) ).
% 5.02/5.35
% 5.02/5.35 % fact_1
% 5.02/5.35 thf(fact_8127_fact__1,axiom,
% 5.02/5.35 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.02/5.35 = one_one_rat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_1
% 5.02/5.35 thf(fact_8128_fact__1,axiom,
% 5.02/5.35 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.02/5.35 = one_one_int ) ).
% 5.02/5.35
% 5.02/5.35 % fact_1
% 5.02/5.35 thf(fact_8129_fact__1,axiom,
% 5.02/5.35 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % fact_1
% 5.02/5.35 thf(fact_8130_fact__1,axiom,
% 5.02/5.35 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.02/5.35 = one_one_nat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_1
% 5.02/5.35 thf(fact_8131_fact__Suc__0,axiom,
% 5.02/5.35 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.02/5.35 = one_one_complex ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc_0
% 5.02/5.35 thf(fact_8132_fact__Suc__0,axiom,
% 5.02/5.35 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.02/5.35 = one_one_rat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc_0
% 5.02/5.35 thf(fact_8133_fact__Suc__0,axiom,
% 5.02/5.35 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.02/5.35 = one_one_int ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc_0
% 5.02/5.35 thf(fact_8134_fact__Suc__0,axiom,
% 5.02/5.35 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc_0
% 5.02/5.35 thf(fact_8135_fact__Suc__0,axiom,
% 5.02/5.35 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.02/5.35 = one_one_nat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc_0
% 5.02/5.35 thf(fact_8136_fact__Suc,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 5.02/5.35 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc
% 5.02/5.35 thf(fact_8137_fact__Suc,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri773545260158071498ct_rat @ ( suc @ N2 ) )
% 5.02/5.35 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc
% 5.02/5.35 thf(fact_8138_fact__Suc,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri2265585572941072030t_real @ ( suc @ N2 ) )
% 5.02/5.35 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc
% 5.02/5.35 thf(fact_8139_fact__Suc,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 5.02/5.35 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_Suc
% 5.02/5.35 thf(fact_8140_fact__2,axiom,
% 5.02/5.35 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_2
% 5.02/5.35 thf(fact_8141_fact__2,axiom,
% 5.02/5.35 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_2
% 5.02/5.35 thf(fact_8142_fact__2,axiom,
% 5.02/5.35 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_2
% 5.02/5.35 thf(fact_8143_fact__2,axiom,
% 5.02/5.35 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_2
% 5.02/5.35 thf(fact_8144_fact__2,axiom,
% 5.02/5.35 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.35 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_2
% 5.02/5.35 thf(fact_8145_norm__cos__sin,axiom,
% 5.02/5.35 ! [T2: real] :
% 5.02/5.35 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T2 ) @ ( sin_real @ T2 ) ) )
% 5.02/5.35 = one_one_real ) ).
% 5.02/5.35
% 5.02/5.35 % norm_cos_sin
% 5.02/5.35 thf(fact_8146_fact__nonzero,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri5044797733671781792omplex @ N2 )
% 5.02/5.35 != zero_zero_complex ) ).
% 5.02/5.35
% 5.02/5.35 % fact_nonzero
% 5.02/5.35 thf(fact_8147_fact__nonzero,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri773545260158071498ct_rat @ N2 )
% 5.02/5.35 != zero_zero_rat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_nonzero
% 5.02/5.35 thf(fact_8148_fact__nonzero,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1406184849735516958ct_int @ N2 )
% 5.02/5.35 != zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % fact_nonzero
% 5.02/5.35 thf(fact_8149_fact__nonzero,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri2265585572941072030t_real @ N2 )
% 5.02/5.35 != zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % fact_nonzero
% 5.02/5.35 thf(fact_8150_fact__nonzero,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ( ( semiri1408675320244567234ct_nat @ N2 )
% 5.02/5.35 != zero_zero_nat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_nonzero
% 5.02/5.35 thf(fact_8151_fact__ge__zero,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_ge_zero
% 5.02/5.35 thf(fact_8152_fact__ge__zero,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_ge_zero
% 5.02/5.35 thf(fact_8153_fact__ge__zero,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_ge_zero
% 5.02/5.35 thf(fact_8154_fact__ge__zero,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_ge_zero
% 5.02/5.35 thf(fact_8155_fact__gt__zero,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_gt_zero
% 5.02/5.35 thf(fact_8156_fact__gt__zero,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_gt_zero
% 5.02/5.35 thf(fact_8157_fact__gt__zero,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_gt_zero
% 5.02/5.35 thf(fact_8158_fact__gt__zero,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_gt_zero
% 5.02/5.35 thf(fact_8159_fact__not__neg,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ zero_zero_rat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_not_neg
% 5.02/5.35 thf(fact_8160_fact__not__neg,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 5.02/5.35
% 5.02/5.35 % fact_not_neg
% 5.02/5.35 thf(fact_8161_fact__not__neg,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N2 ) @ zero_zero_real ) ).
% 5.02/5.35
% 5.02/5.35 % fact_not_neg
% 5.02/5.35 thf(fact_8162_fact__not__neg,axiom,
% 5.02/5.35 ! [N2: nat] :
% 5.02/5.35 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 5.02/5.35
% 5.02/5.35 % fact_not_neg
% 5.02/5.35 thf(fact_8163_fact__ge__1,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_ge_1
% 5.02/5.35 thf(fact_8164_fact__ge__1,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_ge_1
% 5.02/5.35 thf(fact_8165_fact__ge__1,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_ge_1
% 5.02/5.35 thf(fact_8166_fact__ge__1,axiom,
% 5.02/5.35 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_ge_1
% 5.02/5.35 thf(fact_8167_fact__mono,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_mono
% 5.02/5.35 thf(fact_8168_fact__mono,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_mono
% 5.02/5.35 thf(fact_8169_fact__mono,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_mono
% 5.02/5.35 thf(fact_8170_fact__mono,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_mono
% 5.02/5.35 thf(fact_8171_fact__dvd,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_dvd
% 5.02/5.35 thf(fact_8172_fact__dvd,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_dvd
% 5.02/5.35 thf(fact_8173_fact__dvd,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_dvd
% 5.02/5.35 thf(fact_8174_fact__dvd,axiom,
% 5.02/5.35 ! [N2: nat,M: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.35 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_dvd
% 5.02/5.35 thf(fact_8175_complex__add,axiom,
% 5.02/5.35 ! [A: real,B: real,C: real,D: real] :
% 5.02/5.35 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.02/5.35 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % complex_add
% 5.02/5.35 thf(fact_8176_fact__less__mono,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.35 => ( ( ord_less_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_less_mono
% 5.02/5.35 thf(fact_8177_fact__less__mono,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.35 => ( ( ord_less_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_less_mono
% 5.02/5.35 thf(fact_8178_fact__less__mono,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.35 => ( ( ord_less_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_less_mono
% 5.02/5.35 thf(fact_8179_fact__less__mono,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.35 => ( ( ord_less_nat @ M @ N2 )
% 5.02/5.35 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_less_mono
% 5.02/5.35 thf(fact_8180_fact__fact__dvd__fact,axiom,
% 5.02/5.35 ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_fact_dvd_fact
% 5.02/5.35 thf(fact_8181_fact__fact__dvd__fact,axiom,
% 5.02/5.35 ! [K: nat,N2: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N2 ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_fact_dvd_fact
% 5.02/5.35 thf(fact_8182_fact__fact__dvd__fact,axiom,
% 5.02/5.35 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_fact_dvd_fact
% 5.02/5.35 thf(fact_8183_fact__fact__dvd__fact,axiom,
% 5.02/5.35 ! [K: nat,N2: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_fact_dvd_fact
% 5.02/5.35 thf(fact_8184_fact__fact__dvd__fact,axiom,
% 5.02/5.35 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.02/5.35
% 5.02/5.35 % fact_fact_dvd_fact
% 5.02/5.35 thf(fact_8185_fact__mod,axiom,
% 5.02/5.35 ! [M: nat,N2: nat] :
% 5.02/5.35 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.35 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.02/5.36 = zero_zero_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_mod
% 5.02/5.36 thf(fact_8186_fact__mod,axiom,
% 5.02/5.36 ! [M: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.02/5.36 = zero_zero_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_mod
% 5.02/5.36 thf(fact_8187_fact__le__power,axiom,
% 5.02/5.36 ! [N2: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_le_power
% 5.02/5.36 thf(fact_8188_fact__le__power,axiom,
% 5.02/5.36 ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_le_power
% 5.02/5.36 thf(fact_8189_fact__le__power,axiom,
% 5.02/5.36 ! [N2: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_le_power
% 5.02/5.36 thf(fact_8190_fact__le__power,axiom,
% 5.02/5.36 ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_le_power
% 5.02/5.36 thf(fact_8191_complex__mult,axiom,
% 5.02/5.36 ! [A: real,B: real,C: real,D: real] :
% 5.02/5.36 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.02/5.36 = ( 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 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % complex_mult
% 5.02/5.36 thf(fact_8192_one__complex_Ocode,axiom,
% 5.02/5.36 ( one_one_complex
% 5.02/5.36 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % one_complex.code
% 5.02/5.36 thf(fact_8193_Complex__eq__1,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( ( complex2 @ A @ B )
% 5.02/5.36 = one_one_complex )
% 5.02/5.36 = ( ( A = one_one_real )
% 5.02/5.36 & ( B = zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Complex_eq_1
% 5.02/5.36 thf(fact_8194_choose__dvd,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_dvd
% 5.02/5.36 thf(fact_8195_choose__dvd,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_dvd
% 5.02/5.36 thf(fact_8196_choose__dvd,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_dvd
% 5.02/5.36 thf(fact_8197_choose__dvd,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_dvd
% 5.02/5.36 thf(fact_8198_choose__dvd,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_dvd
% 5.02/5.36 thf(fact_8199_fact__numeral,axiom,
% 5.02/5.36 ! [K: num] :
% 5.02/5.36 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.02/5.36 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_numeral
% 5.02/5.36 thf(fact_8200_fact__numeral,axiom,
% 5.02/5.36 ! [K: num] :
% 5.02/5.36 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.02/5.36 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_numeral
% 5.02/5.36 thf(fact_8201_fact__numeral,axiom,
% 5.02/5.36 ! [K: num] :
% 5.02/5.36 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.02/5.36 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_numeral
% 5.02/5.36 thf(fact_8202_fact__numeral,axiom,
% 5.02/5.36 ! [K: num] :
% 5.02/5.36 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.02/5.36 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_numeral
% 5.02/5.36 thf(fact_8203_fact__numeral,axiom,
% 5.02/5.36 ! [K: num] :
% 5.02/5.36 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.02/5.36 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_numeral
% 5.02/5.36 thf(fact_8204_Complex__eq__neg__1,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( ( complex2 @ A @ B )
% 5.02/5.36 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.02/5.36 = ( ( A
% 5.02/5.36 = ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.36 & ( B = zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Complex_eq_neg_1
% 5.02/5.36 thf(fact_8205_square__fact__le__2__fact,axiom,
% 5.02/5.36 ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % square_fact_le_2_fact
% 5.02/5.36 thf(fact_8206_fact__num__eq__if,axiom,
% 5.02/5.36 ( semiri5044797733671781792omplex
% 5.02/5.36 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_num_eq_if
% 5.02/5.36 thf(fact_8207_fact__num__eq__if,axiom,
% 5.02/5.36 ( semiri1406184849735516958ct_int
% 5.02/5.36 = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_num_eq_if
% 5.02/5.36 thf(fact_8208_fact__num__eq__if,axiom,
% 5.02/5.36 ( semiri773545260158071498ct_rat
% 5.02/5.36 = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_num_eq_if
% 5.02/5.36 thf(fact_8209_fact__num__eq__if,axiom,
% 5.02/5.36 ( semiri2265585572941072030t_real
% 5.02/5.36 = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_num_eq_if
% 5.02/5.36 thf(fact_8210_fact__num__eq__if,axiom,
% 5.02/5.36 ( semiri1408675320244567234ct_nat
% 5.02/5.36 = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_num_eq_if
% 5.02/5.36 thf(fact_8211_fact__reduce,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( semiri1406184849735516958ct_int @ N2 )
% 5.02/5.36 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_reduce
% 5.02/5.36 thf(fact_8212_fact__reduce,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( semiri773545260158071498ct_rat @ N2 )
% 5.02/5.36 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_reduce
% 5.02/5.36 thf(fact_8213_fact__reduce,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( semiri2265585572941072030t_real @ N2 )
% 5.02/5.36 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_reduce
% 5.02/5.36 thf(fact_8214_fact__reduce,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 5.02/5.36 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_reduce
% 5.02/5.36 thf(fact_8215_complex__norm,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( real_V1022390504157884413omplex @ ( complex2 @ X2 @ Y ) )
% 5.02/5.36 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % complex_norm
% 5.02/5.36 thf(fact_8216_Maclaurin__zero,axiom,
% 5.02/5.36 ! [X2: real,N2: nat,Diff: nat > complex > real] :
% 5.02/5.36 ( ( X2 = zero_zero_real )
% 5.02/5.36 => ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_zero
% 5.02/5.36 thf(fact_8217_Maclaurin__zero,axiom,
% 5.02/5.36 ! [X2: real,N2: nat,Diff: nat > real > real] :
% 5.02/5.36 ( ( X2 = zero_zero_real )
% 5.02/5.36 => ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_zero
% 5.02/5.36 thf(fact_8218_Maclaurin__zero,axiom,
% 5.02/5.36 ! [X2: real,N2: nat,Diff: nat > rat > real] :
% 5.02/5.36 ( ( X2 = zero_zero_real )
% 5.02/5.36 => ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_zero
% 5.02/5.36 thf(fact_8219_Maclaurin__zero,axiom,
% 5.02/5.36 ! [X2: real,N2: nat,Diff: nat > nat > real] :
% 5.02/5.36 ( ( X2 = zero_zero_real )
% 5.02/5.36 => ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_zero
% 5.02/5.36 thf(fact_8220_Maclaurin__zero,axiom,
% 5.02/5.36 ! [X2: real,N2: nat,Diff: nat > int > real] :
% 5.02/5.36 ( ( X2 = zero_zero_real )
% 5.02/5.36 => ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_zero
% 5.02/5.36 thf(fact_8221_Maclaurin__lemma,axiom,
% 5.02/5.36 ! [H2: real,F: real > real,J: nat > real,N2: nat] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.02/5.36 => ? [B8: real] :
% 5.02/5.36 ( ( F @ H2 )
% 5.02/5.36 = ( plus_plus_real
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_lemma
% 5.02/5.36 thf(fact_8222_Maclaurin__exp__le,axiom,
% 5.02/5.36 ! [X2: real,N2: nat] :
% 5.02/5.36 ? [T3: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.02/5.36 & ( ( exp_real @ X2 )
% 5.02/5.36 = ( plus_plus_real
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X2 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_exp_le
% 5.02/5.36 thf(fact_8223_cos__coeff__def,axiom,
% 5.02/5.36 ( cos_coeff
% 5.02/5.36 = ( ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N3 ) ) @ zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % cos_coeff_def
% 5.02/5.36 thf(fact_8224_Maclaurin__sin__expansion3,axiom,
% 5.02/5.36 ! [N2: nat,X2: real] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.36 => ? [T3: real] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.02/5.36 & ( ord_less_real @ T3 @ X2 )
% 5.02/5.36 & ( ( sin_real @ X2 )
% 5.02/5.36 = ( plus_plus_real
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_sin_expansion3
% 5.02/5.36 thf(fact_8225_Maclaurin__sin__expansion4,axiom,
% 5.02/5.36 ! [X2: real,N2: nat] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.36 => ? [T3: real] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.02/5.36 & ( ord_less_eq_real @ T3 @ X2 )
% 5.02/5.36 & ( ( sin_real @ X2 )
% 5.02/5.36 = ( plus_plus_real
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_sin_expansion4
% 5.02/5.36 thf(fact_8226_Maclaurin__sin__expansion2,axiom,
% 5.02/5.36 ! [X2: real,N2: nat] :
% 5.02/5.36 ? [T3: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.02/5.36 & ( ( sin_real @ X2 )
% 5.02/5.36 = ( plus_plus_real
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_sin_expansion2
% 5.02/5.36 thf(fact_8227_Maclaurin__sin__expansion,axiom,
% 5.02/5.36 ! [X2: real,N2: nat] :
% 5.02/5.36 ? [T3: real] :
% 5.02/5.36 ( ( sin_real @ X2 )
% 5.02/5.36 = ( plus_plus_real
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_sin_expansion
% 5.02/5.36 thf(fact_8228_sin__coeff__def,axiom,
% 5.02/5.36 ( sin_coeff
% 5.02/5.36 = ( ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sin_coeff_def
% 5.02/5.36 thf(fact_8229_sin__coeff__0,axiom,
% 5.02/5.36 ( ( sin_coeff @ zero_zero_nat )
% 5.02/5.36 = zero_zero_real ) ).
% 5.02/5.36
% 5.02/5.36 % sin_coeff_0
% 5.02/5.36 thf(fact_8230_fact__mono__nat,axiom,
% 5.02/5.36 ! [M: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_mono_nat
% 5.02/5.36 thf(fact_8231_fact__ge__self,axiom,
% 5.02/5.36 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_ge_self
% 5.02/5.36 thf(fact_8232_fact__less__mono__nat,axiom,
% 5.02/5.36 ! [M: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.36 => ( ( ord_less_nat @ M @ N2 )
% 5.02/5.36 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_less_mono_nat
% 5.02/5.36 thf(fact_8233_fact__ge__Suc__0__nat,axiom,
% 5.02/5.36 ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_ge_Suc_0_nat
% 5.02/5.36 thf(fact_8234_dvd__fact,axiom,
% 5.02/5.36 ! [M: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.02/5.36 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % dvd_fact
% 5.02/5.36 thf(fact_8235_fact__diff__Suc,axiom,
% 5.02/5.36 ! [N2: nat,M: nat] :
% 5.02/5.36 ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.02/5.36 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 5.02/5.36 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_diff_Suc
% 5.02/5.36 thf(fact_8236_fact__div__fact__le__pow,axiom,
% 5.02/5.36 ! [R2: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ R2 @ N2 )
% 5.02/5.36 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R2 ) ) ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_div_fact_le_pow
% 5.02/5.36 thf(fact_8237_sin__coeff__Suc,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( sin_coeff @ ( suc @ N2 ) )
% 5.02/5.36 = ( divide_divide_real @ ( cos_coeff @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sin_coeff_Suc
% 5.02/5.36 thf(fact_8238_cos__coeff__Suc,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( cos_coeff @ ( suc @ N2 ) )
% 5.02/5.36 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N2 ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % cos_coeff_Suc
% 5.02/5.36 thf(fact_8239_sin__paired,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.02/5.36 @ ( sin_real @ X2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % sin_paired
% 5.02/5.36 thf(fact_8240_cos__arcsin,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.36 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.02/5.36 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % cos_arcsin
% 5.02/5.36 thf(fact_8241_sin__arccos__abs,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.02/5.36 => ( ( sin_real @ ( arccos @ Y ) )
% 5.02/5.36 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sin_arccos_abs
% 5.02/5.36 thf(fact_8242_sin__arccos,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.36 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.02/5.36 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sin_arccos
% 5.02/5.36 thf(fact_8243_geometric__deriv__sums,axiom,
% 5.02/5.36 ! [Z: real] :
% 5.02/5.36 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) @ ( power_power_real @ Z @ N3 ) )
% 5.02/5.36 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % geometric_deriv_sums
% 5.02/5.36 thf(fact_8244_geometric__deriv__sums,axiom,
% 5.02/5.36 ! [Z: complex] :
% 5.02/5.36 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.02/5.36 => ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N3 ) ) @ ( power_power_complex @ Z @ N3 ) )
% 5.02/5.36 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % geometric_deriv_sums
% 5.02/5.36 thf(fact_8245_sums__zero,axiom,
% 5.02/5.36 ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : zero_zero_complex
% 5.02/5.36 @ zero_zero_complex ) ).
% 5.02/5.36
% 5.02/5.36 % sums_zero
% 5.02/5.36 thf(fact_8246_sums__zero,axiom,
% 5.02/5.36 ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : zero_zero_real
% 5.02/5.36 @ zero_zero_real ) ).
% 5.02/5.36
% 5.02/5.36 % sums_zero
% 5.02/5.36 thf(fact_8247_sums__zero,axiom,
% 5.02/5.36 ( sums_nat
% 5.02/5.36 @ ^ [N3: nat] : zero_zero_nat
% 5.02/5.36 @ zero_zero_nat ) ).
% 5.02/5.36
% 5.02/5.36 % sums_zero
% 5.02/5.36 thf(fact_8248_sums__zero,axiom,
% 5.02/5.36 ( sums_int
% 5.02/5.36 @ ^ [N3: nat] : zero_zero_int
% 5.02/5.36 @ zero_zero_int ) ).
% 5.02/5.36
% 5.02/5.36 % sums_zero
% 5.02/5.36 thf(fact_8249_arccos__1,axiom,
% 5.02/5.36 ( ( arccos @ one_one_real )
% 5.02/5.36 = zero_zero_real ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_1
% 5.02/5.36 thf(fact_8250_arccos__minus__1,axiom,
% 5.02/5.36 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.36 = pi ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_minus_1
% 5.02/5.36 thf(fact_8251_cos__arccos,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( cos_real @ ( arccos @ Y ) )
% 5.02/5.36 = Y ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % cos_arccos
% 5.02/5.36 thf(fact_8252_sin__arcsin,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.02/5.36 = Y ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sin_arcsin
% 5.02/5.36 thf(fact_8253_powser__sums__zero__iff,axiom,
% 5.02/5.36 ! [A: nat > complex,X2: complex] :
% 5.02/5.36 ( ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( A @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) )
% 5.02/5.36 @ X2 )
% 5.02/5.36 = ( ( A @ zero_zero_nat )
% 5.02/5.36 = X2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % powser_sums_zero_iff
% 5.02/5.36 thf(fact_8254_powser__sums__zero__iff,axiom,
% 5.02/5.36 ! [A: nat > real,X2: real] :
% 5.02/5.36 ( ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( A @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) )
% 5.02/5.36 @ X2 )
% 5.02/5.36 = ( ( A @ zero_zero_nat )
% 5.02/5.36 = X2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % powser_sums_zero_iff
% 5.02/5.36 thf(fact_8255_arccos__0,axiom,
% 5.02/5.36 ( ( arccos @ zero_zero_real )
% 5.02/5.36 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_0
% 5.02/5.36 thf(fact_8256_arcsin__1,axiom,
% 5.02/5.36 ( ( arcsin @ one_one_real )
% 5.02/5.36 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_1
% 5.02/5.36 thf(fact_8257_arcsin__minus__1,axiom,
% 5.02/5.36 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.36 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_minus_1
% 5.02/5.36 thf(fact_8258_sums__le,axiom,
% 5.02/5.36 ! [F: nat > real,G: nat > real,S2: real,T2: real] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( G @ N ) )
% 5.02/5.36 => ( ( sums_real @ F @ S2 )
% 5.02/5.36 => ( ( sums_real @ G @ T2 )
% 5.02/5.36 => ( ord_less_eq_real @ S2 @ T2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_le
% 5.02/5.36 thf(fact_8259_sums__le,axiom,
% 5.02/5.36 ! [F: nat > nat,G: nat > nat,S2: nat,T2: nat] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ ( G @ N ) )
% 5.02/5.36 => ( ( sums_nat @ F @ S2 )
% 5.02/5.36 => ( ( sums_nat @ G @ T2 )
% 5.02/5.36 => ( ord_less_eq_nat @ S2 @ T2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_le
% 5.02/5.36 thf(fact_8260_sums__le,axiom,
% 5.02/5.36 ! [F: nat > int,G: nat > int,S2: int,T2: int] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_int @ ( F @ N ) @ ( G @ N ) )
% 5.02/5.36 => ( ( sums_int @ F @ S2 )
% 5.02/5.36 => ( ( sums_int @ G @ T2 )
% 5.02/5.36 => ( ord_less_eq_int @ S2 @ T2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_le
% 5.02/5.36 thf(fact_8261_sums__0,axiom,
% 5.02/5.36 ! [F: nat > complex] :
% 5.02/5.36 ( ! [N: nat] :
% 5.02/5.36 ( ( F @ N )
% 5.02/5.36 = zero_zero_complex )
% 5.02/5.36 => ( sums_complex @ F @ zero_zero_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_0
% 5.02/5.36 thf(fact_8262_sums__0,axiom,
% 5.02/5.36 ! [F: nat > real] :
% 5.02/5.36 ( ! [N: nat] :
% 5.02/5.36 ( ( F @ N )
% 5.02/5.36 = zero_zero_real )
% 5.02/5.36 => ( sums_real @ F @ zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_0
% 5.02/5.36 thf(fact_8263_sums__0,axiom,
% 5.02/5.36 ! [F: nat > nat] :
% 5.02/5.36 ( ! [N: nat] :
% 5.02/5.36 ( ( F @ N )
% 5.02/5.36 = zero_zero_nat )
% 5.02/5.36 => ( sums_nat @ F @ zero_zero_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_0
% 5.02/5.36 thf(fact_8264_sums__0,axiom,
% 5.02/5.36 ! [F: nat > int] :
% 5.02/5.36 ( ! [N: nat] :
% 5.02/5.36 ( ( F @ N )
% 5.02/5.36 = zero_zero_int )
% 5.02/5.36 => ( sums_int @ F @ zero_zero_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_0
% 5.02/5.36 thf(fact_8265_sums__single,axiom,
% 5.02/5.36 ! [I3: nat,F: nat > complex] :
% 5.02/5.36 ( sums_complex
% 5.02/5.36 @ ^ [R5: nat] : ( if_complex @ ( R5 = I3 ) @ ( F @ R5 ) @ zero_zero_complex )
% 5.02/5.36 @ ( F @ I3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_single
% 5.02/5.36 thf(fact_8266_sums__single,axiom,
% 5.02/5.36 ! [I3: nat,F: nat > real] :
% 5.02/5.36 ( sums_real
% 5.02/5.36 @ ^ [R5: nat] : ( if_real @ ( R5 = I3 ) @ ( F @ R5 ) @ zero_zero_real )
% 5.02/5.36 @ ( F @ I3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_single
% 5.02/5.36 thf(fact_8267_sums__single,axiom,
% 5.02/5.36 ! [I3: nat,F: nat > nat] :
% 5.02/5.36 ( sums_nat
% 5.02/5.36 @ ^ [R5: nat] : ( if_nat @ ( R5 = I3 ) @ ( F @ R5 ) @ zero_zero_nat )
% 5.02/5.36 @ ( F @ I3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_single
% 5.02/5.36 thf(fact_8268_sums__single,axiom,
% 5.02/5.36 ! [I3: nat,F: nat > int] :
% 5.02/5.36 ( sums_int
% 5.02/5.36 @ ^ [R5: nat] : ( if_int @ ( R5 = I3 ) @ ( F @ R5 ) @ zero_zero_int )
% 5.02/5.36 @ ( F @ I3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_single
% 5.02/5.36 thf(fact_8269_sums__mult,axiom,
% 5.02/5.36 ! [F: nat > real,A: real,C: real] :
% 5.02/5.36 ( ( sums_real @ F @ A )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.02/5.36 @ ( times_times_real @ C @ A ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_mult
% 5.02/5.36 thf(fact_8270_sums__mult2,axiom,
% 5.02/5.36 ! [F: nat > real,A: real,C: real] :
% 5.02/5.36 ( ( sums_real @ F @ A )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C )
% 5.02/5.36 @ ( times_times_real @ A @ C ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_mult2
% 5.02/5.36 thf(fact_8271_sums__add,axiom,
% 5.02/5.36 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.02/5.36 ( ( sums_real @ F @ A )
% 5.02/5.36 => ( ( sums_real @ G @ B )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( plus_plus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.02/5.36 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_add
% 5.02/5.36 thf(fact_8272_sums__add,axiom,
% 5.02/5.36 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.02/5.36 ( ( sums_nat @ F @ A )
% 5.02/5.36 => ( ( sums_nat @ G @ B )
% 5.02/5.36 => ( sums_nat
% 5.02/5.36 @ ^ [N3: nat] : ( plus_plus_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.02/5.36 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_add
% 5.02/5.36 thf(fact_8273_sums__add,axiom,
% 5.02/5.36 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.02/5.36 ( ( sums_int @ F @ A )
% 5.02/5.36 => ( ( sums_int @ G @ B )
% 5.02/5.36 => ( sums_int
% 5.02/5.36 @ ^ [N3: nat] : ( plus_plus_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.02/5.36 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_add
% 5.02/5.36 thf(fact_8274_sums__divide,axiom,
% 5.02/5.36 ! [F: nat > complex,A: complex,C: complex] :
% 5.02/5.36 ( ( sums_complex @ F @ A )
% 5.02/5.36 => ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( divide1717551699836669952omplex @ ( F @ N3 ) @ C )
% 5.02/5.36 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_divide
% 5.02/5.36 thf(fact_8275_sums__divide,axiom,
% 5.02/5.36 ! [F: nat > real,A: real,C: real] :
% 5.02/5.36 ( ( sums_real @ F @ A )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( divide_divide_real @ ( F @ N3 ) @ C )
% 5.02/5.36 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_divide
% 5.02/5.36 thf(fact_8276_sums__mult__iff,axiom,
% 5.02/5.36 ! [C: complex,F: nat > complex,D: complex] :
% 5.02/5.36 ( ( C != zero_zero_complex )
% 5.02/5.36 => ( ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) )
% 5.02/5.36 @ ( times_times_complex @ C @ D ) )
% 5.02/5.36 = ( sums_complex @ F @ D ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_mult_iff
% 5.02/5.36 thf(fact_8277_sums__mult__iff,axiom,
% 5.02/5.36 ! [C: real,F: nat > real,D: real] :
% 5.02/5.36 ( ( C != zero_zero_real )
% 5.02/5.36 => ( ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.02/5.36 @ ( times_times_real @ C @ D ) )
% 5.02/5.36 = ( sums_real @ F @ D ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_mult_iff
% 5.02/5.36 thf(fact_8278_sums__mult2__iff,axiom,
% 5.02/5.36 ! [C: complex,F: nat > complex,D: complex] :
% 5.02/5.36 ( ( C != zero_zero_complex )
% 5.02/5.36 => ( ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( F @ N3 ) @ C )
% 5.02/5.36 @ ( times_times_complex @ D @ C ) )
% 5.02/5.36 = ( sums_complex @ F @ D ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_mult2_iff
% 5.02/5.36 thf(fact_8279_sums__mult2__iff,axiom,
% 5.02/5.36 ! [C: real,F: nat > real,D: real] :
% 5.02/5.36 ( ( C != zero_zero_real )
% 5.02/5.36 => ( ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ C )
% 5.02/5.36 @ ( times_times_real @ D @ C ) )
% 5.02/5.36 = ( sums_real @ F @ D ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_mult2_iff
% 5.02/5.36 thf(fact_8280_sums__mult__D,axiom,
% 5.02/5.36 ! [C: complex,F: nat > complex,A: complex] :
% 5.02/5.36 ( ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ C @ ( F @ N3 ) )
% 5.02/5.36 @ A )
% 5.02/5.36 => ( ( C != zero_zero_complex )
% 5.02/5.36 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_mult_D
% 5.02/5.36 thf(fact_8281_sums__mult__D,axiom,
% 5.02/5.36 ! [C: real,F: nat > real,A: real] :
% 5.02/5.36 ( ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ C @ ( F @ N3 ) )
% 5.02/5.36 @ A )
% 5.02/5.36 => ( ( C != zero_zero_real )
% 5.02/5.36 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_mult_D
% 5.02/5.36 thf(fact_8282_sums__Suc__imp,axiom,
% 5.02/5.36 ! [F: nat > complex,S2: complex] :
% 5.02/5.36 ( ( ( F @ zero_zero_nat )
% 5.02/5.36 = zero_zero_complex )
% 5.02/5.36 => ( ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.02/5.36 @ S2 )
% 5.02/5.36 => ( sums_complex @ F @ S2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_Suc_imp
% 5.02/5.36 thf(fact_8283_sums__Suc__imp,axiom,
% 5.02/5.36 ! [F: nat > real,S2: real] :
% 5.02/5.36 ( ( ( F @ zero_zero_nat )
% 5.02/5.36 = zero_zero_real )
% 5.02/5.36 => ( ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.02/5.36 @ S2 )
% 5.02/5.36 => ( sums_real @ F @ S2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_Suc_imp
% 5.02/5.36 thf(fact_8284_sums__Suc__iff,axiom,
% 5.02/5.36 ! [F: nat > real,S2: real] :
% 5.02/5.36 ( ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.02/5.36 @ S2 )
% 5.02/5.36 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_Suc_iff
% 5.02/5.36 thf(fact_8285_sums__Suc,axiom,
% 5.02/5.36 ! [F: nat > real,L: real] :
% 5.02/5.36 ( ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.02/5.36 @ L )
% 5.02/5.36 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_Suc
% 5.02/5.36 thf(fact_8286_sums__Suc,axiom,
% 5.02/5.36 ! [F: nat > nat,L: nat] :
% 5.02/5.36 ( ( sums_nat
% 5.02/5.36 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.02/5.36 @ L )
% 5.02/5.36 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_Suc
% 5.02/5.36 thf(fact_8287_sums__Suc,axiom,
% 5.02/5.36 ! [F: nat > int,L: int] :
% 5.02/5.36 ( ( sums_int
% 5.02/5.36 @ ^ [N3: nat] : ( F @ ( suc @ N3 ) )
% 5.02/5.36 @ L )
% 5.02/5.36 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_Suc
% 5.02/5.36 thf(fact_8288_sums__zero__iff__shift,axiom,
% 5.02/5.36 ! [N2: nat,F: nat > complex,S2: complex] :
% 5.02/5.36 ( ! [I2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ I2 @ N2 )
% 5.02/5.36 => ( ( F @ I2 )
% 5.02/5.36 = zero_zero_complex ) )
% 5.02/5.36 => ( ( sums_complex
% 5.02/5.36 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.02/5.36 @ S2 )
% 5.02/5.36 = ( sums_complex @ F @ S2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_zero_iff_shift
% 5.02/5.36 thf(fact_8289_sums__zero__iff__shift,axiom,
% 5.02/5.36 ! [N2: nat,F: nat > real,S2: real] :
% 5.02/5.36 ( ! [I2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ I2 @ N2 )
% 5.02/5.36 => ( ( F @ I2 )
% 5.02/5.36 = zero_zero_real ) )
% 5.02/5.36 => ( ( sums_real
% 5.02/5.36 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.02/5.36 @ S2 )
% 5.02/5.36 = ( sums_real @ F @ S2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_zero_iff_shift
% 5.02/5.36 thf(fact_8290_arccos__le__arccos,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_le_arccos
% 5.02/5.36 thf(fact_8291_arccos__eq__iff,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.36 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.02/5.36 => ( ( ( arccos @ X2 )
% 5.02/5.36 = ( arccos @ Y ) )
% 5.02/5.36 = ( X2 = Y ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_eq_iff
% 5.02/5.36 thf(fact_8292_arccos__le__mono,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( arccos @ X2 ) @ ( arccos @ Y ) )
% 5.02/5.36 = ( ord_less_eq_real @ Y @ X2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_le_mono
% 5.02/5.36 thf(fact_8293_arcsin__le__arcsin,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_le_arcsin
% 5.02/5.36 thf(fact_8294_arcsin__minus,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.36 => ( ( arcsin @ ( uminus_uminus_real @ X2 ) )
% 5.02/5.36 = ( uminus_uminus_real @ ( arcsin @ X2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_minus
% 5.02/5.36 thf(fact_8295_arcsin__eq__iff,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.02/5.36 => ( ( ( arcsin @ X2 )
% 5.02/5.36 = ( arcsin @ Y ) )
% 5.02/5.36 = ( X2 = Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_eq_iff
% 5.02/5.36 thf(fact_8296_arcsin__le__mono,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ ( arcsin @ Y ) )
% 5.02/5.36 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_le_mono
% 5.02/5.36 thf(fact_8297_powser__sums__if,axiom,
% 5.02/5.36 ! [M: nat,Z: complex] :
% 5.02/5.36 ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( if_complex @ ( N3 = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N3 ) )
% 5.02/5.36 @ ( power_power_complex @ Z @ M ) ) ).
% 5.02/5.36
% 5.02/5.36 % powser_sums_if
% 5.02/5.36 thf(fact_8298_powser__sums__if,axiom,
% 5.02/5.36 ! [M: nat,Z: real] :
% 5.02/5.36 ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( if_real @ ( N3 = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N3 ) )
% 5.02/5.36 @ ( power_power_real @ Z @ M ) ) ).
% 5.02/5.36
% 5.02/5.36 % powser_sums_if
% 5.02/5.36 thf(fact_8299_powser__sums__if,axiom,
% 5.02/5.36 ! [M: nat,Z: int] :
% 5.02/5.36 ( sums_int
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_int @ ( if_int @ ( N3 = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N3 ) )
% 5.02/5.36 @ ( power_power_int @ Z @ M ) ) ).
% 5.02/5.36
% 5.02/5.36 % powser_sums_if
% 5.02/5.36 thf(fact_8300_powser__sums__zero,axiom,
% 5.02/5.36 ! [A: nat > complex] :
% 5.02/5.36 ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( A @ N3 ) @ ( power_power_complex @ zero_zero_complex @ N3 ) )
% 5.02/5.36 @ ( A @ zero_zero_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % powser_sums_zero
% 5.02/5.36 thf(fact_8301_powser__sums__zero,axiom,
% 5.02/5.36 ! [A: nat > real] :
% 5.02/5.36 ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( A @ N3 ) @ ( power_power_real @ zero_zero_real @ N3 ) )
% 5.02/5.36 @ ( A @ zero_zero_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % powser_sums_zero
% 5.02/5.36 thf(fact_8302_sums__iff__shift,axiom,
% 5.02/5.36 ! [F: nat > real,N2: nat,S2: real] :
% 5.02/5.36 ( ( sums_real
% 5.02/5.36 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.02/5.36 @ S2 )
% 5.02/5.36 = ( sums_real @ F @ ( plus_plus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_iff_shift
% 5.02/5.36 thf(fact_8303_sums__split__initial__segment,axiom,
% 5.02/5.36 ! [F: nat > real,S2: real,N2: nat] :
% 5.02/5.36 ( ( sums_real @ F @ S2 )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.02/5.36 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_split_initial_segment
% 5.02/5.36 thf(fact_8304_sums__iff__shift_H,axiom,
% 5.02/5.36 ! [F: nat > real,N2: nat,S2: real] :
% 5.02/5.36 ( ( sums_real
% 5.02/5.36 @ ^ [I5: nat] : ( F @ ( plus_plus_nat @ I5 @ N2 ) )
% 5.02/5.36 @ ( minus_minus_real @ S2 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.02/5.36 = ( sums_real @ F @ S2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_iff_shift'
% 5.02/5.36 thf(fact_8305_arccos__lbound,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_lbound
% 5.02/5.36 thf(fact_8306_arccos__less__arccos,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_real @ X2 @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_less_arccos
% 5.02/5.36 thf(fact_8307_arccos__less__mono,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_real @ ( arccos @ X2 ) @ ( arccos @ Y ) )
% 5.02/5.36 = ( ord_less_real @ Y @ X2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_less_mono
% 5.02/5.36 thf(fact_8308_arccos__ubound,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_ubound
% 5.02/5.36 thf(fact_8309_arcsin__less__arcsin,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_real @ X2 @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_less_arcsin
% 5.02/5.36 thf(fact_8310_arcsin__less__mono,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.02/5.36 => ( ( ord_less_real @ ( arcsin @ X2 ) @ ( arcsin @ Y ) )
% 5.02/5.36 = ( ord_less_real @ X2 @ Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_less_mono
% 5.02/5.36 thf(fact_8311_cos__arccos__abs,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.02/5.36 => ( ( cos_real @ ( arccos @ Y ) )
% 5.02/5.36 = Y ) ) ).
% 5.02/5.36
% 5.02/5.36 % cos_arccos_abs
% 5.02/5.36 thf(fact_8312_arccos__lt__bounded,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.02/5.36 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_lt_bounded
% 5.02/5.36 thf(fact_8313_arccos__bounded,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_bounded
% 5.02/5.36 thf(fact_8314_sin__arccos__nonzero,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.36 => ( ( sin_real @ ( arccos @ X2 ) )
% 5.02/5.36 != zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sin_arccos_nonzero
% 5.02/5.36 thf(fact_8315_arccos__minus,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.36 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.02/5.36 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_minus
% 5.02/5.36 thf(fact_8316_cos__arcsin__nonzero,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.36 => ( ( cos_real @ ( arcsin @ X2 ) )
% 5.02/5.36 != zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % cos_arcsin_nonzero
% 5.02/5.36 thf(fact_8317_geometric__sums,axiom,
% 5.02/5.36 ! [C: real] :
% 5.02/5.36 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.02/5.36 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % geometric_sums
% 5.02/5.36 thf(fact_8318_geometric__sums,axiom,
% 5.02/5.36 ! [C: complex] :
% 5.02/5.36 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.02/5.36 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % geometric_sums
% 5.02/5.36 thf(fact_8319_power__half__series,axiom,
% 5.02/5.36 ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N3 ) )
% 5.02/5.36 @ one_one_real ) ).
% 5.02/5.36
% 5.02/5.36 % power_half_series
% 5.02/5.36 thf(fact_8320_arccos,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.02/5.36 & ( ( cos_real @ ( arccos @ Y ) )
% 5.02/5.36 = Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos
% 5.02/5.36 thf(fact_8321_arccos__minus__abs,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.36 => ( ( arccos @ ( uminus_uminus_real @ X2 ) )
% 5.02/5.36 = ( minus_minus_real @ pi @ ( arccos @ X2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_minus_abs
% 5.02/5.36 thf(fact_8322_sums__if_H,axiom,
% 5.02/5.36 ! [G: nat > real,X2: real] :
% 5.02/5.36 ( ( sums_real @ G @ X2 )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.36 @ X2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_if'
% 5.02/5.36 thf(fact_8323_sums__if,axiom,
% 5.02/5.36 ! [G: nat > real,X2: real,F: nat > real,Y: real] :
% 5.02/5.36 ( ( sums_real @ G @ X2 )
% 5.02/5.36 => ( ( sums_real @ F @ Y )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ ( F @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N3 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.36 @ ( plus_plus_real @ X2 @ Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sums_if
% 5.02/5.36 thf(fact_8324_arccos__le__pi2,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_le_pi2
% 5.02/5.36 thf(fact_8325_arcsin__lt__bounded,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.02/5.36 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_lt_bounded
% 5.02/5.36 thf(fact_8326_arcsin__lbound,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_lbound
% 5.02/5.36 thf(fact_8327_arcsin__ubound,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_ubound
% 5.02/5.36 thf(fact_8328_arcsin__bounded,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_bounded
% 5.02/5.36 thf(fact_8329_arcsin__sin,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.36 => ( ( arcsin @ ( sin_real @ X2 ) )
% 5.02/5.36 = X2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_sin
% 5.02/5.36 thf(fact_8330_cos__paired,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) @ ( power_power_real @ X2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.02/5.36 @ ( cos_real @ X2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % cos_paired
% 5.02/5.36 thf(fact_8331_le__arcsin__iff,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X2 ) )
% 5.02/5.36 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % le_arcsin_iff
% 5.02/5.36 thf(fact_8332_arcsin__le__iff,axiom,
% 5.02/5.36 ! [X2: real,Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.36 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( arcsin @ X2 ) @ Y )
% 5.02/5.36 = ( ord_less_eq_real @ X2 @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_le_iff
% 5.02/5.36 thf(fact_8333_arcsin__pi,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.02/5.36 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.02/5.36 = Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin_pi
% 5.02/5.36 thf(fact_8334_arcsin,axiom,
% 5.02/5.36 ! [Y: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.02/5.36 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.36 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.02/5.36 = Y ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arcsin
% 5.02/5.36 thf(fact_8335_arccos__cos__eq__abs__2pi,axiom,
% 5.02/5.36 ! [Theta: real] :
% 5.02/5.36 ~ ! [K2: int] :
% 5.02/5.36 ( ( arccos @ ( cos_real @ Theta ) )
% 5.02/5.36 != ( 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 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % arccos_cos_eq_abs_2pi
% 5.02/5.36 thf(fact_8336_diffs__equiv,axiom,
% 5.02/5.36 ! [C: nat > complex,X2: complex] :
% 5.02/5.36 ( ( summable_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) )
% 5.02/5.36 => ( sums_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N3 ) @ ( C @ N3 ) ) @ ( power_power_complex @ X2 @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) ) )
% 5.02/5.36 @ ( suminf_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % diffs_equiv
% 5.02/5.36 thf(fact_8337_diffs__equiv,axiom,
% 5.02/5.36 ! [C: nat > real,X2: real] :
% 5.02/5.36 ( ( summable_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) )
% 5.02/5.36 => ( sums_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( C @ N3 ) ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) ) ) )
% 5.02/5.36 @ ( suminf_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % diffs_equiv
% 5.02/5.36 thf(fact_8338_monoI1,axiom,
% 5.02/5.36 ! [X8: nat > real] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_real @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.02/5.36 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI1
% 5.02/5.36 thf(fact_8339_monoI1,axiom,
% 5.02/5.36 ! [X8: nat > set_nat] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_set_nat @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.02/5.36 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI1
% 5.02/5.36 thf(fact_8340_monoI1,axiom,
% 5.02/5.36 ! [X8: nat > rat] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_rat @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.02/5.36 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI1
% 5.02/5.36 thf(fact_8341_monoI1,axiom,
% 5.02/5.36 ! [X8: nat > num] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_num @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.02/5.36 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI1
% 5.02/5.36 thf(fact_8342_monoI1,axiom,
% 5.02/5.36 ! [X8: nat > nat] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_nat @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.02/5.36 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI1
% 5.02/5.36 thf(fact_8343_monoI1,axiom,
% 5.02/5.36 ! [X8: nat > int] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_int @ ( X8 @ M3 ) @ ( X8 @ N ) ) )
% 5.02/5.36 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI1
% 5.02/5.36 thf(fact_8344_monoI2,axiom,
% 5.02/5.36 ! [X8: nat > real] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_real @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.02/5.36 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI2
% 5.02/5.36 thf(fact_8345_monoI2,axiom,
% 5.02/5.36 ! [X8: nat > set_nat] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_set_nat @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.02/5.36 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI2
% 5.02/5.36 thf(fact_8346_monoI2,axiom,
% 5.02/5.36 ! [X8: nat > rat] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_rat @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.02/5.36 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI2
% 5.02/5.36 thf(fact_8347_monoI2,axiom,
% 5.02/5.36 ! [X8: nat > num] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_num @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.02/5.36 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI2
% 5.02/5.36 thf(fact_8348_monoI2,axiom,
% 5.02/5.36 ! [X8: nat > nat] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_nat @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.02/5.36 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI2
% 5.02/5.36 thf(fact_8349_monoI2,axiom,
% 5.02/5.36 ! [X8: nat > int] :
% 5.02/5.36 ( ! [M3: nat,N: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M3 @ N )
% 5.02/5.36 => ( ord_less_eq_int @ ( X8 @ N ) @ ( X8 @ M3 ) ) )
% 5.02/5.36 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoI2
% 5.02/5.36 thf(fact_8350_monoseq__def,axiom,
% 5.02/5.36 ( topolo6980174941875973593q_real
% 5.02/5.36 = ( ^ [X4: nat > real] :
% 5.02/5.36 ( ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_real @ ( X4 @ M6 ) @ ( X4 @ N3 ) ) )
% 5.02/5.36 | ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_real @ ( X4 @ N3 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_def
% 5.02/5.36 thf(fact_8351_monoseq__def,axiom,
% 5.02/5.36 ( topolo7278393974255667507et_nat
% 5.02/5.36 = ( ^ [X4: nat > set_nat] :
% 5.02/5.36 ( ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_set_nat @ ( X4 @ M6 ) @ ( X4 @ N3 ) ) )
% 5.02/5.36 | ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_set_nat @ ( X4 @ N3 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_def
% 5.02/5.36 thf(fact_8352_monoseq__def,axiom,
% 5.02/5.36 ( topolo4267028734544971653eq_rat
% 5.02/5.36 = ( ^ [X4: nat > rat] :
% 5.02/5.36 ( ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_rat @ ( X4 @ M6 ) @ ( X4 @ N3 ) ) )
% 5.02/5.36 | ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_rat @ ( X4 @ N3 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_def
% 5.02/5.36 thf(fact_8353_monoseq__def,axiom,
% 5.02/5.36 ( topolo1459490580787246023eq_num
% 5.02/5.36 = ( ^ [X4: nat > num] :
% 5.02/5.36 ( ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_num @ ( X4 @ M6 ) @ ( X4 @ N3 ) ) )
% 5.02/5.36 | ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_num @ ( X4 @ N3 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_def
% 5.02/5.36 thf(fact_8354_monoseq__def,axiom,
% 5.02/5.36 ( topolo4902158794631467389eq_nat
% 5.02/5.36 = ( ^ [X4: nat > nat] :
% 5.02/5.36 ( ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_nat @ ( X4 @ M6 ) @ ( X4 @ N3 ) ) )
% 5.02/5.36 | ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_nat @ ( X4 @ N3 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_def
% 5.02/5.36 thf(fact_8355_monoseq__def,axiom,
% 5.02/5.36 ( topolo4899668324122417113eq_int
% 5.02/5.36 = ( ^ [X4: nat > int] :
% 5.02/5.36 ( ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_int @ ( X4 @ M6 ) @ ( X4 @ N3 ) ) )
% 5.02/5.36 | ! [M6: nat,N3: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.36 => ( ord_less_eq_int @ ( X4 @ N3 ) @ ( X4 @ M6 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_def
% 5.02/5.36 thf(fact_8356_pochhammer__double,axiom,
% 5.02/5.36 ! [Z: complex,N2: nat] :
% 5.02/5.36 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.36 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_double
% 5.02/5.36 thf(fact_8357_pochhammer__double,axiom,
% 5.02/5.36 ! [Z: real,N2: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.36 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_double
% 5.02/5.36 thf(fact_8358_pochhammer__double,axiom,
% 5.02/5.36 ! [Z: rat,N2: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.36 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_double
% 5.02/5.36 thf(fact_8359_pochhammer__0,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_complex ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0
% 5.02/5.36 thf(fact_8360_pochhammer__0,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_real ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0
% 5.02/5.36 thf(fact_8361_pochhammer__0,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_rat ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0
% 5.02/5.36 thf(fact_8362_pochhammer__0,axiom,
% 5.02/5.36 ! [A: nat] :
% 5.02/5.36 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_nat ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0
% 5.02/5.36 thf(fact_8363_pochhammer__0,axiom,
% 5.02/5.36 ! [A: int] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_int ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0
% 5.02/5.36 thf(fact_8364_pochhammer__pos,axiom,
% 5.02/5.36 ! [X2: real,N2: nat] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.36 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_pos
% 5.02/5.36 thf(fact_8365_pochhammer__pos,axiom,
% 5.02/5.36 ! [X2: rat,N2: nat] :
% 5.02/5.36 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.02/5.36 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_pos
% 5.02/5.36 thf(fact_8366_pochhammer__pos,axiom,
% 5.02/5.36 ! [X2: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.02/5.36 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_pos
% 5.02/5.36 thf(fact_8367_pochhammer__pos,axiom,
% 5.02/5.36 ! [X2: int,N2: nat] :
% 5.02/5.36 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.02/5.36 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_pos
% 5.02/5.36 thf(fact_8368_pochhammer__neq__0__mono,axiom,
% 5.02/5.36 ! [A: complex,M: nat,N2: nat] :
% 5.02/5.36 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.02/5.36 != zero_zero_complex )
% 5.02/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.36 => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.02/5.36 != zero_zero_complex ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_neq_0_mono
% 5.02/5.36 thf(fact_8369_pochhammer__neq__0__mono,axiom,
% 5.02/5.36 ! [A: real,M: nat,N2: nat] :
% 5.02/5.36 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.02/5.36 != zero_zero_real )
% 5.02/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.36 => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.02/5.36 != zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_neq_0_mono
% 5.02/5.36 thf(fact_8370_pochhammer__neq__0__mono,axiom,
% 5.02/5.36 ! [A: rat,M: nat,N2: nat] :
% 5.02/5.36 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.02/5.36 != zero_zero_rat )
% 5.02/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.36 => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.02/5.36 != zero_zero_rat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_neq_0_mono
% 5.02/5.36 thf(fact_8371_pochhammer__eq__0__mono,axiom,
% 5.02/5.36 ! [A: complex,N2: nat,M: nat] :
% 5.02/5.36 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.02/5.36 = zero_zero_complex )
% 5.02/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.36 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.02/5.36 = zero_zero_complex ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_eq_0_mono
% 5.02/5.36 thf(fact_8372_pochhammer__eq__0__mono,axiom,
% 5.02/5.36 ! [A: real,N2: nat,M: nat] :
% 5.02/5.36 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.02/5.36 = zero_zero_real )
% 5.02/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.36 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.02/5.36 = zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_eq_0_mono
% 5.02/5.36 thf(fact_8373_pochhammer__eq__0__mono,axiom,
% 5.02/5.36 ! [A: rat,N2: nat,M: nat] :
% 5.02/5.36 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.02/5.36 = zero_zero_rat )
% 5.02/5.36 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.36 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.02/5.36 = zero_zero_rat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_eq_0_mono
% 5.02/5.36 thf(fact_8374_pochhammer__fact,axiom,
% 5.02/5.36 ( semiri5044797733671781792omplex
% 5.02/5.36 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_fact
% 5.02/5.36 thf(fact_8375_pochhammer__fact,axiom,
% 5.02/5.36 ( semiri773545260158071498ct_rat
% 5.02/5.36 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_fact
% 5.02/5.36 thf(fact_8376_pochhammer__fact,axiom,
% 5.02/5.36 ( semiri1406184849735516958ct_int
% 5.02/5.36 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_fact
% 5.02/5.36 thf(fact_8377_pochhammer__fact,axiom,
% 5.02/5.36 ( semiri2265585572941072030t_real
% 5.02/5.36 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_fact
% 5.02/5.36 thf(fact_8378_pochhammer__fact,axiom,
% 5.02/5.36 ( semiri1408675320244567234ct_nat
% 5.02/5.36 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_fact
% 5.02/5.36 thf(fact_8379_pochhammer__nonneg,axiom,
% 5.02/5.36 ! [X2: real,N2: nat] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.36 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_nonneg
% 5.02/5.36 thf(fact_8380_pochhammer__nonneg,axiom,
% 5.02/5.36 ! [X2: rat,N2: nat] :
% 5.02/5.36 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.02/5.36 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_nonneg
% 5.02/5.36 thf(fact_8381_pochhammer__nonneg,axiom,
% 5.02/5.36 ! [X2: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ X2 )
% 5.02/5.36 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_nonneg
% 5.02/5.36 thf(fact_8382_pochhammer__nonneg,axiom,
% 5.02/5.36 ! [X2: int,N2: nat] :
% 5.02/5.36 ( ( ord_less_int @ zero_zero_int @ X2 )
% 5.02/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X2 @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_nonneg
% 5.02/5.36 thf(fact_8383_pochhammer__0__left,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ( N2 = zero_zero_nat )
% 5.02/5.36 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.02/5.36 = one_one_complex ) )
% 5.02/5.36 & ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.02/5.36 = zero_zero_complex ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0_left
% 5.02/5.36 thf(fact_8384_pochhammer__0__left,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ( N2 = zero_zero_nat )
% 5.02/5.36 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.02/5.36 = one_one_real ) )
% 5.02/5.36 & ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.02/5.36 = zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0_left
% 5.02/5.36 thf(fact_8385_pochhammer__0__left,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ( N2 = zero_zero_nat )
% 5.02/5.36 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 5.02/5.36 = one_one_rat ) )
% 5.02/5.36 & ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 5.02/5.36 = zero_zero_rat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0_left
% 5.02/5.36 thf(fact_8386_pochhammer__0__left,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ( N2 = zero_zero_nat )
% 5.02/5.36 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 = one_one_nat ) )
% 5.02/5.36 & ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 = zero_zero_nat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0_left
% 5.02/5.36 thf(fact_8387_pochhammer__0__left,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ( N2 = zero_zero_nat )
% 5.02/5.36 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.02/5.36 = one_one_int ) )
% 5.02/5.36 & ( ( N2 != zero_zero_nat )
% 5.02/5.36 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.02/5.36 = zero_zero_int ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_0_left
% 5.02/5.36 thf(fact_8388_pochhammer__rec,axiom,
% 5.02/5.36 ! [A: complex,N2: nat] :
% 5.02/5.36 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec
% 5.02/5.36 thf(fact_8389_pochhammer__rec,axiom,
% 5.02/5.36 ! [A: real,N2: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec
% 5.02/5.36 thf(fact_8390_pochhammer__rec,axiom,
% 5.02/5.36 ! [A: rat,N2: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec
% 5.02/5.36 thf(fact_8391_pochhammer__rec,axiom,
% 5.02/5.36 ! [A: nat,N2: nat] :
% 5.02/5.36 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec
% 5.02/5.36 thf(fact_8392_pochhammer__rec,axiom,
% 5.02/5.36 ! [A: int,N2: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec
% 5.02/5.36 thf(fact_8393_diffs__def,axiom,
% 5.02/5.36 ( diffs_int
% 5.02/5.36 = ( ^ [C2: nat > int,N3: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) @ ( C2 @ ( suc @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % diffs_def
% 5.02/5.36 thf(fact_8394_diffs__def,axiom,
% 5.02/5.36 ( diffs_real
% 5.02/5.36 = ( ^ [C2: nat > real,N3: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) @ ( C2 @ ( suc @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % diffs_def
% 5.02/5.36 thf(fact_8395_diffs__def,axiom,
% 5.02/5.36 ( diffs_rat
% 5.02/5.36 = ( ^ [C2: nat > rat,N3: nat] : ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) @ ( C2 @ ( suc @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % diffs_def
% 5.02/5.36 thf(fact_8396_pochhammer__Suc,axiom,
% 5.02/5.36 ! [A: int,N2: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc
% 5.02/5.36 thf(fact_8397_pochhammer__Suc,axiom,
% 5.02/5.36 ! [A: real,N2: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc
% 5.02/5.36 thf(fact_8398_pochhammer__Suc,axiom,
% 5.02/5.36 ! [A: nat,N2: nat] :
% 5.02/5.36 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc
% 5.02/5.36 thf(fact_8399_pochhammer__Suc,axiom,
% 5.02/5.36 ! [A: rat,N2: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc
% 5.02/5.36 thf(fact_8400_pochhammer__rec_H,axiom,
% 5.02/5.36 ! [Z: int,N2: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec'
% 5.02/5.36 thf(fact_8401_pochhammer__rec_H,axiom,
% 5.02/5.36 ! [Z: real,N2: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec'
% 5.02/5.36 thf(fact_8402_pochhammer__rec_H,axiom,
% 5.02/5.36 ! [Z: nat,N2: nat] :
% 5.02/5.36 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec'
% 5.02/5.36 thf(fact_8403_pochhammer__rec_H,axiom,
% 5.02/5.36 ! [Z: rat,N2: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 5.02/5.36 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_rec'
% 5.02/5.36 thf(fact_8404_pochhammer__eq__0__iff,axiom,
% 5.02/5.36 ! [A: complex,N2: nat] :
% 5.02/5.36 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.02/5.36 = zero_zero_complex )
% 5.02/5.36 = ( ? [K3: nat] :
% 5.02/5.36 ( ( ord_less_nat @ K3 @ N2 )
% 5.02/5.36 & ( A
% 5.02/5.36 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_eq_0_iff
% 5.02/5.36 thf(fact_8405_pochhammer__eq__0__iff,axiom,
% 5.02/5.36 ! [A: real,N2: nat] :
% 5.02/5.36 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.02/5.36 = zero_zero_real )
% 5.02/5.36 = ( ? [K3: nat] :
% 5.02/5.36 ( ( ord_less_nat @ K3 @ N2 )
% 5.02/5.36 & ( A
% 5.02/5.36 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_eq_0_iff
% 5.02/5.36 thf(fact_8406_pochhammer__eq__0__iff,axiom,
% 5.02/5.36 ! [A: rat,N2: nat] :
% 5.02/5.36 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.02/5.36 = zero_zero_rat )
% 5.02/5.36 = ( ? [K3: nat] :
% 5.02/5.36 ( ( ord_less_nat @ K3 @ N2 )
% 5.02/5.36 & ( A
% 5.02/5.36 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_eq_0_iff
% 5.02/5.36 thf(fact_8407_pochhammer__of__nat__eq__0__iff,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.02/5.36 = zero_zero_complex )
% 5.02/5.36 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_iff
% 5.02/5.36 thf(fact_8408_pochhammer__of__nat__eq__0__iff,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.02/5.36 = zero_z3403309356797280102nteger )
% 5.02/5.36 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_iff
% 5.02/5.36 thf(fact_8409_pochhammer__of__nat__eq__0__iff,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.02/5.36 = zero_zero_int )
% 5.02/5.36 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_iff
% 5.02/5.36 thf(fact_8410_pochhammer__of__nat__eq__0__iff,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.02/5.36 = zero_zero_real )
% 5.02/5.36 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_iff
% 5.02/5.36 thf(fact_8411_pochhammer__of__nat__eq__0__iff,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.02/5.36 = zero_zero_rat )
% 5.02/5.36 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_iff
% 5.02/5.36 thf(fact_8412_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ N2 @ K )
% 5.02/5.36 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.02/5.36 = zero_zero_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma
% 5.02/5.36 thf(fact_8413_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ N2 @ K )
% 5.02/5.36 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.02/5.36 = zero_z3403309356797280102nteger ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma
% 5.02/5.36 thf(fact_8414_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ N2 @ K )
% 5.02/5.36 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.02/5.36 = zero_zero_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma
% 5.02/5.36 thf(fact_8415_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ N2 @ K )
% 5.02/5.36 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.02/5.36 = zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma
% 5.02/5.36 thf(fact_8416_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ N2 @ K )
% 5.02/5.36 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.02/5.36 = zero_zero_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma
% 5.02/5.36 thf(fact_8417_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.02/5.36 != zero_zero_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma'
% 5.02/5.36 thf(fact_8418_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.02/5.36 != zero_z3403309356797280102nteger ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma'
% 5.02/5.36 thf(fact_8419_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.02/5.36 != zero_zero_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma'
% 5.02/5.36 thf(fact_8420_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.02/5.36 != zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma'
% 5.02/5.36 thf(fact_8421_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.02/5.36 != zero_zero_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_of_nat_eq_0_lemma'
% 5.02/5.36 thf(fact_8422_pochhammer__product_H,axiom,
% 5.02/5.36 ! [Z: int,N2: nat,M: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.02/5.36 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_product'
% 5.02/5.36 thf(fact_8423_pochhammer__product_H,axiom,
% 5.02/5.36 ! [Z: real,N2: nat,M: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.02/5.36 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_product'
% 5.02/5.36 thf(fact_8424_pochhammer__product_H,axiom,
% 5.02/5.36 ! [Z: nat,N2: nat,M: nat] :
% 5.02/5.36 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.02/5.36 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_product'
% 5.02/5.36 thf(fact_8425_pochhammer__product_H,axiom,
% 5.02/5.36 ! [Z: rat,N2: nat,M: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.02/5.36 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_product'
% 5.02/5.36 thf(fact_8426_termdiff__converges__all,axiom,
% 5.02/5.36 ! [C: nat > complex,X2: complex] :
% 5.02/5.36 ( ! [X5: complex] :
% 5.02/5.36 ( summable_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( C @ N3 ) @ ( power_power_complex @ X5 @ N3 ) ) )
% 5.02/5.36 => ( summable_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % termdiff_converges_all
% 5.02/5.36 thf(fact_8427_termdiff__converges__all,axiom,
% 5.02/5.36 ! [C: nat > real,X2: real] :
% 5.02/5.36 ( ! [X5: real] :
% 5.02/5.36 ( summable_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( C @ N3 ) @ ( power_power_real @ X5 @ N3 ) ) )
% 5.02/5.36 => ( summable_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % termdiff_converges_all
% 5.02/5.36 thf(fact_8428_pochhammer__product,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,Z: int] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 5.02/5.36 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_product
% 5.02/5.36 thf(fact_8429_pochhammer__product,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,Z: real] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( comm_s7457072308508201937r_real @ Z @ N2 )
% 5.02/5.36 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_product
% 5.02/5.36 thf(fact_8430_pochhammer__product,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,Z: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 5.02/5.36 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_product
% 5.02/5.36 thf(fact_8431_pochhammer__product,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,Z: rat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 5.02/5.36 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_product
% 5.02/5.36 thf(fact_8432_pochhammer__absorb__comp,axiom,
% 5.02/5.36 ! [R2: complex,K: nat] :
% 5.02/5.36 ( ( times_times_complex @ ( minus_minus_complex @ R2 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R2 ) @ K ) )
% 5.02/5.36 = ( times_times_complex @ R2 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R2 ) @ one_one_complex ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_absorb_comp
% 5.02/5.36 thf(fact_8433_pochhammer__absorb__comp,axiom,
% 5.02/5.36 ! [R2: code_integer,K: nat] :
% 5.02/5.36 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R2 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R2 ) @ K ) )
% 5.02/5.36 = ( times_3573771949741848930nteger @ R2 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R2 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_absorb_comp
% 5.02/5.36 thf(fact_8434_pochhammer__absorb__comp,axiom,
% 5.02/5.36 ! [R2: int,K: nat] :
% 5.02/5.36 ( ( times_times_int @ ( minus_minus_int @ R2 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R2 ) @ K ) )
% 5.02/5.36 = ( times_times_int @ R2 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R2 ) @ one_one_int ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_absorb_comp
% 5.02/5.36 thf(fact_8435_pochhammer__absorb__comp,axiom,
% 5.02/5.36 ! [R2: real,K: nat] :
% 5.02/5.36 ( ( times_times_real @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R2 ) @ K ) )
% 5.02/5.36 = ( times_times_real @ R2 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R2 ) @ one_one_real ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_absorb_comp
% 5.02/5.36 thf(fact_8436_pochhammer__absorb__comp,axiom,
% 5.02/5.36 ! [R2: rat,K: nat] :
% 5.02/5.36 ( ( times_times_rat @ ( minus_minus_rat @ R2 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R2 ) @ K ) )
% 5.02/5.36 = ( times_times_rat @ R2 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R2 ) @ one_one_rat ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_absorb_comp
% 5.02/5.36 thf(fact_8437_pochhammer__same,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ N2 )
% 5.02/5.36 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_same
% 5.02/5.36 thf(fact_8438_pochhammer__same,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 5.02/5.36 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_same
% 5.02/5.36 thf(fact_8439_pochhammer__same,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 5.02/5.36 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_same
% 5.02/5.36 thf(fact_8440_pochhammer__same,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 5.02/5.36 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_same
% 5.02/5.36 thf(fact_8441_pochhammer__same,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ N2 )
% 5.02/5.36 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_same
% 5.02/5.36 thf(fact_8442_pochhammer__minus_H,axiom,
% 5.02/5.36 ! [B: complex,K: nat] :
% 5.02/5.36 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.02/5.36 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus'
% 5.02/5.36 thf(fact_8443_pochhammer__minus_H,axiom,
% 5.02/5.36 ! [B: code_integer,K: nat] :
% 5.02/5.36 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.02/5.36 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus'
% 5.02/5.36 thf(fact_8444_pochhammer__minus_H,axiom,
% 5.02/5.36 ! [B: int,K: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.02/5.36 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus'
% 5.02/5.36 thf(fact_8445_pochhammer__minus_H,axiom,
% 5.02/5.36 ! [B: real,K: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.02/5.36 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus'
% 5.02/5.36 thf(fact_8446_pochhammer__minus_H,axiom,
% 5.02/5.36 ! [B: rat,K: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.02/5.36 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus'
% 5.02/5.36 thf(fact_8447_pochhammer__minus,axiom,
% 5.02/5.36 ! [B: complex,K: nat] :
% 5.02/5.36 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.02/5.36 = ( 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 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus
% 5.02/5.36 thf(fact_8448_pochhammer__minus,axiom,
% 5.02/5.36 ! [B: code_integer,K: nat] :
% 5.02/5.36 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.02/5.36 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus
% 5.02/5.36 thf(fact_8449_pochhammer__minus,axiom,
% 5.02/5.36 ! [B: int,K: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.02/5.36 = ( 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 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus
% 5.02/5.36 thf(fact_8450_pochhammer__minus,axiom,
% 5.02/5.36 ! [B: real,K: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.02/5.36 = ( 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 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus
% 5.02/5.36 thf(fact_8451_pochhammer__minus,axiom,
% 5.02/5.36 ! [B: rat,K: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.02/5.36 = ( 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 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_minus
% 5.02/5.36 thf(fact_8452_termdiff__converges,axiom,
% 5.02/5.36 ! [X2: real,K5: real,C: nat > real] :
% 5.02/5.36 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X2 ) @ K5 )
% 5.02/5.36 => ( ! [X5: real] :
% 5.02/5.36 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X5 ) @ K5 )
% 5.02/5.36 => ( summable_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( C @ N3 ) @ ( power_power_real @ X5 @ N3 ) ) ) )
% 5.02/5.36 => ( summable_real
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_real @ ( diffs_real @ C @ N3 ) @ ( power_power_real @ X2 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % termdiff_converges
% 5.02/5.36 thf(fact_8453_termdiff__converges,axiom,
% 5.02/5.36 ! [X2: complex,K5: real,C: nat > complex] :
% 5.02/5.36 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X2 ) @ K5 )
% 5.02/5.36 => ( ! [X5: complex] :
% 5.02/5.36 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X5 ) @ K5 )
% 5.02/5.36 => ( summable_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( C @ N3 ) @ ( power_power_complex @ X5 @ N3 ) ) ) )
% 5.02/5.36 => ( summable_complex
% 5.02/5.36 @ ^ [N3: nat] : ( times_times_complex @ ( diffs_complex @ C @ N3 ) @ ( power_power_complex @ X2 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % termdiff_converges
% 5.02/5.36 thf(fact_8454_fact__double,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.36 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_double
% 5.02/5.36 thf(fact_8455_fact__double,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.36 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_double
% 5.02/5.36 thf(fact_8456_fact__double,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.36 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_double
% 5.02/5.36 thf(fact_8457_monoseq__Suc,axiom,
% 5.02/5.36 ( topolo6980174941875973593q_real
% 5.02/5.36 = ( ^ [X4: nat > real] :
% 5.02/5.36 ( ! [N3: nat] : ( ord_less_eq_real @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.02/5.36 | ! [N3: nat] : ( ord_less_eq_real @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_Suc
% 5.02/5.36 thf(fact_8458_monoseq__Suc,axiom,
% 5.02/5.36 ( topolo7278393974255667507et_nat
% 5.02/5.36 = ( ^ [X4: nat > set_nat] :
% 5.02/5.36 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.02/5.36 | ! [N3: nat] : ( ord_less_eq_set_nat @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_Suc
% 5.02/5.36 thf(fact_8459_monoseq__Suc,axiom,
% 5.02/5.36 ( topolo4267028734544971653eq_rat
% 5.02/5.36 = ( ^ [X4: nat > rat] :
% 5.02/5.36 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.02/5.36 | ! [N3: nat] : ( ord_less_eq_rat @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_Suc
% 5.02/5.36 thf(fact_8460_monoseq__Suc,axiom,
% 5.02/5.36 ( topolo1459490580787246023eq_num
% 5.02/5.36 = ( ^ [X4: nat > num] :
% 5.02/5.36 ( ! [N3: nat] : ( ord_less_eq_num @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.02/5.36 | ! [N3: nat] : ( ord_less_eq_num @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_Suc
% 5.02/5.36 thf(fact_8461_monoseq__Suc,axiom,
% 5.02/5.36 ( topolo4902158794631467389eq_nat
% 5.02/5.36 = ( ^ [X4: nat > nat] :
% 5.02/5.36 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.02/5.36 | ! [N3: nat] : ( ord_less_eq_nat @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_Suc
% 5.02/5.36 thf(fact_8462_monoseq__Suc,axiom,
% 5.02/5.36 ( topolo4899668324122417113eq_int
% 5.02/5.36 = ( ^ [X4: nat > int] :
% 5.02/5.36 ( ! [N3: nat] : ( ord_less_eq_int @ ( X4 @ N3 ) @ ( X4 @ ( suc @ N3 ) ) )
% 5.02/5.36 | ! [N3: nat] : ( ord_less_eq_int @ ( X4 @ ( suc @ N3 ) ) @ ( X4 @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % monoseq_Suc
% 5.02/5.36 thf(fact_8463_mono__SucI2,axiom,
% 5.02/5.36 ! [X8: nat > real] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.02/5.36 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI2
% 5.02/5.36 thf(fact_8464_mono__SucI2,axiom,
% 5.02/5.36 ! [X8: nat > set_nat] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.02/5.36 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI2
% 5.02/5.36 thf(fact_8465_mono__SucI2,axiom,
% 5.02/5.36 ! [X8: nat > rat] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.02/5.36 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI2
% 5.02/5.36 thf(fact_8466_mono__SucI2,axiom,
% 5.02/5.36 ! [X8: nat > num] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.02/5.36 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI2
% 5.02/5.36 thf(fact_8467_mono__SucI2,axiom,
% 5.02/5.36 ! [X8: nat > nat] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.02/5.36 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI2
% 5.02/5.36 thf(fact_8468_mono__SucI2,axiom,
% 5.02/5.36 ! [X8: nat > int] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N ) ) @ ( X8 @ N ) )
% 5.02/5.36 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI2
% 5.02/5.36 thf(fact_8469_mono__SucI1,axiom,
% 5.02/5.36 ! [X8: nat > real] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_real @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.02/5.36 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI1
% 5.02/5.36 thf(fact_8470_mono__SucI1,axiom,
% 5.02/5.36 ! [X8: nat > set_nat] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_set_nat @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.02/5.36 => ( topolo7278393974255667507et_nat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI1
% 5.02/5.36 thf(fact_8471_mono__SucI1,axiom,
% 5.02/5.36 ! [X8: nat > rat] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_rat @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.02/5.36 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI1
% 5.02/5.36 thf(fact_8472_mono__SucI1,axiom,
% 5.02/5.36 ! [X8: nat > num] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_num @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.02/5.36 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI1
% 5.02/5.36 thf(fact_8473_mono__SucI1,axiom,
% 5.02/5.36 ! [X8: nat > nat] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_nat @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.02/5.36 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI1
% 5.02/5.36 thf(fact_8474_mono__SucI1,axiom,
% 5.02/5.36 ! [X8: nat > int] :
% 5.02/5.36 ( ! [N: nat] : ( ord_less_eq_int @ ( X8 @ N ) @ ( X8 @ ( suc @ N ) ) )
% 5.02/5.36 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.02/5.36
% 5.02/5.36 % mono_SucI1
% 5.02/5.36 thf(fact_8475_pochhammer__times__pochhammer__half,axiom,
% 5.02/5.36 ! [Z: complex,N2: nat] :
% 5.02/5.36 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( groups6464643781859351333omplex
% 5.02/5.36 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_times_pochhammer_half
% 5.02/5.36 thf(fact_8476_pochhammer__times__pochhammer__half,axiom,
% 5.02/5.36 ! [Z: real,N2: nat] :
% 5.02/5.36 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_times_pochhammer_half
% 5.02/5.36 thf(fact_8477_pochhammer__times__pochhammer__half,axiom,
% 5.02/5.36 ! [Z: rat,N2: nat] :
% 5.02/5.36 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_times_pochhammer_half
% 5.02/5.36 thf(fact_8478_pochhammer__code,axiom,
% 5.02/5.36 ( comm_s2602460028002588243omplex
% 5.02/5.36 = ( ^ [A5: complex,N3: nat] :
% 5.02/5.36 ( if_complex @ ( N3 = zero_zero_nat ) @ one_one_complex
% 5.02/5.36 @ ( set_fo1517530859248394432omplex
% 5.02/5.36 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A5 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.02/5.36 @ zero_zero_nat
% 5.02/5.36 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.02/5.36 @ one_one_complex ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_code
% 5.02/5.36 thf(fact_8479_pochhammer__code,axiom,
% 5.02/5.36 ( comm_s4660882817536571857er_int
% 5.02/5.36 = ( ^ [A5: int,N3: nat] :
% 5.02/5.36 ( if_int @ ( N3 = zero_zero_nat ) @ one_one_int
% 5.02/5.36 @ ( set_fo2581907887559384638at_int
% 5.02/5.36 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.02/5.36 @ zero_zero_nat
% 5.02/5.36 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.02/5.36 @ one_one_int ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_code
% 5.02/5.36 thf(fact_8480_pochhammer__code,axiom,
% 5.02/5.36 ( comm_s7457072308508201937r_real
% 5.02/5.36 = ( ^ [A5: real,N3: nat] :
% 5.02/5.36 ( if_real @ ( N3 = zero_zero_nat ) @ one_one_real
% 5.02/5.36 @ ( set_fo3111899725591712190t_real
% 5.02/5.36 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A5 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.02/5.36 @ zero_zero_nat
% 5.02/5.36 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.02/5.36 @ one_one_real ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_code
% 5.02/5.36 thf(fact_8481_pochhammer__code,axiom,
% 5.02/5.36 ( comm_s4028243227959126397er_rat
% 5.02/5.36 = ( ^ [A5: rat,N3: nat] :
% 5.02/5.36 ( if_rat @ ( N3 = zero_zero_nat ) @ one_one_rat
% 5.02/5.36 @ ( set_fo1949268297981939178at_rat
% 5.02/5.36 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.02/5.36 @ zero_zero_nat
% 5.02/5.36 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.02/5.36 @ one_one_rat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_code
% 5.02/5.36 thf(fact_8482_pochhammer__code,axiom,
% 5.02/5.36 ( comm_s4663373288045622133er_nat
% 5.02/5.36 = ( ^ [A5: nat,N3: nat] :
% 5.02/5.36 ( if_nat @ ( N3 = zero_zero_nat ) @ one_one_nat
% 5.02/5.36 @ ( set_fo2584398358068434914at_nat
% 5.02/5.36 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.02/5.36 @ zero_zero_nat
% 5.02/5.36 @ ( minus_minus_nat @ N3 @ one_one_nat )
% 5.02/5.36 @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_code
% 5.02/5.36 thf(fact_8483_of__nat__code,axiom,
% 5.02/5.36 ( semiri8010041392384452111omplex
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri2816024913162550771omplex
% 5.02/5.36 @ ^ [I5: complex] : ( plus_plus_complex @ I5 @ one_one_complex )
% 5.02/5.36 @ N3
% 5.02/5.36 @ zero_zero_complex ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_code
% 5.02/5.36 thf(fact_8484_of__nat__code,axiom,
% 5.02/5.36 ( semiri1314217659103216013at_int
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri8420488043553186161ux_int
% 5.02/5.36 @ ^ [I5: int] : ( plus_plus_int @ I5 @ one_one_int )
% 5.02/5.36 @ N3
% 5.02/5.36 @ zero_zero_int ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_code
% 5.02/5.36 thf(fact_8485_of__nat__code,axiom,
% 5.02/5.36 ( semiri5074537144036343181t_real
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri7260567687927622513x_real
% 5.02/5.36 @ ^ [I5: real] : ( plus_plus_real @ I5 @ one_one_real )
% 5.02/5.36 @ N3
% 5.02/5.36 @ zero_zero_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_code
% 5.02/5.36 thf(fact_8486_of__nat__code,axiom,
% 5.02/5.36 ( semiri1316708129612266289at_nat
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri8422978514062236437ux_nat
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ one_one_nat )
% 5.02/5.36 @ N3
% 5.02/5.36 @ zero_zero_nat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_code
% 5.02/5.36 thf(fact_8487_of__nat__code,axiom,
% 5.02/5.36 ( semiri681578069525770553at_rat
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri7787848453975740701ux_rat
% 5.02/5.36 @ ^ [I5: rat] : ( plus_plus_rat @ I5 @ one_one_rat )
% 5.02/5.36 @ N3
% 5.02/5.36 @ zero_zero_rat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_code
% 5.02/5.36 thf(fact_8488_gchoose__row__sum__weighted,axiom,
% 5.02/5.36 ! [R2: complex,M: nat] :
% 5.02/5.36 ( ( groups2073611262835488442omplex
% 5.02/5.36 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R2 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R2 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.02/5.36 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R2 @ ( suc @ M ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gchoose_row_sum_weighted
% 5.02/5.36 thf(fact_8489_gchoose__row__sum__weighted,axiom,
% 5.02/5.36 ! [R2: rat,M: nat] :
% 5.02/5.36 ( ( groups2906978787729119204at_rat
% 5.02/5.36 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R2 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R2 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.02/5.36 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R2 @ ( suc @ M ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gchoose_row_sum_weighted
% 5.02/5.36 thf(fact_8490_gchoose__row__sum__weighted,axiom,
% 5.02/5.36 ! [R2: real,M: nat] :
% 5.02/5.36 ( ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R2 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.02/5.36 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R2 @ ( suc @ M ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gchoose_row_sum_weighted
% 5.02/5.36 thf(fact_8491_central__binomial__lower__bound,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % central_binomial_lower_bound
% 5.02/5.36 thf(fact_8492_binomial__Suc__n,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( binomial @ ( suc @ N2 ) @ N2 )
% 5.02/5.36 = ( suc @ N2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_Suc_n
% 5.02/5.36 thf(fact_8493_binomial__n__n,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( binomial @ N2 @ N2 )
% 5.02/5.36 = one_one_nat ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_n_n
% 5.02/5.36 thf(fact_8494_prod_Oneutral__const,axiom,
% 5.02/5.36 ! [A3: set_nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [Uu3: nat] : one_one_nat
% 5.02/5.36 @ A3 )
% 5.02/5.36 = one_one_nat ) ).
% 5.02/5.36
% 5.02/5.36 % prod.neutral_const
% 5.02/5.36 thf(fact_8495_prod_Oneutral__const,axiom,
% 5.02/5.36 ! [A3: set_nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [Uu3: nat] : one_one_int
% 5.02/5.36 @ A3 )
% 5.02/5.36 = one_one_int ) ).
% 5.02/5.36
% 5.02/5.36 % prod.neutral_const
% 5.02/5.36 thf(fact_8496_prod_Oneutral__const,axiom,
% 5.02/5.36 ! [A3: set_int] :
% 5.02/5.36 ( ( groups1705073143266064639nt_int
% 5.02/5.36 @ ^ [Uu3: int] : one_one_int
% 5.02/5.36 @ A3 )
% 5.02/5.36 = one_one_int ) ).
% 5.02/5.36
% 5.02/5.36 % prod.neutral_const
% 5.02/5.36 thf(fact_8497_of__nat__prod,axiom,
% 5.02/5.36 ! [F: int > nat,A3: set_int] :
% 5.02/5.36 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups1705073143266064639nt_int
% 5.02/5.36 @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_prod
% 5.02/5.36 thf(fact_8498_of__nat__prod,axiom,
% 5.02/5.36 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( semiri5074537144036343181t_real @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [X: nat] : ( semiri5074537144036343181t_real @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_prod
% 5.02/5.36 thf(fact_8499_of__nat__prod,axiom,
% 5.02/5.36 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [X: nat] : ( semiri681578069525770553at_rat @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_prod
% 5.02/5.36 thf(fact_8500_of__nat__prod,axiom,
% 5.02/5.36 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : ( semiri1316708129612266289at_nat @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_prod
% 5.02/5.36 thf(fact_8501_of__nat__prod,axiom,
% 5.02/5.36 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_nat_prod
% 5.02/5.36 thf(fact_8502_of__int__prod,axiom,
% 5.02/5.36 ! [F: nat > int,A3: set_nat] :
% 5.02/5.36 ( ( ring_1_of_int_real @ ( groups705719431365010083at_int @ F @ A3 ) )
% 5.02/5.36 = ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [X: nat] : ( ring_1_of_int_real @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_int_prod
% 5.02/5.36 thf(fact_8503_of__int__prod,axiom,
% 5.02/5.36 ! [F: nat > int,A3: set_nat] :
% 5.02/5.36 ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A3 ) )
% 5.02/5.36 = ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [X: nat] : ( ring_1_of_int_rat @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_int_prod
% 5.02/5.36 thf(fact_8504_of__int__prod,axiom,
% 5.02/5.36 ! [F: nat > int,A3: set_nat] :
% 5.02/5.36 ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A3 ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [X: nat] : ( ring_1_of_int_int @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_int_prod
% 5.02/5.36 thf(fact_8505_of__int__prod,axiom,
% 5.02/5.36 ! [F: int > int,A3: set_int] :
% 5.02/5.36 ( ( ring_1_of_int_real @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 5.02/5.36 = ( groups2316167850115554303t_real
% 5.02/5.36 @ ^ [X: int] : ( ring_1_of_int_real @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_int_prod
% 5.02/5.36 thf(fact_8506_of__int__prod,axiom,
% 5.02/5.36 ! [F: int > int,A3: set_int] :
% 5.02/5.36 ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 5.02/5.36 = ( groups1072433553688619179nt_rat
% 5.02/5.36 @ ^ [X: int] : ( ring_1_of_int_rat @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_int_prod
% 5.02/5.36 thf(fact_8507_of__int__prod,axiom,
% 5.02/5.36 ! [F: int > int,A3: set_int] :
% 5.02/5.36 ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 5.02/5.36 = ( groups1705073143266064639nt_int
% 5.02/5.36 @ ^ [X: int] : ( ring_1_of_int_int @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % of_int_prod
% 5.02/5.36 thf(fact_8508_prod_Oempty,axiom,
% 5.02/5.36 ! [G: nat > complex] :
% 5.02/5.36 ( ( groups6464643781859351333omplex @ G @ bot_bot_set_nat )
% 5.02/5.36 = one_one_complex ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8509_prod_Oempty,axiom,
% 5.02/5.36 ! [G: nat > real] :
% 5.02/5.36 ( ( groups129246275422532515t_real @ G @ bot_bot_set_nat )
% 5.02/5.36 = one_one_real ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8510_prod_Oempty,axiom,
% 5.02/5.36 ! [G: nat > rat] :
% 5.02/5.36 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.02/5.36 = one_one_rat ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8511_prod_Oempty,axiom,
% 5.02/5.36 ! [G: int > complex] :
% 5.02/5.36 ( ( groups7440179247065528705omplex @ G @ bot_bot_set_int )
% 5.02/5.36 = one_one_complex ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8512_prod_Oempty,axiom,
% 5.02/5.36 ! [G: int > real] :
% 5.02/5.36 ( ( groups2316167850115554303t_real @ G @ bot_bot_set_int )
% 5.02/5.36 = one_one_real ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8513_prod_Oempty,axiom,
% 5.02/5.36 ! [G: int > rat] :
% 5.02/5.36 ( ( groups1072433553688619179nt_rat @ G @ bot_bot_set_int )
% 5.02/5.36 = one_one_rat ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8514_prod_Oempty,axiom,
% 5.02/5.36 ! [G: int > nat] :
% 5.02/5.36 ( ( groups1707563613775114915nt_nat @ G @ bot_bot_set_int )
% 5.02/5.36 = one_one_nat ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8515_prod_Oempty,axiom,
% 5.02/5.36 ! [G: real > complex] :
% 5.02/5.36 ( ( groups713298508707869441omplex @ G @ bot_bot_set_real )
% 5.02/5.36 = one_one_complex ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8516_prod_Oempty,axiom,
% 5.02/5.36 ! [G: real > real] :
% 5.02/5.36 ( ( groups1681761925125756287l_real @ G @ bot_bot_set_real )
% 5.02/5.36 = one_one_real ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8517_prod_Oempty,axiom,
% 5.02/5.36 ! [G: real > rat] :
% 5.02/5.36 ( ( groups4061424788464935467al_rat @ G @ bot_bot_set_real )
% 5.02/5.36 = one_one_rat ) ).
% 5.02/5.36
% 5.02/5.36 % prod.empty
% 5.02/5.36 thf(fact_8518_gbinomial__0_I2_J,axiom,
% 5.02/5.36 ! [K: nat] :
% 5.02/5.36 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.02/5.36 = zero_zero_complex ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(2)
% 5.02/5.36 thf(fact_8519_gbinomial__0_I2_J,axiom,
% 5.02/5.36 ! [K: nat] :
% 5.02/5.36 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.02/5.36 = zero_zero_real ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(2)
% 5.02/5.36 thf(fact_8520_gbinomial__0_I2_J,axiom,
% 5.02/5.36 ! [K: nat] :
% 5.02/5.36 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.02/5.36 = zero_zero_rat ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(2)
% 5.02/5.36 thf(fact_8521_gbinomial__0_I2_J,axiom,
% 5.02/5.36 ! [K: nat] :
% 5.02/5.36 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.02/5.36 = zero_zero_nat ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(2)
% 5.02/5.36 thf(fact_8522_gbinomial__0_I2_J,axiom,
% 5.02/5.36 ! [K: nat] :
% 5.02/5.36 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.02/5.36 = zero_zero_int ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(2)
% 5.02/5.36 thf(fact_8523_binomial__1,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 5.02/5.36 = N2 ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_1
% 5.02/5.36 thf(fact_8524_binomial__0__Suc,axiom,
% 5.02/5.36 ! [K: nat] :
% 5.02/5.36 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.02/5.36 = zero_zero_nat ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_0_Suc
% 5.02/5.36 thf(fact_8525_binomial__eq__0__iff,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ( binomial @ N2 @ K )
% 5.02/5.36 = zero_zero_nat )
% 5.02/5.36 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_eq_0_iff
% 5.02/5.36 thf(fact_8526_gbinomial__0_I1_J,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_complex ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(1)
% 5.02/5.36 thf(fact_8527_gbinomial__0_I1_J,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_real ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(1)
% 5.02/5.36 thf(fact_8528_gbinomial__0_I1_J,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_rat ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(1)
% 5.02/5.36 thf(fact_8529_gbinomial__0_I1_J,axiom,
% 5.02/5.36 ! [A: nat] :
% 5.02/5.36 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_nat ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(1)
% 5.02/5.36 thf(fact_8530_gbinomial__0_I1_J,axiom,
% 5.02/5.36 ! [A: int] :
% 5.02/5.36 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.02/5.36 = one_one_int ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_0(1)
% 5.02/5.36 thf(fact_8531_binomial__Suc__Suc,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.02/5.36 = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_Suc_Suc
% 5.02/5.36 thf(fact_8532_binomial__n__0,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( binomial @ N2 @ zero_zero_nat )
% 5.02/5.36 = one_one_nat ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_n_0
% 5.02/5.36 thf(fact_8533_zero__less__binomial__iff,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 5.02/5.36 = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % zero_less_binomial_iff
% 5.02/5.36 thf(fact_8534_prod_OlessThan__Suc,axiom,
% 5.02/5.36 ! [G: nat > real,N2: nat] :
% 5.02/5.36 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.lessThan_Suc
% 5.02/5.36 thf(fact_8535_prod_OlessThan__Suc,axiom,
% 5.02/5.36 ! [G: nat > rat,N2: nat] :
% 5.02/5.36 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.lessThan_Suc
% 5.02/5.36 thf(fact_8536_prod_OlessThan__Suc,axiom,
% 5.02/5.36 ! [G: nat > nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.lessThan_Suc
% 5.02/5.36 thf(fact_8537_prod_OlessThan__Suc,axiom,
% 5.02/5.36 ! [G: nat > int,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.lessThan_Suc
% 5.02/5.36 thf(fact_8538_prod_Ocl__ivl__Suc,axiom,
% 5.02/5.36 ! [N2: nat,M: nat,G: nat > complex] :
% 5.02/5.36 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = one_one_complex ) )
% 5.02/5.36 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.cl_ivl_Suc
% 5.02/5.36 thf(fact_8539_prod_Ocl__ivl__Suc,axiom,
% 5.02/5.36 ! [N2: nat,M: nat,G: nat > real] :
% 5.02/5.36 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = one_one_real ) )
% 5.02/5.36 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.cl_ivl_Suc
% 5.02/5.36 thf(fact_8540_prod_Ocl__ivl__Suc,axiom,
% 5.02/5.36 ! [N2: nat,M: nat,G: nat > rat] :
% 5.02/5.36 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = one_one_rat ) )
% 5.02/5.36 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.cl_ivl_Suc
% 5.02/5.36 thf(fact_8541_prod_Ocl__ivl__Suc,axiom,
% 5.02/5.36 ! [N2: nat,M: nat,G: nat > nat] :
% 5.02/5.36 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = one_one_nat ) )
% 5.02/5.36 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.cl_ivl_Suc
% 5.02/5.36 thf(fact_8542_prod_Ocl__ivl__Suc,axiom,
% 5.02/5.36 ! [N2: nat,M: nat,G: nat > int] :
% 5.02/5.36 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = one_one_int ) )
% 5.02/5.36 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.02/5.36 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.cl_ivl_Suc
% 5.02/5.36 thf(fact_8543_choose__one,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( binomial @ N2 @ one_one_nat )
% 5.02/5.36 = N2 ) ).
% 5.02/5.36
% 5.02/5.36 % choose_one
% 5.02/5.36 thf(fact_8544_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: complex > complex,A3: set_complex] :
% 5.02/5.36 ( ( ( groups3708469109370488835omplex @ G @ A3 )
% 5.02/5.36 != one_one_complex )
% 5.02/5.36 => ~ ! [A4: complex] :
% 5.02/5.36 ( ( member_complex @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_complex ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8545_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: real > complex,A3: set_real] :
% 5.02/5.36 ( ( ( groups713298508707869441omplex @ G @ A3 )
% 5.02/5.36 != one_one_complex )
% 5.02/5.36 => ~ ! [A4: real] :
% 5.02/5.36 ( ( member_real @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_complex ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8546_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: nat > complex,A3: set_nat] :
% 5.02/5.36 ( ( ( groups6464643781859351333omplex @ G @ A3 )
% 5.02/5.36 != one_one_complex )
% 5.02/5.36 => ~ ! [A4: nat] :
% 5.02/5.36 ( ( member_nat @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_complex ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8547_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: int > complex,A3: set_int] :
% 5.02/5.36 ( ( ( groups7440179247065528705omplex @ G @ A3 )
% 5.02/5.36 != one_one_complex )
% 5.02/5.36 => ~ ! [A4: int] :
% 5.02/5.36 ( ( member_int @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_complex ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8548_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: complex > real,A3: set_complex] :
% 5.02/5.36 ( ( ( groups766887009212190081x_real @ G @ A3 )
% 5.02/5.36 != one_one_real )
% 5.02/5.36 => ~ ! [A4: complex] :
% 5.02/5.36 ( ( member_complex @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8549_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: real > real,A3: set_real] :
% 5.02/5.36 ( ( ( groups1681761925125756287l_real @ G @ A3 )
% 5.02/5.36 != one_one_real )
% 5.02/5.36 => ~ ! [A4: real] :
% 5.02/5.36 ( ( member_real @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8550_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: nat > real,A3: set_nat] :
% 5.02/5.36 ( ( ( groups129246275422532515t_real @ G @ A3 )
% 5.02/5.36 != one_one_real )
% 5.02/5.36 => ~ ! [A4: nat] :
% 5.02/5.36 ( ( member_nat @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8551_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: int > real,A3: set_int] :
% 5.02/5.36 ( ( ( groups2316167850115554303t_real @ G @ A3 )
% 5.02/5.36 != one_one_real )
% 5.02/5.36 => ~ ! [A4: int] :
% 5.02/5.36 ( ( member_int @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_real ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8552_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: complex > rat,A3: set_complex] :
% 5.02/5.36 ( ( ( groups225925009352817453ex_rat @ G @ A3 )
% 5.02/5.36 != one_one_rat )
% 5.02/5.36 => ~ ! [A4: complex] :
% 5.02/5.36 ( ( member_complex @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_rat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8553_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.02/5.36 ! [G: real > rat,A3: set_real] :
% 5.02/5.36 ( ( ( groups4061424788464935467al_rat @ G @ A3 )
% 5.02/5.36 != one_one_rat )
% 5.02/5.36 => ~ ! [A4: real] :
% 5.02/5.36 ( ( member_real @ A4 @ A3 )
% 5.02/5.36 => ( ( G @ A4 )
% 5.02/5.36 = one_one_rat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.not_neutral_contains_not_neutral
% 5.02/5.36 thf(fact_8554_prod_Oneutral,axiom,
% 5.02/5.36 ! [A3: set_nat,G: nat > nat] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ( G @ X5 )
% 5.02/5.36 = one_one_nat ) )
% 5.02/5.36 => ( ( groups708209901874060359at_nat @ G @ A3 )
% 5.02/5.36 = one_one_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.neutral
% 5.02/5.36 thf(fact_8555_prod_Oneutral,axiom,
% 5.02/5.36 ! [A3: set_nat,G: nat > int] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ( G @ X5 )
% 5.02/5.36 = one_one_int ) )
% 5.02/5.36 => ( ( groups705719431365010083at_int @ G @ A3 )
% 5.02/5.36 = one_one_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.neutral
% 5.02/5.36 thf(fact_8556_prod_Oneutral,axiom,
% 5.02/5.36 ! [A3: set_int,G: int > int] :
% 5.02/5.36 ( ! [X5: int] :
% 5.02/5.36 ( ( member_int @ X5 @ A3 )
% 5.02/5.36 => ( ( G @ X5 )
% 5.02/5.36 = one_one_int ) )
% 5.02/5.36 => ( ( groups1705073143266064639nt_int @ G @ A3 )
% 5.02/5.36 = one_one_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.neutral
% 5.02/5.36 thf(fact_8557_prod_Odistrib,axiom,
% 5.02/5.36 ! [G: nat > nat,H2: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : ( times_times_nat @ ( G @ X ) @ ( H2 @ X ) )
% 5.02/5.36 @ A3 )
% 5.02/5.36 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A3 ) @ ( groups708209901874060359at_nat @ H2 @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.distrib
% 5.02/5.36 thf(fact_8558_prod_Odistrib,axiom,
% 5.02/5.36 ! [G: nat > int,H2: nat > int,A3: set_nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [X: nat] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.02/5.36 @ A3 )
% 5.02/5.36 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A3 ) @ ( groups705719431365010083at_int @ H2 @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.distrib
% 5.02/5.36 thf(fact_8559_prod_Odistrib,axiom,
% 5.02/5.36 ! [G: int > int,H2: int > int,A3: set_int] :
% 5.02/5.36 ( ( groups1705073143266064639nt_int
% 5.02/5.36 @ ^ [X: int] : ( times_times_int @ ( G @ X ) @ ( H2 @ X ) )
% 5.02/5.36 @ A3 )
% 5.02/5.36 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A3 ) @ ( groups1705073143266064639nt_int @ H2 @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.distrib
% 5.02/5.36 thf(fact_8560_prod__power__distrib,axiom,
% 5.02/5.36 ! [F: nat > nat,A3: set_nat,N2: nat] :
% 5.02/5.36 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ N2 )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N2 )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_power_distrib
% 5.02/5.36 thf(fact_8561_prod__power__distrib,axiom,
% 5.02/5.36 ! [F: nat > int,A3: set_nat,N2: nat] :
% 5.02/5.36 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A3 ) @ N2 )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N2 )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_power_distrib
% 5.02/5.36 thf(fact_8562_prod__power__distrib,axiom,
% 5.02/5.36 ! [F: int > int,A3: set_int,N2: nat] :
% 5.02/5.36 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ N2 )
% 5.02/5.36 = ( groups1705073143266064639nt_int
% 5.02/5.36 @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N2 )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_power_distrib
% 5.02/5.36 thf(fact_8563_mod__prod__eq,axiom,
% 5.02/5.36 ! [F: nat > nat,A: nat,A3: set_nat] :
% 5.02/5.36 ( ( modulo_modulo_nat
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( modulo_modulo_nat @ ( F @ I5 ) @ A )
% 5.02/5.36 @ A3 )
% 5.02/5.36 @ A )
% 5.02/5.36 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % mod_prod_eq
% 5.02/5.36 thf(fact_8564_mod__prod__eq,axiom,
% 5.02/5.36 ! [F: nat > int,A: int,A3: set_nat] :
% 5.02/5.36 ( ( modulo_modulo_int
% 5.02/5.36 @ ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 5.02/5.36 @ A3 )
% 5.02/5.36 @ A )
% 5.02/5.36 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A3 ) @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % mod_prod_eq
% 5.02/5.36 thf(fact_8565_mod__prod__eq,axiom,
% 5.02/5.36 ! [F: int > int,A: int,A3: set_int] :
% 5.02/5.36 ( ( modulo_modulo_int
% 5.02/5.36 @ ( groups1705073143266064639nt_int
% 5.02/5.36 @ ^ [I5: int] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 5.02/5.36 @ A3 )
% 5.02/5.36 @ A )
% 5.02/5.36 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % mod_prod_eq
% 5.02/5.36 thf(fact_8566_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > real,G: complex > real] :
% 5.02/5.36 ( ! [I2: complex] :
% 5.02/5.36 ( ( member_complex @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A3 ) @ ( groups766887009212190081x_real @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8567_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > real,G: real > real] :
% 5.02/5.36 ( ! [I2: real] :
% 5.02/5.36 ( ( member_real @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ ( groups1681761925125756287l_real @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8568_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > real,G: nat > real] :
% 5.02/5.36 ( ! [I2: nat] :
% 5.02/5.36 ( ( member_nat @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A3 ) @ ( groups129246275422532515t_real @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8569_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_int,F: int > real,G: int > real] :
% 5.02/5.36 ( ! [I2: int] :
% 5.02/5.36 ( ( member_int @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ ( groups2316167850115554303t_real @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8570_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > rat,G: complex > rat] :
% 5.02/5.36 ( ! [I2: complex] :
% 5.02/5.36 ( ( member_complex @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) @ ( groups225925009352817453ex_rat @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8571_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > rat,G: real > rat] :
% 5.02/5.36 ( ! [I2: real] :
% 5.02/5.36 ( ( member_real @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ ( groups4061424788464935467al_rat @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8572_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 5.02/5.36 ( ! [I2: nat] :
% 5.02/5.36 ( ( member_nat @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8573_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_int,F: int > rat,G: int > rat] :
% 5.02/5.36 ( ! [I2: int] :
% 5.02/5.36 ( ( member_int @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_rat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8574_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > nat,G: complex > nat] :
% 5.02/5.36 ( ! [I2: complex] :
% 5.02/5.36 ( ( member_complex @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A3 ) @ ( groups861055069439313189ex_nat @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8575_prod__mono,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > nat,G: real > nat] :
% 5.02/5.36 ( ! [I2: real] :
% 5.02/5.36 ( ( member_real @ I2 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.02/5.36 & ( ord_less_eq_nat @ ( F @ I2 ) @ ( G @ I2 ) ) ) )
% 5.02/5.36 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) @ ( groups4696554848551431203al_nat @ G @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_mono
% 5.02/5.36 thf(fact_8576_prod__nonneg,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > nat] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_nonneg
% 5.02/5.36 thf(fact_8577_prod__nonneg,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > int] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_nonneg
% 5.02/5.36 thf(fact_8578_prod__nonneg,axiom,
% 5.02/5.36 ! [A3: set_int,F: int > int] :
% 5.02/5.36 ( ! [X5: int] :
% 5.02/5.36 ( ( member_int @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_nonneg
% 5.02/5.36 thf(fact_8579_prod__pos,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > nat] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_pos
% 5.02/5.36 thf(fact_8580_prod__pos,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > int] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_pos
% 5.02/5.36 thf(fact_8581_prod__pos,axiom,
% 5.02/5.36 ! [A3: set_int,F: int > int] :
% 5.02/5.36 ( ! [X5: int] :
% 5.02/5.36 ( ( member_int @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_pos
% 5.02/5.36 thf(fact_8582_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > real] :
% 5.02/5.36 ( ! [X5: complex] :
% 5.02/5.36 ( ( member_complex @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8583_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > real] :
% 5.02/5.36 ( ! [X5: real] :
% 5.02/5.36 ( ( member_real @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8584_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > real] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8585_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_int,F: int > real] :
% 5.02/5.36 ( ! [X5: int] :
% 5.02/5.36 ( ( member_int @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8586_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > rat] :
% 5.02/5.36 ( ! [X5: complex] :
% 5.02/5.36 ( ( member_complex @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8587_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > rat] :
% 5.02/5.36 ( ! [X5: real] :
% 5.02/5.36 ( ( member_real @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8588_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > rat] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8589_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_int,F: int > rat] :
% 5.02/5.36 ( ! [X5: int] :
% 5.02/5.36 ( ( member_int @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8590_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > nat] :
% 5.02/5.36 ( ! [X5: complex] :
% 5.02/5.36 ( ( member_complex @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_nat @ one_one_nat @ ( groups861055069439313189ex_nat @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8591_prod__ge__1,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > nat] :
% 5.02/5.36 ( ! [X5: real] :
% 5.02/5.36 ( ( member_real @ X5 @ A3 )
% 5.02/5.36 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X5 ) ) )
% 5.02/5.36 => ( ord_less_eq_nat @ one_one_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_ge_1
% 5.02/5.36 thf(fact_8592_binomial__eq__0,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ N2 @ K )
% 5.02/5.36 => ( ( binomial @ N2 @ K )
% 5.02/5.36 = zero_zero_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_eq_0
% 5.02/5.36 thf(fact_8593_prod__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > complex,A: nat,B: nat] :
% 5.02/5.36 ( ( groups6464643781859351333omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo1517530859248394432omplex
% 5.02/5.36 @ ^ [A5: nat] : ( times_times_complex @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ one_one_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_atLeastAtMost_code
% 5.02/5.36 thf(fact_8594_prod__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > real,A: nat,B: nat] :
% 5.02/5.36 ( ( groups129246275422532515t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo3111899725591712190t_real
% 5.02/5.36 @ ^ [A5: nat] : ( times_times_real @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_atLeastAtMost_code
% 5.02/5.36 thf(fact_8595_prod__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > rat,A: nat,B: nat] :
% 5.02/5.36 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo1949268297981939178at_rat
% 5.02/5.36 @ ^ [A5: nat] : ( times_times_rat @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_atLeastAtMost_code
% 5.02/5.36 thf(fact_8596_prod__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > nat,A: nat,B: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo2584398358068434914at_nat
% 5.02/5.36 @ ^ [A5: nat] : ( times_times_nat @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ one_one_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_atLeastAtMost_code
% 5.02/5.36 thf(fact_8597_prod__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > int,A: nat,B: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo2581907887559384638at_int
% 5.02/5.36 @ ^ [A5: nat] : ( times_times_int @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ one_one_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_atLeastAtMost_code
% 5.02/5.36 thf(fact_8598_Suc__times__binomial__eq,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) )
% 5.02/5.36 = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Suc_times_binomial_eq
% 5.02/5.36 thf(fact_8599_Suc__times__binomial,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) )
% 5.02/5.36 = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Suc_times_binomial
% 5.02/5.36 thf(fact_8600_binomial__symmetric,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( binomial @ N2 @ K )
% 5.02/5.36 = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_symmetric
% 5.02/5.36 thf(fact_8601_choose__mult__lemma,axiom,
% 5.02/5.36 ! [M: nat,R2: nat,K: nat] :
% 5.02/5.36 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.02/5.36 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R2 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R2 ) @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_mult_lemma
% 5.02/5.36 thf(fact_8602_binomial__le__pow,axiom,
% 5.02/5.36 ! [R2: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ R2 @ N2 )
% 5.02/5.36 => ( ord_less_eq_nat @ ( binomial @ N2 @ R2 ) @ ( power_power_nat @ N2 @ R2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_le_pow
% 5.02/5.36 thf(fact_8603_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.02/5.36 ! [G: nat > nat,M: nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.shift_bounds_cl_Suc_ivl
% 5.02/5.36 thf(fact_8604_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.02/5.36 ! [G: nat > int,M: nat,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.shift_bounds_cl_Suc_ivl
% 5.02/5.36 thf(fact_8605_power__sum,axiom,
% 5.02/5.36 ! [C: real,F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( power_power_real @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [A5: nat] : ( power_power_real @ C @ ( F @ A5 ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % power_sum
% 5.02/5.36 thf(fact_8606_power__sum,axiom,
% 5.02/5.36 ! [C: complex,F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( power_power_complex @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups6464643781859351333omplex
% 5.02/5.36 @ ^ [A5: nat] : ( power_power_complex @ C @ ( F @ A5 ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % power_sum
% 5.02/5.36 thf(fact_8607_power__sum,axiom,
% 5.02/5.36 ! [C: nat,F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [A5: nat] : ( power_power_nat @ C @ ( F @ A5 ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % power_sum
% 5.02/5.36 thf(fact_8608_power__sum,axiom,
% 5.02/5.36 ! [C: int,F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [A5: nat] : ( power_power_int @ C @ ( F @ A5 ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % power_sum
% 5.02/5.36 thf(fact_8609_power__sum,axiom,
% 5.02/5.36 ! [C: int,F: int > nat,A3: set_int] :
% 5.02/5.36 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups1705073143266064639nt_int
% 5.02/5.36 @ ^ [A5: int] : ( power_power_int @ C @ ( F @ A5 ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % power_sum
% 5.02/5.36 thf(fact_8610_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.02/5.36 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.shift_bounds_cl_nat_ivl
% 5.02/5.36 thf(fact_8611_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.02/5.36 ! [G: nat > int,M: nat,K: nat,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.shift_bounds_cl_nat_ivl
% 5.02/5.36 thf(fact_8612_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > real] :
% 5.02/5.36 ( ! [X5: complex] :
% 5.02/5.36 ( ( member_complex @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8613_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > real] :
% 5.02/5.36 ( ! [X5: real] :
% 5.02/5.36 ( ( member_real @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8614_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > real] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8615_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_int,F: int > real] :
% 5.02/5.36 ( ! [X5: int] :
% 5.02/5.36 ( ( member_int @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_real @ ( F @ X5 ) @ one_one_real ) ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F @ A3 ) @ one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8616_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > rat] :
% 5.02/5.36 ( ! [X5: complex] :
% 5.02/5.36 ( ( member_complex @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_rat @ ( F @ X5 ) @ one_one_rat ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8617_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > rat] :
% 5.02/5.36 ( ! [X5: real] :
% 5.02/5.36 ( ( member_real @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_rat @ ( F @ X5 ) @ one_one_rat ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8618_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_nat,F: nat > rat] :
% 5.02/5.36 ( ! [X5: nat] :
% 5.02/5.36 ( ( member_nat @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_rat @ ( F @ X5 ) @ one_one_rat ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8619_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_int,F: int > rat] :
% 5.02/5.36 ( ! [X5: int] :
% 5.02/5.36 ( ( member_int @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_rat @ ( F @ X5 ) @ one_one_rat ) ) )
% 5.02/5.36 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8620_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_complex,F: complex > nat] :
% 5.02/5.36 ( ! [X5: complex] :
% 5.02/5.36 ( ( member_complex @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_nat @ ( F @ X5 ) @ one_one_nat ) ) )
% 5.02/5.36 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8621_prod__le__1,axiom,
% 5.02/5.36 ! [A3: set_real,F: real > nat] :
% 5.02/5.36 ( ! [X5: real] :
% 5.02/5.36 ( ( member_real @ X5 @ A3 )
% 5.02/5.36 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) )
% 5.02/5.36 & ( ord_less_eq_nat @ ( F @ X5 ) @ one_one_nat ) ) )
% 5.02/5.36 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod_le_1
% 5.02/5.36 thf(fact_8622_zero__less__binomial,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % zero_less_binomial
% 5.02/5.36 thf(fact_8623_Suc__times__binomial__add,axiom,
% 5.02/5.36 ! [A: nat,B: nat] :
% 5.02/5.36 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.02/5.36 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Suc_times_binomial_add
% 5.02/5.36 thf(fact_8624_choose__mult,axiom,
% 5.02/5.36 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ M )
% 5.02/5.36 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 5.02/5.36 = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_mult
% 5.02/5.36 thf(fact_8625_binomial__Suc__Suc__eq__times,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.02/5.36 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) @ ( suc @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_Suc_Suc_eq_times
% 5.02/5.36 thf(fact_8626_binomial__absorb__comp,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 5.02/5.36 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_absorb_comp
% 5.02/5.36 thf(fact_8627_gbinomial__Suc__Suc,axiom,
% 5.02/5.36 ! [A: complex,K: nat] :
% 5.02/5.36 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.02/5.36 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_Suc_Suc
% 5.02/5.36 thf(fact_8628_gbinomial__Suc__Suc,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.02/5.36 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_Suc_Suc
% 5.02/5.36 thf(fact_8629_gbinomial__Suc__Suc,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.02/5.36 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_Suc_Suc
% 5.02/5.36 thf(fact_8630_gbinomial__of__nat__symmetric,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 5.02/5.36 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_of_nat_symmetric
% 5.02/5.36 thf(fact_8631_gbinomial__of__nat__symmetric,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K )
% 5.02/5.36 = ( gbinomial_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_of_nat_symmetric
% 5.02/5.36 thf(fact_8632_prod_Onat__diff__reindex,axiom,
% 5.02/5.36 ! [G: nat > nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.nat_diff_reindex
% 5.02/5.36 thf(fact_8633_prod_Onat__diff__reindex,axiom,
% 5.02/5.36 ! [G: nat > int,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I5 ) ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.36 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.nat_diff_reindex
% 5.02/5.36 thf(fact_8634_prod_OatLeastAtMost__rev,axiom,
% 5.02/5.36 ! [G: nat > nat,N2: nat,M: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeastAtMost_rev
% 5.02/5.36 thf(fact_8635_prod_OatLeastAtMost__rev,axiom,
% 5.02/5.36 ! [G: nat > int,N2: nat,M: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeastAtMost_rev
% 5.02/5.36 thf(fact_8636_gbinomial__Suc,axiom,
% 5.02/5.36 ! [A: complex,K: nat] :
% 5.02/5.36 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.02/5.36 = ( divide1717551699836669952omplex
% 5.02/5.36 @ ( groups6464643781859351333omplex
% 5.02/5.36 @ ^ [I5: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.02/5.36 @ ( semiri5044797733671781792omplex @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_Suc
% 5.02/5.36 thf(fact_8637_gbinomial__Suc,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.02/5.36 = ( divide_divide_rat
% 5.02/5.36 @ ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [I5: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.02/5.36 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_Suc
% 5.02/5.36 thf(fact_8638_gbinomial__Suc,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.02/5.36 = ( divide_divide_real
% 5.02/5.36 @ ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [I5: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.02/5.36 @ ( semiri2265585572941072030t_real @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_Suc
% 5.02/5.36 thf(fact_8639_gbinomial__Suc,axiom,
% 5.02/5.36 ! [A: nat,K: nat] :
% 5.02/5.36 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.02/5.36 = ( divide_divide_nat
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.02/5.36 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_Suc
% 5.02/5.36 thf(fact_8640_gbinomial__Suc,axiom,
% 5.02/5.36 ! [A: int,K: nat] :
% 5.02/5.36 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.02/5.36 = ( divide_divide_int
% 5.02/5.36 @ ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.02/5.36 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_Suc
% 5.02/5.36 thf(fact_8641_prod_OatLeast0__atMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > real,N2: nat] :
% 5.02/5.36 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast0_atMost_Suc
% 5.02/5.36 thf(fact_8642_prod_OatLeast0__atMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > rat,N2: nat] :
% 5.02/5.36 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast0_atMost_Suc
% 5.02/5.36 thf(fact_8643_prod_OatLeast0__atMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast0_atMost_Suc
% 5.02/5.36 thf(fact_8644_prod_OatLeast0__atMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > int,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast0_atMost_Suc
% 5.02/5.36 thf(fact_8645_prod_OatLeast__Suc__atMost,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > real] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.36 = ( times_times_real @ ( G @ M ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast_Suc_atMost
% 5.02/5.36 thf(fact_8646_prod_OatLeast__Suc__atMost,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > rat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.36 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast_Suc_atMost
% 5.02/5.36 thf(fact_8647_prod_OatLeast__Suc__atMost,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.36 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast_Suc_atMost
% 5.02/5.36 thf(fact_8648_prod_OatLeast__Suc__atMost,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > int] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.36 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast_Suc_atMost
% 5.02/5.36 thf(fact_8649_prod_Onat__ivl__Suc_H,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > real] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.36 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_real @ ( G @ ( suc @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.nat_ivl_Suc'
% 5.02/5.36 thf(fact_8650_prod_Onat__ivl__Suc_H,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > rat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.36 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_rat @ ( G @ ( suc @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.nat_ivl_Suc'
% 5.02/5.36 thf(fact_8651_prod_Onat__ivl__Suc_H,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.36 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.nat_ivl_Suc'
% 5.02/5.36 thf(fact_8652_prod_Onat__ivl__Suc_H,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > int] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.02/5.36 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.nat_ivl_Suc'
% 5.02/5.36 thf(fact_8653_binomial__absorption,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 5.02/5.36 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_absorption
% 5.02/5.36 thf(fact_8654_gbinomial__addition__formula,axiom,
% 5.02/5.36 ! [A: complex,K: nat] :
% 5.02/5.36 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.02/5.36 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_addition_formula
% 5.02/5.36 thf(fact_8655_gbinomial__addition__formula,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.02/5.36 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_addition_formula
% 5.02/5.36 thf(fact_8656_gbinomial__addition__formula,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.02/5.36 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_addition_formula
% 5.02/5.36 thf(fact_8657_gbinomial__absorb__comp,axiom,
% 5.02/5.36 ! [A: complex,K: nat] :
% 5.02/5.36 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.02/5.36 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorb_comp
% 5.02/5.36 thf(fact_8658_gbinomial__absorb__comp,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.02/5.36 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorb_comp
% 5.02/5.36 thf(fact_8659_gbinomial__absorb__comp,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.02/5.36 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorb_comp
% 5.02/5.36 thf(fact_8660_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.02/5.36 ! [K: nat,A: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.02/5.36 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_ge_n_over_k_pow_k
% 5.02/5.36 thf(fact_8661_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.02/5.36 ! [K: nat,A: rat] :
% 5.02/5.36 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.02/5.36 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_ge_n_over_k_pow_k
% 5.02/5.36 thf(fact_8662_gbinomial__mult__1,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.02/5.36 = ( 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 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_mult_1
% 5.02/5.36 thf(fact_8663_gbinomial__mult__1,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.02/5.36 = ( 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 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_mult_1
% 5.02/5.36 thf(fact_8664_gbinomial__mult__1_H,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.02/5.36 = ( 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 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_mult_1'
% 5.02/5.36 thf(fact_8665_gbinomial__mult__1_H,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.02/5.36 = ( 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 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_mult_1'
% 5.02/5.36 thf(fact_8666_binomial__fact__lemma,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 5.02/5.36 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_fact_lemma
% 5.02/5.36 thf(fact_8667_prod_OlessThan__Suc__shift,axiom,
% 5.02/5.36 ! [G: nat > real,N2: nat] :
% 5.02/5.36 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.02/5.36 @ ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.lessThan_Suc_shift
% 5.02/5.36 thf(fact_8668_prod_OlessThan__Suc__shift,axiom,
% 5.02/5.36 ! [G: nat > rat,N2: nat] :
% 5.02/5.36 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.02/5.36 @ ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.lessThan_Suc_shift
% 5.02/5.36 thf(fact_8669_prod_OlessThan__Suc__shift,axiom,
% 5.02/5.36 ! [G: nat > nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.lessThan_Suc_shift
% 5.02/5.36 thf(fact_8670_prod_OlessThan__Suc__shift,axiom,
% 5.02/5.36 ! [G: nat > int,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.02/5.36 @ ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.lessThan_Suc_shift
% 5.02/5.36 thf(fact_8671_prod_OSuc__reindex__ivl,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > real] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_real @ ( G @ M )
% 5.02/5.36 @ ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.Suc_reindex_ivl
% 5.02/5.36 thf(fact_8672_prod_OSuc__reindex__ivl,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > rat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_rat @ ( G @ M )
% 5.02/5.36 @ ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.Suc_reindex_ivl
% 5.02/5.36 thf(fact_8673_prod_OSuc__reindex__ivl,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_nat @ ( G @ M )
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.Suc_reindex_ivl
% 5.02/5.36 thf(fact_8674_prod_OSuc__reindex__ivl,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > int] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.36 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_int @ ( G @ M )
% 5.02/5.36 @ ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.Suc_reindex_ivl
% 5.02/5.36 thf(fact_8675_prod_OatLeast1__atMost__eq,axiom,
% 5.02/5.36 ! [G: nat > nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast1_atMost_eq
% 5.02/5.36 thf(fact_8676_prod_OatLeast1__atMost__eq,axiom,
% 5.02/5.36 ! [G: nat > int,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atLeast1_atMost_eq
% 5.02/5.36 thf(fact_8677_fact__prod,axiom,
% 5.02/5.36 ( semiri1406184849735516958ct_int
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri1314217659103216013at_int
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : X
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_prod
% 5.02/5.36 thf(fact_8678_fact__prod,axiom,
% 5.02/5.36 ( semiri773545260158071498ct_rat
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri681578069525770553at_rat
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : X
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_prod
% 5.02/5.36 thf(fact_8679_fact__prod,axiom,
% 5.02/5.36 ( semiri2265585572941072030t_real
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri5074537144036343181t_real
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : X
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_prod
% 5.02/5.36 thf(fact_8680_fact__prod,axiom,
% 5.02/5.36 ( semiri1408675320244567234ct_nat
% 5.02/5.36 = ( ^ [N3: nat] :
% 5.02/5.36 ( semiri1316708129612266289at_nat
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : X
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_prod
% 5.02/5.36 thf(fact_8681_binomial__ge__n__over__k__pow__k,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_ge_n_over_k_pow_k
% 5.02/5.36 thf(fact_8682_binomial__ge__n__over__k__pow__k,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_ge_n_over_k_pow_k
% 5.02/5.36 thf(fact_8683_binomial__mono,axiom,
% 5.02/5.36 ! [K: nat,K6: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ K6 )
% 5.02/5.36 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.02/5.36 => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_mono
% 5.02/5.36 thf(fact_8684_binomial__maximum_H,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_maximum'
% 5.02/5.36 thf(fact_8685_binomial__maximum,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_maximum
% 5.02/5.36 thf(fact_8686_binomial__antimono,axiom,
% 5.02/5.36 ! [K: nat,K6: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ K6 )
% 5.02/5.36 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.02/5.36 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.02/5.36 => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_antimono
% 5.02/5.36 thf(fact_8687_binomial__le__pow2,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_le_pow2
% 5.02/5.36 thf(fact_8688_choose__reduce__nat,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.36 => ( ( binomial @ N2 @ K )
% 5.02/5.36 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_reduce_nat
% 5.02/5.36 thf(fact_8689_times__binomial__minus1__eq,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.36 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 5.02/5.36 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % times_binomial_minus1_eq
% 5.02/5.36 thf(fact_8690_prod_Oub__add__nat,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > real,P2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.02/5.36 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.02/5.36 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.ub_add_nat
% 5.02/5.36 thf(fact_8691_prod_Oub__add__nat,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > rat,P2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.02/5.36 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.02/5.36 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.ub_add_nat
% 5.02/5.36 thf(fact_8692_prod_Oub__add__nat,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > nat,P2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.02/5.36 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.02/5.36 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.ub_add_nat
% 5.02/5.36 thf(fact_8693_prod_Oub__add__nat,axiom,
% 5.02/5.36 ! [M: nat,N2: nat,G: nat > int,P2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.02/5.36 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.02/5.36 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.ub_add_nat
% 5.02/5.36 thf(fact_8694_Suc__times__gbinomial,axiom,
% 5.02/5.36 ! [K: nat,A: complex] :
% 5.02/5.36 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.02/5.36 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Suc_times_gbinomial
% 5.02/5.36 thf(fact_8695_Suc__times__gbinomial,axiom,
% 5.02/5.36 ! [K: nat,A: real] :
% 5.02/5.36 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.02/5.36 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Suc_times_gbinomial
% 5.02/5.36 thf(fact_8696_Suc__times__gbinomial,axiom,
% 5.02/5.36 ! [K: nat,A: rat] :
% 5.02/5.36 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.02/5.36 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Suc_times_gbinomial
% 5.02/5.36 thf(fact_8697_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.02/5.36 ! [X2: nat > nat > nat,Xa2: nat,Xb3: nat,Xc: nat,Y: nat] :
% 5.02/5.36 ( ( ( set_fo2584398358068434914at_nat @ X2 @ Xa2 @ Xb3 @ Xc )
% 5.02/5.36 = Y )
% 5.02/5.36 => ( ( ( ord_less_nat @ Xb3 @ Xa2 )
% 5.02/5.36 => ( Y = Xc ) )
% 5.02/5.36 & ( ~ ( ord_less_nat @ Xb3 @ Xa2 )
% 5.02/5.36 => ( Y
% 5.02/5.36 = ( set_fo2584398358068434914at_nat @ X2 @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb3 @ ( X2 @ Xa2 @ Xc ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fold_atLeastAtMost_nat.elims
% 5.02/5.36 thf(fact_8698_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.02/5.36 ( set_fo2584398358068434914at_nat
% 5.02/5.36 = ( ^ [F3: nat > nat > nat,A5: nat,B5: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B5 @ A5 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B5 @ ( F3 @ A5 @ Acc2 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fold_atLeastAtMost_nat.simps
% 5.02/5.36 thf(fact_8699_gbinomial__absorption,axiom,
% 5.02/5.36 ! [K: nat,A: complex] :
% 5.02/5.36 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.02/5.36 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorption
% 5.02/5.36 thf(fact_8700_gbinomial__absorption,axiom,
% 5.02/5.36 ! [K: nat,A: real] :
% 5.02/5.36 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.02/5.36 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorption
% 5.02/5.36 thf(fact_8701_gbinomial__absorption,axiom,
% 5.02/5.36 ! [K: nat,A: rat] :
% 5.02/5.36 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.02/5.36 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorption
% 5.02/5.36 thf(fact_8702_binomial__altdef__nat,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( binomial @ N2 @ K )
% 5.02/5.36 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_altdef_nat
% 5.02/5.36 thf(fact_8703_gbinomial__trinomial__revision,axiom,
% 5.02/5.36 ! [K: nat,M: nat,A: real] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ M )
% 5.02/5.36 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.02/5.36 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_trinomial_revision
% 5.02/5.36 thf(fact_8704_gbinomial__trinomial__revision,axiom,
% 5.02/5.36 ! [K: nat,M: nat,A: rat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ M )
% 5.02/5.36 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.02/5.36 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_trinomial_revision
% 5.02/5.36 thf(fact_8705_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_complex,Z: complex > real,W: complex > real] :
% 5.02/5.36 ( ! [I2: complex] :
% 5.02/5.36 ( ( member_complex @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: complex] :
% 5.02/5.36 ( ( member_complex @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups766887009212190081x_real @ Z @ I6 ) @ ( groups766887009212190081x_real @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups5808333547571424918x_real
% 5.02/5.36 @ ^ [I5: complex] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8706_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_real,Z: real > real,W: real > real] :
% 5.02/5.36 ( ! [I2: real] :
% 5.02/5.36 ( ( member_real @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: real] :
% 5.02/5.36 ( ( member_real @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups1681761925125756287l_real @ Z @ I6 ) @ ( groups1681761925125756287l_real @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups8097168146408367636l_real
% 5.02/5.36 @ ^ [I5: real] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8707_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_set_nat,Z: set_nat > real,W: set_nat > real] :
% 5.02/5.36 ( ! [I2: set_nat] :
% 5.02/5.36 ( ( member_set_nat @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: set_nat] :
% 5.02/5.36 ( ( member_set_nat @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups3619160379726066777t_real @ Z @ I6 ) @ ( groups3619160379726066777t_real @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups5107569545109728110t_real
% 5.02/5.36 @ ^ [I5: set_nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8708_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_int,Z: int > real,W: int > real] :
% 5.02/5.36 ( ! [I2: int] :
% 5.02/5.36 ( ( member_int @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: int] :
% 5.02/5.36 ( ( member_int @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups2316167850115554303t_real @ Z @ I6 ) @ ( groups2316167850115554303t_real @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups8778361861064173332t_real
% 5.02/5.36 @ ^ [I5: int] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8709_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_complex,Z: complex > complex,W: complex > complex] :
% 5.02/5.36 ( ! [I2: complex] :
% 5.02/5.36 ( ( member_complex @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: complex] :
% 5.02/5.36 ( ( member_complex @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups3708469109370488835omplex @ Z @ I6 ) @ ( groups3708469109370488835omplex @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups5808333547571424918x_real
% 5.02/5.36 @ ^ [I5: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8710_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_real,Z: real > complex,W: real > complex] :
% 5.02/5.36 ( ! [I2: real] :
% 5.02/5.36 ( ( member_real @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: real] :
% 5.02/5.36 ( ( member_real @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups713298508707869441omplex @ Z @ I6 ) @ ( groups713298508707869441omplex @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups8097168146408367636l_real
% 5.02/5.36 @ ^ [I5: real] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8711_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_set_nat,Z: set_nat > complex,W: set_nat > complex] :
% 5.02/5.36 ( ! [I2: set_nat] :
% 5.02/5.36 ( ( member_set_nat @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: set_nat] :
% 5.02/5.36 ( ( member_set_nat @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups1092910753850256091omplex @ Z @ I6 ) @ ( groups1092910753850256091omplex @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups5107569545109728110t_real
% 5.02/5.36 @ ^ [I5: set_nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8712_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_int,Z: int > complex,W: int > complex] :
% 5.02/5.36 ( ! [I2: int] :
% 5.02/5.36 ( ( member_int @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: int] :
% 5.02/5.36 ( ( member_int @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups7440179247065528705omplex @ Z @ I6 ) @ ( groups7440179247065528705omplex @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups8778361861064173332t_real
% 5.02/5.36 @ ^ [I5: int] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8713_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_nat,Z: nat > real,W: nat > real] :
% 5.02/5.36 ( ! [I2: nat] :
% 5.02/5.36 ( ( member_nat @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: nat] :
% 5.02/5.36 ( ( member_nat @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( groups129246275422532515t_real @ Z @ I6 ) @ ( groups129246275422532515t_real @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [I5: nat] : ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8714_norm__prod__diff,axiom,
% 5.02/5.36 ! [I6: set_nat,Z: nat > complex,W: nat > complex] :
% 5.02/5.36 ( ! [I2: nat] :
% 5.02/5.36 ( ( member_nat @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( Z @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ! [I2: nat] :
% 5.02/5.36 ( ( member_nat @ I2 @ I6 )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( W @ I2 ) ) @ one_one_real ) )
% 5.02/5.36 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( groups6464643781859351333omplex @ Z @ I6 ) @ ( groups6464643781859351333omplex @ W @ I6 ) ) )
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [I5: nat] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( Z @ I5 ) @ ( W @ I5 ) ) )
% 5.02/5.36 @ I6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % norm_prod_diff
% 5.02/5.36 thf(fact_8715_fact__eq__fact__times,axiom,
% 5.02/5.36 ! [N2: nat,M: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.36 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.02/5.36 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 5.02/5.36 @ ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : X
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_eq_fact_times
% 5.02/5.36 thf(fact_8716_binomial__less__binomial__Suc,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.36 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_less_binomial_Suc
% 5.02/5.36 thf(fact_8717_binomial__strict__mono,axiom,
% 5.02/5.36 ! [K: nat,K6: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ K @ K6 )
% 5.02/5.36 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.02/5.36 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_strict_mono
% 5.02/5.36 thf(fact_8718_binomial__strict__antimono,axiom,
% 5.02/5.36 ! [K: nat,K6: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ K @ K6 )
% 5.02/5.36 => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.02/5.36 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.02/5.36 => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_strict_antimono
% 5.02/5.36 thf(fact_8719_gbinomial__code,axiom,
% 5.02/5.36 ( gbinomial_complex
% 5.02/5.36 = ( ^ [A5: complex,K3: nat] :
% 5.02/5.36 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.02/5.36 @ ( divide1717551699836669952omplex
% 5.02/5.36 @ ( set_fo1517530859248394432omplex
% 5.02/5.36 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A5 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 5.02/5.36 @ zero_zero_nat
% 5.02/5.36 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.02/5.36 @ one_one_complex )
% 5.02/5.36 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_code
% 5.02/5.36 thf(fact_8720_gbinomial__code,axiom,
% 5.02/5.36 ( gbinomial_rat
% 5.02/5.36 = ( ^ [A5: rat,K3: nat] :
% 5.02/5.36 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.02/5.36 @ ( divide_divide_rat
% 5.02/5.36 @ ( set_fo1949268297981939178at_rat
% 5.02/5.36 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 5.02/5.36 @ zero_zero_nat
% 5.02/5.36 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.02/5.36 @ one_one_rat )
% 5.02/5.36 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_code
% 5.02/5.36 thf(fact_8721_gbinomial__code,axiom,
% 5.02/5.36 ( gbinomial_real
% 5.02/5.36 = ( ^ [A5: real,K3: nat] :
% 5.02/5.36 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.02/5.36 @ ( divide_divide_real
% 5.02/5.36 @ ( set_fo3111899725591712190t_real
% 5.02/5.36 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A5 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 5.02/5.36 @ zero_zero_nat
% 5.02/5.36 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.02/5.36 @ one_one_real )
% 5.02/5.36 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_code
% 5.02/5.36 thf(fact_8722_central__binomial__odd,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.36 => ( ( binomial @ N2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.36 = ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % central_binomial_odd
% 5.02/5.36 thf(fact_8723_binomial__addition__formula,axiom,
% 5.02/5.36 ! [N2: nat,K: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( binomial @ N2 @ ( suc @ K ) )
% 5.02/5.36 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_addition_formula
% 5.02/5.36 thf(fact_8724_binomial__fact,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) )
% 5.02/5.36 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_fact
% 5.02/5.36 thf(fact_8725_binomial__fact,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) )
% 5.02/5.36 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_fact
% 5.02/5.36 thf(fact_8726_binomial__fact,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) )
% 5.02/5.36 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_fact
% 5.02/5.36 thf(fact_8727_fact__binomial,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) ) )
% 5.02/5.36 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_binomial
% 5.02/5.36 thf(fact_8728_fact__binomial,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) )
% 5.02/5.36 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_binomial
% 5.02/5.36 thf(fact_8729_fact__binomial,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.36 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) )
% 5.02/5.36 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_binomial
% 5.02/5.36 thf(fact_8730_gbinomial__factors,axiom,
% 5.02/5.36 ! [A: complex,K: nat] :
% 5.02/5.36 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.02/5.36 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_factors
% 5.02/5.36 thf(fact_8731_gbinomial__factors,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.02/5.36 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_factors
% 5.02/5.36 thf(fact_8732_gbinomial__factors,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.02/5.36 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_factors
% 5.02/5.36 thf(fact_8733_gbinomial__rec,axiom,
% 5.02/5.36 ! [A: complex,K: nat] :
% 5.02/5.36 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.02/5.36 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_rec
% 5.02/5.36 thf(fact_8734_gbinomial__rec,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.02/5.36 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_rec
% 5.02/5.36 thf(fact_8735_gbinomial__rec,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.02/5.36 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_rec
% 5.02/5.36 thf(fact_8736_gbinomial__index__swap,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ K ) )
% 5.02/5.36 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_index_swap
% 5.02/5.36 thf(fact_8737_gbinomial__index__swap,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ K ) )
% 5.02/5.36 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_index_swap
% 5.02/5.36 thf(fact_8738_gbinomial__index__swap,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K ) )
% 5.02/5.36 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_index_swap
% 5.02/5.36 thf(fact_8739_gbinomial__negated__upper,axiom,
% 5.02/5.36 ( gbinomial_complex
% 5.02/5.36 = ( ^ [A5: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A5 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_negated_upper
% 5.02/5.36 thf(fact_8740_gbinomial__negated__upper,axiom,
% 5.02/5.36 ( gbinomial_real
% 5.02/5.36 = ( ^ [A5: 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 ) @ A5 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_negated_upper
% 5.02/5.36 thf(fact_8741_gbinomial__negated__upper,axiom,
% 5.02/5.36 ( gbinomial_rat
% 5.02/5.36 = ( ^ [A5: 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 ) @ A5 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_negated_upper
% 5.02/5.36 thf(fact_8742_pochhammer__Suc__prod,axiom,
% 5.02/5.36 ! [A: real,N2: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc_prod
% 5.02/5.36 thf(fact_8743_pochhammer__Suc__prod,axiom,
% 5.02/5.36 ! [A: rat,N2: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc_prod
% 5.02/5.36 thf(fact_8744_pochhammer__Suc__prod,axiom,
% 5.02/5.36 ! [A: nat,N2: nat] :
% 5.02/5.36 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc_prod
% 5.02/5.36 thf(fact_8745_pochhammer__Suc__prod,axiom,
% 5.02/5.36 ! [A: int,N2: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I5 ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc_prod
% 5.02/5.36 thf(fact_8746_pochhammer__prod__rev,axiom,
% 5.02/5.36 ( comm_s7457072308508201937r_real
% 5.02/5.36 = ( ^ [A5: real,N3: nat] :
% 5.02/5.36 ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_real @ A5 @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N3 @ I5 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_prod_rev
% 5.02/5.36 thf(fact_8747_pochhammer__prod__rev,axiom,
% 5.02/5.36 ( comm_s4028243227959126397er_rat
% 5.02/5.36 = ( ^ [A5: rat,N3: nat] :
% 5.02/5.36 ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N3 @ I5 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_prod_rev
% 5.02/5.36 thf(fact_8748_pochhammer__prod__rev,axiom,
% 5.02/5.36 ( comm_s4663373288045622133er_nat
% 5.02/5.36 = ( ^ [A5: nat,N3: nat] :
% 5.02/5.36 ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N3 @ I5 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_prod_rev
% 5.02/5.36 thf(fact_8749_pochhammer__prod__rev,axiom,
% 5.02/5.36 ( comm_s4660882817536571857er_int
% 5.02/5.36 = ( ^ [A5: int,N3: nat] :
% 5.02/5.36 ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N3 @ I5 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_prod_rev
% 5.02/5.36 thf(fact_8750_binomial__code,axiom,
% 5.02/5.36 ( binomial
% 5.02/5.36 = ( ^ [N3: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N3 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N3 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N3 @ ( minus_minus_nat @ N3 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N3 @ K3 ) @ one_one_nat ) @ N3 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % binomial_code
% 5.02/5.36 thf(fact_8751_fact__div__fact,axiom,
% 5.02/5.36 ! [N2: nat,M: nat] :
% 5.02/5.36 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.36 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [X: nat] : X
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_div_fact
% 5.02/5.36 thf(fact_8752_choose__two,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.36 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_two
% 5.02/5.36 thf(fact_8753_gbinomial__minus,axiom,
% 5.02/5.36 ! [A: complex,K: nat] :
% 5.02/5.36 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.02/5.36 = ( 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 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_minus
% 5.02/5.36 thf(fact_8754_gbinomial__minus,axiom,
% 5.02/5.36 ! [A: real,K: nat] :
% 5.02/5.36 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.02/5.36 = ( 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 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_minus
% 5.02/5.36 thf(fact_8755_gbinomial__minus,axiom,
% 5.02/5.36 ! [A: rat,K: nat] :
% 5.02/5.36 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.02/5.36 = ( 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 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_minus
% 5.02/5.36 thf(fact_8756_prod_Oin__pairs,axiom,
% 5.02/5.36 ! [G: nat > real,M: nat,N2: nat] :
% 5.02/5.36 ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.36 = ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [I5: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.in_pairs
% 5.02/5.36 thf(fact_8757_prod_Oin__pairs,axiom,
% 5.02/5.36 ! [G: nat > rat,M: nat,N2: nat] :
% 5.02/5.36 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.36 = ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [I5: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.in_pairs
% 5.02/5.36 thf(fact_8758_prod_Oin__pairs,axiom,
% 5.02/5.36 ! [G: nat > nat,M: nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.in_pairs
% 5.02/5.36 thf(fact_8759_prod_Oin__pairs,axiom,
% 5.02/5.36 ! [G: nat > int,M: nat,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.in_pairs
% 5.02/5.36 thf(fact_8760_gbinomial__reduce__nat,axiom,
% 5.02/5.36 ! [K: nat,A: complex] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.36 => ( ( gbinomial_complex @ A @ K )
% 5.02/5.36 = ( 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 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_reduce_nat
% 5.02/5.36 thf(fact_8761_gbinomial__reduce__nat,axiom,
% 5.02/5.36 ! [K: nat,A: real] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.36 => ( ( gbinomial_real @ A @ K )
% 5.02/5.36 = ( 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 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_reduce_nat
% 5.02/5.36 thf(fact_8762_gbinomial__reduce__nat,axiom,
% 5.02/5.36 ! [K: nat,A: rat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.36 => ( ( gbinomial_rat @ A @ K )
% 5.02/5.36 = ( 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 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_reduce_nat
% 5.02/5.36 thf(fact_8763_sum__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > complex,A: nat,B: nat] :
% 5.02/5.36 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo1517530859248394432omplex
% 5.02/5.36 @ ^ [A5: nat] : ( plus_plus_complex @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ zero_zero_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum_atLeastAtMost_code
% 5.02/5.36 thf(fact_8764_sum__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > rat,A: nat,B: nat] :
% 5.02/5.36 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo1949268297981939178at_rat
% 5.02/5.36 @ ^ [A5: nat] : ( plus_plus_rat @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ zero_zero_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum_atLeastAtMost_code
% 5.02/5.36 thf(fact_8765_sum__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > int,A: nat,B: nat] :
% 5.02/5.36 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo2581907887559384638at_int
% 5.02/5.36 @ ^ [A5: nat] : ( plus_plus_int @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ zero_zero_int ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum_atLeastAtMost_code
% 5.02/5.36 thf(fact_8766_sum__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > nat,A: nat,B: nat] :
% 5.02/5.36 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo2584398358068434914at_nat
% 5.02/5.36 @ ^ [A5: nat] : ( plus_plus_nat @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ zero_zero_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum_atLeastAtMost_code
% 5.02/5.36 thf(fact_8767_sum__atLeastAtMost__code,axiom,
% 5.02/5.36 ! [F: nat > real,A: nat,B: nat] :
% 5.02/5.36 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.02/5.36 = ( set_fo3111899725591712190t_real
% 5.02/5.36 @ ^ [A5: nat] : ( plus_plus_real @ ( F @ A5 ) )
% 5.02/5.36 @ A
% 5.02/5.36 @ B
% 5.02/5.36 @ zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum_atLeastAtMost_code
% 5.02/5.36 thf(fact_8768_pochhammer__Suc__prod__rev,axiom,
% 5.02/5.36 ! [A: real,N2: nat] :
% 5.02/5.36 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( groups129246275422532515t_real
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc_prod_rev
% 5.02/5.36 thf(fact_8769_pochhammer__Suc__prod__rev,axiom,
% 5.02/5.36 ! [A: rat,N2: nat] :
% 5.02/5.36 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( groups73079841787564623at_rat
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc_prod_rev
% 5.02/5.36 thf(fact_8770_pochhammer__Suc__prod__rev,axiom,
% 5.02/5.36 ! [A: nat,N2: nat] :
% 5.02/5.36 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( groups708209901874060359at_nat
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc_prod_rev
% 5.02/5.36 thf(fact_8771_pochhammer__Suc__prod__rev,axiom,
% 5.02/5.36 ! [A: int,N2: nat] :
% 5.02/5.36 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I5 ) ) )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % pochhammer_Suc_prod_rev
% 5.02/5.36 thf(fact_8772_gbinomial__pochhammer,axiom,
% 5.02/5.36 ( gbinomial_complex
% 5.02/5.36 = ( ^ [A5: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A5 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_pochhammer
% 5.02/5.36 thf(fact_8773_gbinomial__pochhammer,axiom,
% 5.02/5.36 ( gbinomial_rat
% 5.02/5.36 = ( ^ [A5: 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 @ A5 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_pochhammer
% 5.02/5.36 thf(fact_8774_gbinomial__pochhammer,axiom,
% 5.02/5.36 ( gbinomial_real
% 5.02/5.36 = ( ^ [A5: 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 @ A5 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_pochhammer
% 5.02/5.36 thf(fact_8775_gbinomial__pochhammer_H,axiom,
% 5.02/5.36 ( gbinomial_complex
% 5.02/5.36 = ( ^ [A5: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A5 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_pochhammer'
% 5.02/5.36 thf(fact_8776_gbinomial__pochhammer_H,axiom,
% 5.02/5.36 ( gbinomial_rat
% 5.02/5.36 = ( ^ [A5: rat,K3: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ K3 ) ) @ one_one_rat ) @ K3 ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_pochhammer'
% 5.02/5.36 thf(fact_8777_gbinomial__pochhammer_H,axiom,
% 5.02/5.36 ( gbinomial_real
% 5.02/5.36 = ( ^ [A5: real,K3: nat] : ( divide_divide_real @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ A5 @ ( semiri5074537144036343181t_real @ K3 ) ) @ one_one_real ) @ K3 ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_pochhammer'
% 5.02/5.36 thf(fact_8778_gbinomial__sum__up__index,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( groups2073611262835488442omplex
% 5.02/5.36 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.36 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_sum_up_index
% 5.02/5.36 thf(fact_8779_gbinomial__sum__up__index,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( groups2906978787729119204at_rat
% 5.02/5.36 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.36 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_sum_up_index
% 5.02/5.36 thf(fact_8780_gbinomial__sum__up__index,axiom,
% 5.02/5.36 ! [K: nat,N2: nat] :
% 5.02/5.36 ( ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.02/5.36 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.36 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_sum_up_index
% 5.02/5.36 thf(fact_8781_gbinomial__absorption_H,axiom,
% 5.02/5.36 ! [K: nat,A: complex] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.36 => ( ( gbinomial_complex @ A @ K )
% 5.02/5.36 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorption'
% 5.02/5.36 thf(fact_8782_gbinomial__absorption_H,axiom,
% 5.02/5.36 ! [K: nat,A: real] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.36 => ( ( gbinomial_real @ A @ K )
% 5.02/5.36 = ( 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 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorption'
% 5.02/5.36 thf(fact_8783_gbinomial__absorption_H,axiom,
% 5.02/5.36 ! [K: nat,A: rat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.36 => ( ( gbinomial_rat @ A @ K )
% 5.02/5.36 = ( 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 ) ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_absorption'
% 5.02/5.36 thf(fact_8784_fact__code,axiom,
% 5.02/5.36 ( semiri1406184849735516958ct_int
% 5.02/5.36 = ( ^ [N3: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_code
% 5.02/5.36 thf(fact_8785_fact__code,axiom,
% 5.02/5.36 ( semiri773545260158071498ct_rat
% 5.02/5.36 = ( ^ [N3: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_code
% 5.02/5.36 thf(fact_8786_fact__code,axiom,
% 5.02/5.36 ( semiri2265585572941072030t_real
% 5.02/5.36 = ( ^ [N3: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_code
% 5.02/5.36 thf(fact_8787_fact__code,axiom,
% 5.02/5.36 ( semiri1408675320244567234ct_nat
% 5.02/5.36 = ( ^ [N3: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % fact_code
% 5.02/5.36 thf(fact_8788_gbinomial__partial__row__sum,axiom,
% 5.02/5.36 ! [A: complex,M: nat] :
% 5.02/5.36 ( ( groups2073611262835488442omplex
% 5.02/5.36 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.02/5.36 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.36 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_partial_row_sum
% 5.02/5.36 thf(fact_8789_gbinomial__partial__row__sum,axiom,
% 5.02/5.36 ! [A: rat,M: nat] :
% 5.02/5.36 ( ( groups2906978787729119204at_rat
% 5.02/5.36 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.02/5.36 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.36 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_partial_row_sum
% 5.02/5.36 thf(fact_8790_gbinomial__partial__row__sum,axiom,
% 5.02/5.36 ! [A: real,M: nat] :
% 5.02/5.36 ( ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.02/5.36 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.36 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_partial_row_sum
% 5.02/5.36 thf(fact_8791_choose__odd__sum,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.02/5.36 @ ( groups2073611262835488442omplex
% 5.02/5.36 @ ^ [I5: nat] :
% 5.02/5.36 ( if_complex
% 5.02/5.36 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.02/5.36 @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) )
% 5.02/5.36 @ zero_zero_complex )
% 5.02/5.36 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.36 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_odd_sum
% 5.02/5.36 thf(fact_8792_choose__odd__sum,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.02/5.36 @ ( groups3539618377306564664at_int
% 5.02/5.36 @ ^ [I5: nat] :
% 5.02/5.36 ( if_int
% 5.02/5.36 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.02/5.36 @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) )
% 5.02/5.36 @ zero_zero_int )
% 5.02/5.36 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.36 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_odd_sum
% 5.02/5.36 thf(fact_8793_choose__odd__sum,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.02/5.36 @ ( groups2906978787729119204at_rat
% 5.02/5.36 @ ^ [I5: nat] :
% 5.02/5.36 ( if_rat
% 5.02/5.36 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.02/5.36 @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) )
% 5.02/5.36 @ zero_zero_rat )
% 5.02/5.36 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.36 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_odd_sum
% 5.02/5.36 thf(fact_8794_choose__odd__sum,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [I5: nat] :
% 5.02/5.36 ( if_real
% 5.02/5.36 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 )
% 5.02/5.36 @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) )
% 5.02/5.36 @ zero_zero_real )
% 5.02/5.36 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.36 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_odd_sum
% 5.02/5.36 thf(fact_8795_choose__even__sum,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.02/5.36 @ ( groups2073611262835488442omplex
% 5.02/5.36 @ ^ [I5: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I5 ) ) @ zero_zero_complex )
% 5.02/5.36 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.36 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_even_sum
% 5.02/5.36 thf(fact_8796_choose__even__sum,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.02/5.36 @ ( groups3539618377306564664at_int
% 5.02/5.36 @ ^ [I5: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I5 ) ) @ zero_zero_int )
% 5.02/5.36 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.36 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_even_sum
% 5.02/5.36 thf(fact_8797_choose__even__sum,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.02/5.36 @ ( groups2906978787729119204at_rat
% 5.02/5.36 @ ^ [I5: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I5 ) ) @ zero_zero_rat )
% 5.02/5.36 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.36 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_even_sum
% 5.02/5.36 thf(fact_8798_choose__even__sum,axiom,
% 5.02/5.36 ! [N2: nat] :
% 5.02/5.36 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.36 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I5 ) ) @ zero_zero_real )
% 5.02/5.36 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.36 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % choose_even_sum
% 5.02/5.36 thf(fact_8799_gbinomial__r__part__sum,axiom,
% 5.02/5.36 ! [M: nat] :
% 5.02/5.36 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.36 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_r_part_sum
% 5.02/5.36 thf(fact_8800_gbinomial__r__part__sum,axiom,
% 5.02/5.36 ! [M: nat] :
% 5.02/5.36 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.36 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_r_part_sum
% 5.02/5.36 thf(fact_8801_gbinomial__r__part__sum,axiom,
% 5.02/5.36 ! [M: nat] :
% 5.02/5.36 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.36 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % gbinomial_r_part_sum
% 5.02/5.36 thf(fact_8802_Maclaurin__sin__bound,axiom,
% 5.02/5.36 ! [X2: real,N2: nat] :
% 5.02/5.36 ( ord_less_eq_real
% 5.02/5.36 @ ( abs_abs_real
% 5.02/5.36 @ ( minus_minus_real @ ( sin_real @ X2 )
% 5.02/5.36 @ ( groups6591440286371151544t_real
% 5.02/5.36 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.36 @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.02/5.36 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( abs_abs_real @ X2 ) @ N2 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Maclaurin_sin_bound
% 5.02/5.36 thf(fact_8803_inverse__eq__iff__eq,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( ( inverse_inverse_real @ A )
% 5.02/5.36 = ( inverse_inverse_real @ B ) )
% 5.02/5.36 = ( A = B ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_iff_eq
% 5.02/5.36 thf(fact_8804_inverse__eq__iff__eq,axiom,
% 5.02/5.36 ! [A: complex,B: complex] :
% 5.02/5.36 ( ( ( invers8013647133539491842omplex @ A )
% 5.02/5.36 = ( invers8013647133539491842omplex @ B ) )
% 5.02/5.36 = ( A = B ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_iff_eq
% 5.02/5.36 thf(fact_8805_inverse__eq__iff__eq,axiom,
% 5.02/5.36 ! [A: rat,B: rat] :
% 5.02/5.36 ( ( ( inverse_inverse_rat @ A )
% 5.02/5.36 = ( inverse_inverse_rat @ B ) )
% 5.02/5.36 = ( A = B ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_iff_eq
% 5.02/5.36 thf(fact_8806_inverse__inverse__eq,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.02/5.36 = A ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_inverse_eq
% 5.02/5.36 thf(fact_8807_inverse__inverse__eq,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.02/5.36 = A ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_inverse_eq
% 5.02/5.36 thf(fact_8808_inverse__inverse__eq,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.02/5.36 = A ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_inverse_eq
% 5.02/5.36 thf(fact_8809_inverse__zero,axiom,
% 5.02/5.36 ( ( inverse_inverse_real @ zero_zero_real )
% 5.02/5.36 = zero_zero_real ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_zero
% 5.02/5.36 thf(fact_8810_inverse__zero,axiom,
% 5.02/5.36 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.02/5.36 = zero_zero_complex ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_zero
% 5.02/5.36 thf(fact_8811_inverse__zero,axiom,
% 5.02/5.36 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.02/5.36 = zero_zero_rat ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_zero
% 5.02/5.36 thf(fact_8812_inverse__nonzero__iff__nonzero,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( ( inverse_inverse_real @ A )
% 5.02/5.36 = zero_zero_real )
% 5.02/5.36 = ( A = zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_nonzero_iff_nonzero
% 5.02/5.36 thf(fact_8813_inverse__nonzero__iff__nonzero,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( ( invers8013647133539491842omplex @ A )
% 5.02/5.36 = zero_zero_complex )
% 5.02/5.36 = ( A = zero_zero_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_nonzero_iff_nonzero
% 5.02/5.36 thf(fact_8814_inverse__nonzero__iff__nonzero,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( ( inverse_inverse_rat @ A )
% 5.02/5.36 = zero_zero_rat )
% 5.02/5.36 = ( A = zero_zero_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_nonzero_iff_nonzero
% 5.02/5.36 thf(fact_8815_inverse__mult__distrib,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.02/5.36 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_mult_distrib
% 5.02/5.36 thf(fact_8816_inverse__mult__distrib,axiom,
% 5.02/5.36 ! [A: complex,B: complex] :
% 5.02/5.36 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.02/5.36 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_mult_distrib
% 5.02/5.36 thf(fact_8817_inverse__mult__distrib,axiom,
% 5.02/5.36 ! [A: rat,B: rat] :
% 5.02/5.36 ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.02/5.36 = ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_mult_distrib
% 5.02/5.36 thf(fact_8818_inverse__eq__1__iff,axiom,
% 5.02/5.36 ! [X2: real] :
% 5.02/5.36 ( ( ( inverse_inverse_real @ X2 )
% 5.02/5.36 = one_one_real )
% 5.02/5.36 = ( X2 = one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_1_iff
% 5.02/5.36 thf(fact_8819_inverse__eq__1__iff,axiom,
% 5.02/5.36 ! [X2: complex] :
% 5.02/5.36 ( ( ( invers8013647133539491842omplex @ X2 )
% 5.02/5.36 = one_one_complex )
% 5.02/5.36 = ( X2 = one_one_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_1_iff
% 5.02/5.36 thf(fact_8820_inverse__eq__1__iff,axiom,
% 5.02/5.36 ! [X2: rat] :
% 5.02/5.36 ( ( ( inverse_inverse_rat @ X2 )
% 5.02/5.36 = one_one_rat )
% 5.02/5.36 = ( X2 = one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_1_iff
% 5.02/5.36 thf(fact_8821_inverse__1,axiom,
% 5.02/5.36 ( ( inverse_inverse_real @ one_one_real )
% 5.02/5.36 = one_one_real ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_1
% 5.02/5.36 thf(fact_8822_inverse__1,axiom,
% 5.02/5.36 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.02/5.36 = one_one_complex ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_1
% 5.02/5.36 thf(fact_8823_inverse__1,axiom,
% 5.02/5.36 ( ( inverse_inverse_rat @ one_one_rat )
% 5.02/5.36 = one_one_rat ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_1
% 5.02/5.36 thf(fact_8824_atMost__iff,axiom,
% 5.02/5.36 ! [I3: real,K: real] :
% 5.02/5.36 ( ( member_real @ I3 @ ( set_ord_atMost_real @ K ) )
% 5.02/5.36 = ( ord_less_eq_real @ I3 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_iff
% 5.02/5.36 thf(fact_8825_atMost__iff,axiom,
% 5.02/5.36 ! [I3: set_nat,K: set_nat] :
% 5.02/5.36 ( ( member_set_nat @ I3 @ ( set_or4236626031148496127et_nat @ K ) )
% 5.02/5.36 = ( ord_less_eq_set_nat @ I3 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_iff
% 5.02/5.36 thf(fact_8826_atMost__iff,axiom,
% 5.02/5.36 ! [I3: rat,K: rat] :
% 5.02/5.36 ( ( member_rat @ I3 @ ( set_ord_atMost_rat @ K ) )
% 5.02/5.36 = ( ord_less_eq_rat @ I3 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_iff
% 5.02/5.36 thf(fact_8827_atMost__iff,axiom,
% 5.02/5.36 ! [I3: num,K: num] :
% 5.02/5.36 ( ( member_num @ I3 @ ( set_ord_atMost_num @ K ) )
% 5.02/5.36 = ( ord_less_eq_num @ I3 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_iff
% 5.02/5.36 thf(fact_8828_atMost__iff,axiom,
% 5.02/5.36 ! [I3: int,K: int] :
% 5.02/5.36 ( ( member_int @ I3 @ ( set_ord_atMost_int @ K ) )
% 5.02/5.36 = ( ord_less_eq_int @ I3 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_iff
% 5.02/5.36 thf(fact_8829_atMost__iff,axiom,
% 5.02/5.36 ! [I3: nat,K: nat] :
% 5.02/5.36 ( ( member_nat @ I3 @ ( set_ord_atMost_nat @ K ) )
% 5.02/5.36 = ( ord_less_eq_nat @ I3 @ K ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_iff
% 5.02/5.36 thf(fact_8830_inverse__divide,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.02/5.36 = ( divide_divide_real @ B @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_divide
% 5.02/5.36 thf(fact_8831_inverse__divide,axiom,
% 5.02/5.36 ! [A: complex,B: complex] :
% 5.02/5.36 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.36 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_divide
% 5.02/5.36 thf(fact_8832_inverse__divide,axiom,
% 5.02/5.36 ! [A: rat,B: rat] :
% 5.02/5.36 ( ( inverse_inverse_rat @ ( divide_divide_rat @ A @ B ) )
% 5.02/5.36 = ( divide_divide_rat @ B @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_divide
% 5.02/5.36 thf(fact_8833_inverse__minus__eq,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.02/5.36 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_minus_eq
% 5.02/5.36 thf(fact_8834_inverse__minus__eq,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.02/5.36 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_minus_eq
% 5.02/5.36 thf(fact_8835_inverse__minus__eq,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.02/5.36 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_minus_eq
% 5.02/5.36 thf(fact_8836_abs__inverse,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.02/5.36 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % abs_inverse
% 5.02/5.36 thf(fact_8837_abs__inverse,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( abs_abs_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.02/5.36 = ( invers8013647133539491842omplex @ ( abs_abs_complex @ A ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % abs_inverse
% 5.02/5.36 thf(fact_8838_abs__inverse,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.02/5.36 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % abs_inverse
% 5.02/5.36 thf(fact_8839_inverse__nonpositive__iff__nonpositive,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.02/5.36 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_nonpositive_iff_nonpositive
% 5.02/5.36 thf(fact_8840_inverse__nonpositive__iff__nonpositive,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.02/5.36 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_nonpositive_iff_nonpositive
% 5.02/5.36 thf(fact_8841_inverse__nonnegative__iff__nonnegative,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.02/5.36 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_nonnegative_iff_nonnegative
% 5.02/5.36 thf(fact_8842_inverse__nonnegative__iff__nonnegative,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.02/5.36 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_nonnegative_iff_nonnegative
% 5.02/5.36 thf(fact_8843_inverse__positive__iff__positive,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.02/5.36 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_positive_iff_positive
% 5.02/5.36 thf(fact_8844_inverse__positive__iff__positive,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.02/5.36 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_positive_iff_positive
% 5.02/5.36 thf(fact_8845_inverse__negative__iff__negative,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.02/5.36 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_negative_iff_negative
% 5.02/5.36 thf(fact_8846_inverse__negative__iff__negative,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.02/5.36 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_negative_iff_negative
% 5.02/5.36 thf(fact_8847_inverse__less__iff__less__neg,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( ord_less_real @ A @ zero_zero_real )
% 5.02/5.36 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.02/5.36 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.36 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_less_iff_less_neg
% 5.02/5.36 thf(fact_8848_inverse__less__iff__less__neg,axiom,
% 5.02/5.36 ! [A: rat,B: rat] :
% 5.02/5.36 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.02/5.36 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.02/5.36 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.36 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_less_iff_less_neg
% 5.02/5.36 thf(fact_8849_inverse__less__iff__less,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.36 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.36 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.36 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_less_iff_less
% 5.02/5.36 thf(fact_8850_inverse__less__iff__less,axiom,
% 5.02/5.36 ! [A: rat,B: rat] :
% 5.02/5.36 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.36 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.02/5.36 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.36 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_less_iff_less
% 5.02/5.36 thf(fact_8851_atMost__subset__iff,axiom,
% 5.02/5.36 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.36 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X2 ) @ ( set_or4236626031148496127et_nat @ Y ) )
% 5.02/5.36 = ( ord_less_eq_set_nat @ X2 @ Y ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_subset_iff
% 5.02/5.36 thf(fact_8852_atMost__subset__iff,axiom,
% 5.02/5.36 ! [X2: rat,Y: rat] :
% 5.02/5.36 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X2 ) @ ( set_ord_atMost_rat @ Y ) )
% 5.02/5.36 = ( ord_less_eq_rat @ X2 @ Y ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_subset_iff
% 5.02/5.36 thf(fact_8853_atMost__subset__iff,axiom,
% 5.02/5.36 ! [X2: num,Y: num] :
% 5.02/5.36 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X2 ) @ ( set_ord_atMost_num @ Y ) )
% 5.02/5.36 = ( ord_less_eq_num @ X2 @ Y ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_subset_iff
% 5.02/5.36 thf(fact_8854_atMost__subset__iff,axiom,
% 5.02/5.36 ! [X2: int,Y: int] :
% 5.02/5.36 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X2 ) @ ( set_ord_atMost_int @ Y ) )
% 5.02/5.36 = ( ord_less_eq_int @ X2 @ Y ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_subset_iff
% 5.02/5.36 thf(fact_8855_atMost__subset__iff,axiom,
% 5.02/5.36 ! [X2: nat,Y: nat] :
% 5.02/5.36 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X2 ) @ ( set_ord_atMost_nat @ Y ) )
% 5.02/5.36 = ( ord_less_eq_nat @ X2 @ Y ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_subset_iff
% 5.02/5.36 thf(fact_8856_inverse__le__iff__le__neg,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( ord_less_real @ A @ zero_zero_real )
% 5.02/5.36 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.36 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_le_iff_le_neg
% 5.02/5.36 thf(fact_8857_inverse__le__iff__le__neg,axiom,
% 5.02/5.36 ! [A: rat,B: rat] :
% 5.02/5.36 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.02/5.36 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.02/5.36 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.36 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_le_iff_le_neg
% 5.02/5.36 thf(fact_8858_inverse__le__iff__le,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.36 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.36 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.36 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_le_iff_le
% 5.02/5.36 thf(fact_8859_inverse__le__iff__le,axiom,
% 5.02/5.36 ! [A: rat,B: rat] :
% 5.02/5.36 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.36 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.02/5.36 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.36 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_le_iff_le
% 5.02/5.36 thf(fact_8860_left__inverse,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( A != zero_zero_real )
% 5.02/5.36 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.02/5.36 = one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % left_inverse
% 5.02/5.36 thf(fact_8861_left__inverse,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( A != zero_zero_complex )
% 5.02/5.36 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.02/5.36 = one_one_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % left_inverse
% 5.02/5.36 thf(fact_8862_left__inverse,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( A != zero_zero_rat )
% 5.02/5.36 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.02/5.36 = one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % left_inverse
% 5.02/5.36 thf(fact_8863_right__inverse,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( A != zero_zero_real )
% 5.02/5.36 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.02/5.36 = one_one_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % right_inverse
% 5.02/5.36 thf(fact_8864_right__inverse,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( A != zero_zero_complex )
% 5.02/5.36 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.02/5.36 = one_one_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % right_inverse
% 5.02/5.36 thf(fact_8865_right__inverse,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( A != zero_zero_rat )
% 5.02/5.36 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 5.02/5.36 = one_one_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % right_inverse
% 5.02/5.36 thf(fact_8866_inverse__eq__divide__numeral,axiom,
% 5.02/5.36 ! [W: num] :
% 5.02/5.36 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 5.02/5.36 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_divide_numeral
% 5.02/5.36 thf(fact_8867_inverse__eq__divide__numeral,axiom,
% 5.02/5.36 ! [W: num] :
% 5.02/5.36 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.02/5.36 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_divide_numeral
% 5.02/5.36 thf(fact_8868_inverse__eq__divide__numeral,axiom,
% 5.02/5.36 ! [W: num] :
% 5.02/5.36 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 5.02/5.36 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_divide_numeral
% 5.02/5.36 thf(fact_8869_Icc__subset__Iic__iff,axiom,
% 5.02/5.36 ! [L: set_nat,H2: set_nat,H3: set_nat] :
% 5.02/5.36 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H2 ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 5.02/5.36 = ( ~ ( ord_less_eq_set_nat @ L @ H2 )
% 5.02/5.36 | ( ord_less_eq_set_nat @ H2 @ H3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Icc_subset_Iic_iff
% 5.02/5.36 thf(fact_8870_Icc__subset__Iic__iff,axiom,
% 5.02/5.36 ! [L: rat,H2: rat,H3: rat] :
% 5.02/5.36 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H2 ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.02/5.36 = ( ~ ( ord_less_eq_rat @ L @ H2 )
% 5.02/5.36 | ( ord_less_eq_rat @ H2 @ H3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Icc_subset_Iic_iff
% 5.02/5.36 thf(fact_8871_Icc__subset__Iic__iff,axiom,
% 5.02/5.36 ! [L: num,H2: num,H3: num] :
% 5.02/5.36 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H2 ) @ ( set_ord_atMost_num @ H3 ) )
% 5.02/5.36 = ( ~ ( ord_less_eq_num @ L @ H2 )
% 5.02/5.36 | ( ord_less_eq_num @ H2 @ H3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Icc_subset_Iic_iff
% 5.02/5.36 thf(fact_8872_Icc__subset__Iic__iff,axiom,
% 5.02/5.36 ! [L: nat,H2: nat,H3: nat] :
% 5.02/5.36 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H2 ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.02/5.36 = ( ~ ( ord_less_eq_nat @ L @ H2 )
% 5.02/5.36 | ( ord_less_eq_nat @ H2 @ H3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Icc_subset_Iic_iff
% 5.02/5.36 thf(fact_8873_Icc__subset__Iic__iff,axiom,
% 5.02/5.36 ! [L: int,H2: int,H3: int] :
% 5.02/5.36 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H2 ) @ ( set_ord_atMost_int @ H3 ) )
% 5.02/5.36 = ( ~ ( ord_less_eq_int @ L @ H2 )
% 5.02/5.36 | ( ord_less_eq_int @ H2 @ H3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Icc_subset_Iic_iff
% 5.02/5.36 thf(fact_8874_Icc__subset__Iic__iff,axiom,
% 5.02/5.36 ! [L: real,H2: real,H3: real] :
% 5.02/5.36 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H2 ) @ ( set_ord_atMost_real @ H3 ) )
% 5.02/5.36 = ( ~ ( ord_less_eq_real @ L @ H2 )
% 5.02/5.36 | ( ord_less_eq_real @ H2 @ H3 ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % Icc_subset_Iic_iff
% 5.02/5.36 thf(fact_8875_sum_OatMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > rat,N2: nat] :
% 5.02/5.36 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum.atMost_Suc
% 5.02/5.36 thf(fact_8876_sum_OatMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > int,N2: nat] :
% 5.02/5.36 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum.atMost_Suc
% 5.02/5.36 thf(fact_8877_sum_OatMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > nat,N2: nat] :
% 5.02/5.36 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum.atMost_Suc
% 5.02/5.36 thf(fact_8878_sum_OatMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > real,N2: nat] :
% 5.02/5.36 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % sum.atMost_Suc
% 5.02/5.36 thf(fact_8879_prod_OatMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > real,N2: nat] :
% 5.02/5.36 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atMost_Suc
% 5.02/5.36 thf(fact_8880_prod_OatMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > rat,N2: nat] :
% 5.02/5.36 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atMost_Suc
% 5.02/5.36 thf(fact_8881_prod_OatMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > nat,N2: nat] :
% 5.02/5.36 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atMost_Suc
% 5.02/5.36 thf(fact_8882_prod_OatMost__Suc,axiom,
% 5.02/5.36 ! [G: nat > int,N2: nat] :
% 5.02/5.36 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.36 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % prod.atMost_Suc
% 5.02/5.36 thf(fact_8883_atMost__0,axiom,
% 5.02/5.36 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.02/5.36 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.02/5.36
% 5.02/5.36 % atMost_0
% 5.02/5.36 thf(fact_8884_inverse__eq__divide__neg__numeral,axiom,
% 5.02/5.36 ! [W: num] :
% 5.02/5.36 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.02/5.36 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_divide_neg_numeral
% 5.02/5.36 thf(fact_8885_inverse__eq__divide__neg__numeral,axiom,
% 5.02/5.36 ! [W: num] :
% 5.02/5.36 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.02/5.36 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_divide_neg_numeral
% 5.02/5.36 thf(fact_8886_inverse__eq__divide__neg__numeral,axiom,
% 5.02/5.36 ! [W: num] :
% 5.02/5.36 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.02/5.36 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_divide_neg_numeral
% 5.02/5.36 thf(fact_8887_int__prod,axiom,
% 5.02/5.36 ! [F: int > nat,A3: set_int] :
% 5.02/5.36 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups1705073143266064639nt_int
% 5.02/5.36 @ ^ [X: int] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % int_prod
% 5.02/5.36 thf(fact_8888_int__prod,axiom,
% 5.02/5.36 ! [F: nat > nat,A3: set_nat] :
% 5.02/5.36 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.02/5.36 = ( groups705719431365010083at_int
% 5.02/5.36 @ ^ [X: nat] : ( semiri1314217659103216013at_int @ ( F @ X ) )
% 5.02/5.36 @ A3 ) ) ).
% 5.02/5.36
% 5.02/5.36 % int_prod
% 5.02/5.36 thf(fact_8889_inverse__eq__imp__eq,axiom,
% 5.02/5.36 ! [A: real,B: real] :
% 5.02/5.36 ( ( ( inverse_inverse_real @ A )
% 5.02/5.36 = ( inverse_inverse_real @ B ) )
% 5.02/5.36 => ( A = B ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_imp_eq
% 5.02/5.36 thf(fact_8890_inverse__eq__imp__eq,axiom,
% 5.02/5.36 ! [A: complex,B: complex] :
% 5.02/5.36 ( ( ( invers8013647133539491842omplex @ A )
% 5.02/5.36 = ( invers8013647133539491842omplex @ B ) )
% 5.02/5.36 => ( A = B ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_imp_eq
% 5.02/5.36 thf(fact_8891_inverse__eq__imp__eq,axiom,
% 5.02/5.36 ! [A: rat,B: rat] :
% 5.02/5.36 ( ( ( inverse_inverse_rat @ A )
% 5.02/5.36 = ( inverse_inverse_rat @ B ) )
% 5.02/5.36 => ( A = B ) ) ).
% 5.02/5.36
% 5.02/5.36 % inverse_eq_imp_eq
% 5.02/5.36 thf(fact_8892_nonzero__imp__inverse__nonzero,axiom,
% 5.02/5.36 ! [A: real] :
% 5.02/5.36 ( ( A != zero_zero_real )
% 5.02/5.36 => ( ( inverse_inverse_real @ A )
% 5.02/5.36 != zero_zero_real ) ) ).
% 5.02/5.36
% 5.02/5.36 % nonzero_imp_inverse_nonzero
% 5.02/5.36 thf(fact_8893_nonzero__imp__inverse__nonzero,axiom,
% 5.02/5.36 ! [A: complex] :
% 5.02/5.36 ( ( A != zero_zero_complex )
% 5.02/5.36 => ( ( invers8013647133539491842omplex @ A )
% 5.02/5.36 != zero_zero_complex ) ) ).
% 5.02/5.36
% 5.02/5.36 % nonzero_imp_inverse_nonzero
% 5.02/5.36 thf(fact_8894_nonzero__imp__inverse__nonzero,axiom,
% 5.02/5.36 ! [A: rat] :
% 5.02/5.36 ( ( A != zero_zero_rat )
% 5.02/5.36 => ( ( inverse_inverse_rat @ A )
% 5.02/5.36 != zero_zero_rat ) ) ).
% 5.02/5.36
% 5.02/5.36 % nonzero_imp_inverse_nonzero
% 5.02/5.37 thf(fact_8895_nonzero__inverse__inverse__eq,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.02/5.37 = A ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_inverse_eq
% 5.02/5.37 thf(fact_8896_nonzero__inverse__inverse__eq,axiom,
% 5.02/5.37 ! [A: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.02/5.37 = A ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_inverse_eq
% 5.02/5.37 thf(fact_8897_nonzero__inverse__inverse__eq,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.02/5.37 = A ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_inverse_eq
% 5.02/5.37 thf(fact_8898_nonzero__inverse__eq__imp__eq,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ( inverse_inverse_real @ A )
% 5.02/5.37 = ( inverse_inverse_real @ B ) )
% 5.02/5.37 => ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( B != zero_zero_real )
% 5.02/5.37 => ( A = B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_eq_imp_eq
% 5.02/5.37 thf(fact_8899_nonzero__inverse__eq__imp__eq,axiom,
% 5.02/5.37 ! [A: complex,B: complex] :
% 5.02/5.37 ( ( ( invers8013647133539491842omplex @ A )
% 5.02/5.37 = ( invers8013647133539491842omplex @ B ) )
% 5.02/5.37 => ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( B != zero_zero_complex )
% 5.02/5.37 => ( A = B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_eq_imp_eq
% 5.02/5.37 thf(fact_8900_nonzero__inverse__eq__imp__eq,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ( inverse_inverse_rat @ A )
% 5.02/5.37 = ( inverse_inverse_rat @ B ) )
% 5.02/5.37 => ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( B != zero_zero_rat )
% 5.02/5.37 => ( A = B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_eq_imp_eq
% 5.02/5.37 thf(fact_8901_inverse__zero__imp__zero,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( ( inverse_inverse_real @ A )
% 5.02/5.37 = zero_zero_real )
% 5.02/5.37 => ( A = zero_zero_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_zero_imp_zero
% 5.02/5.37 thf(fact_8902_inverse__zero__imp__zero,axiom,
% 5.02/5.37 ! [A: complex] :
% 5.02/5.37 ( ( ( invers8013647133539491842omplex @ A )
% 5.02/5.37 = zero_zero_complex )
% 5.02/5.37 => ( A = zero_zero_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_zero_imp_zero
% 5.02/5.37 thf(fact_8903_inverse__zero__imp__zero,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( ( inverse_inverse_rat @ A )
% 5.02/5.37 = zero_zero_rat )
% 5.02/5.37 => ( A = zero_zero_rat ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_zero_imp_zero
% 5.02/5.37 thf(fact_8904_field__class_Ofield__inverse__zero,axiom,
% 5.02/5.37 ( ( inverse_inverse_real @ zero_zero_real )
% 5.02/5.37 = zero_zero_real ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_inverse_zero
% 5.02/5.37 thf(fact_8905_field__class_Ofield__inverse__zero,axiom,
% 5.02/5.37 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.02/5.37 = zero_zero_complex ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_inverse_zero
% 5.02/5.37 thf(fact_8906_field__class_Ofield__inverse__zero,axiom,
% 5.02/5.37 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.02/5.37 = zero_zero_rat ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_inverse_zero
% 5.02/5.37 thf(fact_8907_power__inverse,axiom,
% 5.02/5.37 ! [A: real,N2: nat] :
% 5.02/5.37 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N2 )
% 5.02/5.37 = ( inverse_inverse_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_inverse
% 5.02/5.37 thf(fact_8908_power__inverse,axiom,
% 5.02/5.37 ! [A: complex,N2: nat] :
% 5.02/5.37 ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N2 )
% 5.02/5.37 = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_inverse
% 5.02/5.37 thf(fact_8909_power__inverse,axiom,
% 5.02/5.37 ! [A: rat,N2: nat] :
% 5.02/5.37 ( ( power_power_rat @ ( inverse_inverse_rat @ A ) @ N2 )
% 5.02/5.37 = ( inverse_inverse_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_inverse
% 5.02/5.37 thf(fact_8910_nonzero__norm__inverse,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ A ) )
% 5.02/5.37 = ( inverse_inverse_real @ ( real_V7735802525324610683m_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_norm_inverse
% 5.02/5.37 thf(fact_8911_nonzero__norm__inverse,axiom,
% 5.02/5.37 ! [A: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.02/5.37 = ( inverse_inverse_real @ ( real_V1022390504157884413omplex @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_norm_inverse
% 5.02/5.37 thf(fact_8912_mult__commute__imp__mult__inverse__commute,axiom,
% 5.02/5.37 ! [Y: real,X2: real] :
% 5.02/5.37 ( ( ( times_times_real @ Y @ X2 )
% 5.02/5.37 = ( times_times_real @ X2 @ Y ) )
% 5.02/5.37 => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X2 )
% 5.02/5.37 = ( times_times_real @ X2 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_commute_imp_mult_inverse_commute
% 5.02/5.37 thf(fact_8913_mult__commute__imp__mult__inverse__commute,axiom,
% 5.02/5.37 ! [Y: complex,X2: complex] :
% 5.02/5.37 ( ( ( times_times_complex @ Y @ X2 )
% 5.02/5.37 = ( times_times_complex @ X2 @ Y ) )
% 5.02/5.37 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y ) @ X2 )
% 5.02/5.37 = ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_commute_imp_mult_inverse_commute
% 5.02/5.37 thf(fact_8914_mult__commute__imp__mult__inverse__commute,axiom,
% 5.02/5.37 ! [Y: rat,X2: rat] :
% 5.02/5.37 ( ( ( times_times_rat @ Y @ X2 )
% 5.02/5.37 = ( times_times_rat @ X2 @ Y ) )
% 5.02/5.37 => ( ( times_times_rat @ ( inverse_inverse_rat @ Y ) @ X2 )
% 5.02/5.37 = ( times_times_rat @ X2 @ ( inverse_inverse_rat @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_commute_imp_mult_inverse_commute
% 5.02/5.37 thf(fact_8915_atMost__def,axiom,
% 5.02/5.37 ( set_ord_atMost_real
% 5.02/5.37 = ( ^ [U2: real] :
% 5.02/5.37 ( collect_real
% 5.02/5.37 @ ^ [X: real] : ( ord_less_eq_real @ X @ U2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_def
% 5.02/5.37 thf(fact_8916_atMost__def,axiom,
% 5.02/5.37 ( set_or4236626031148496127et_nat
% 5.02/5.37 = ( ^ [U2: set_nat] :
% 5.02/5.37 ( collect_set_nat
% 5.02/5.37 @ ^ [X: set_nat] : ( ord_less_eq_set_nat @ X @ U2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_def
% 5.02/5.37 thf(fact_8917_atMost__def,axiom,
% 5.02/5.37 ( set_ord_atMost_rat
% 5.02/5.37 = ( ^ [U2: rat] :
% 5.02/5.37 ( collect_rat
% 5.02/5.37 @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_def
% 5.02/5.37 thf(fact_8918_atMost__def,axiom,
% 5.02/5.37 ( set_ord_atMost_num
% 5.02/5.37 = ( ^ [U2: num] :
% 5.02/5.37 ( collect_num
% 5.02/5.37 @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_def
% 5.02/5.37 thf(fact_8919_atMost__def,axiom,
% 5.02/5.37 ( set_ord_atMost_int
% 5.02/5.37 = ( ^ [U2: int] :
% 5.02/5.37 ( collect_int
% 5.02/5.37 @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_def
% 5.02/5.37 thf(fact_8920_atMost__def,axiom,
% 5.02/5.37 ( set_ord_atMost_nat
% 5.02/5.37 = ( ^ [U2: nat] :
% 5.02/5.37 ( collect_nat
% 5.02/5.37 @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_def
% 5.02/5.37 thf(fact_8921_positive__imp__inverse__positive,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % positive_imp_inverse_positive
% 5.02/5.37 thf(fact_8922_positive__imp__inverse__positive,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.37 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % positive_imp_inverse_positive
% 5.02/5.37 thf(fact_8923_negative__imp__inverse__negative,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( ord_less_real @ A @ zero_zero_real )
% 5.02/5.37 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % negative_imp_inverse_negative
% 5.02/5.37 thf(fact_8924_negative__imp__inverse__negative,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.02/5.37 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 5.02/5.37
% 5.02/5.37 % negative_imp_inverse_negative
% 5.02/5.37 thf(fact_8925_inverse__positive__imp__positive,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.02/5.37 => ( ( A != zero_zero_real )
% 5.02/5.37 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_positive_imp_positive
% 5.02/5.37 thf(fact_8926_inverse__positive__imp__positive,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.02/5.37 => ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_positive_imp_positive
% 5.02/5.37 thf(fact_8927_inverse__negative__imp__negative,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.02/5.37 => ( ( A != zero_zero_real )
% 5.02/5.37 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_negative_imp_negative
% 5.02/5.37 thf(fact_8928_inverse__negative__imp__negative,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.02/5.37 => ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_negative_imp_negative
% 5.02/5.37 thf(fact_8929_less__imp__inverse__less__neg,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_real @ A @ B )
% 5.02/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.02/5.37 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % less_imp_inverse_less_neg
% 5.02/5.37 thf(fact_8930_less__imp__inverse__less__neg,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_rat @ A @ B )
% 5.02/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.02/5.37 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % less_imp_inverse_less_neg
% 5.02/5.37 thf(fact_8931_inverse__less__imp__less__neg,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.02/5.37 => ( ord_less_real @ B @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_less_imp_less_neg
% 5.02/5.37 thf(fact_8932_inverse__less__imp__less__neg,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.02/5.37 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_less_imp_less_neg
% 5.02/5.37 thf(fact_8933_less__imp__inverse__less,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_real @ A @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % less_imp_inverse_less
% 5.02/5.37 thf(fact_8934_less__imp__inverse__less,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_rat @ A @ B )
% 5.02/5.37 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.37 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % less_imp_inverse_less
% 5.02/5.37 thf(fact_8935_inverse__less__imp__less,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ord_less_real @ B @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_less_imp_less
% 5.02/5.37 thf(fact_8936_inverse__less__imp__less,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.37 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_less_imp_less
% 5.02/5.37 thf(fact_8937_nonzero__inverse__mult__distrib,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( B != zero_zero_real )
% 5.02/5.37 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.02/5.37 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_mult_distrib
% 5.02/5.37 thf(fact_8938_nonzero__inverse__mult__distrib,axiom,
% 5.02/5.37 ! [A: complex,B: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( B != zero_zero_complex )
% 5.02/5.37 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.02/5.37 = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_mult_distrib
% 5.02/5.37 thf(fact_8939_nonzero__inverse__mult__distrib,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( B != zero_zero_rat )
% 5.02/5.37 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.02/5.37 = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_mult_distrib
% 5.02/5.37 thf(fact_8940_nonzero__inverse__minus__eq,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.02/5.37 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_minus_eq
% 5.02/5.37 thf(fact_8941_nonzero__inverse__minus__eq,axiom,
% 5.02/5.37 ! [A: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_minus_eq
% 5.02/5.37 thf(fact_8942_nonzero__inverse__minus__eq,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.02/5.37 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_minus_eq
% 5.02/5.37 thf(fact_8943_inverse__numeral__1,axiom,
% 5.02/5.37 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.02/5.37 = ( numeral_numeral_real @ one ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_numeral_1
% 5.02/5.37 thf(fact_8944_inverse__numeral__1,axiom,
% 5.02/5.37 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.02/5.37 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_numeral_1
% 5.02/5.37 thf(fact_8945_inverse__numeral__1,axiom,
% 5.02/5.37 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ one ) )
% 5.02/5.37 = ( numeral_numeral_rat @ one ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_numeral_1
% 5.02/5.37 thf(fact_8946_inverse__unique,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ( times_times_real @ A @ B )
% 5.02/5.37 = one_one_real )
% 5.02/5.37 => ( ( inverse_inverse_real @ A )
% 5.02/5.37 = B ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_unique
% 5.02/5.37 thf(fact_8947_inverse__unique,axiom,
% 5.02/5.37 ! [A: complex,B: complex] :
% 5.02/5.37 ( ( ( times_times_complex @ A @ B )
% 5.02/5.37 = one_one_complex )
% 5.02/5.37 => ( ( invers8013647133539491842omplex @ A )
% 5.02/5.37 = B ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_unique
% 5.02/5.37 thf(fact_8948_inverse__unique,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ( times_times_rat @ A @ B )
% 5.02/5.37 = one_one_rat )
% 5.02/5.37 => ( ( inverse_inverse_rat @ A )
% 5.02/5.37 = B ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_unique
% 5.02/5.37 thf(fact_8949_field__class_Ofield__divide__inverse,axiom,
% 5.02/5.37 ( divide_divide_real
% 5.02/5.37 = ( ^ [A5: real,B5: real] : ( times_times_real @ A5 @ ( inverse_inverse_real @ B5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_divide_inverse
% 5.02/5.37 thf(fact_8950_field__class_Ofield__divide__inverse,axiom,
% 5.02/5.37 ( divide1717551699836669952omplex
% 5.02/5.37 = ( ^ [A5: complex,B5: complex] : ( times_times_complex @ A5 @ ( invers8013647133539491842omplex @ B5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_divide_inverse
% 5.02/5.37 thf(fact_8951_field__class_Ofield__divide__inverse,axiom,
% 5.02/5.37 ( divide_divide_rat
% 5.02/5.37 = ( ^ [A5: rat,B5: rat] : ( times_times_rat @ A5 @ ( inverse_inverse_rat @ B5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_divide_inverse
% 5.02/5.37 thf(fact_8952_divide__inverse,axiom,
% 5.02/5.37 ( divide_divide_real
% 5.02/5.37 = ( ^ [A5: real,B5: real] : ( times_times_real @ A5 @ ( inverse_inverse_real @ B5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_inverse
% 5.02/5.37 thf(fact_8953_divide__inverse,axiom,
% 5.02/5.37 ( divide1717551699836669952omplex
% 5.02/5.37 = ( ^ [A5: complex,B5: complex] : ( times_times_complex @ A5 @ ( invers8013647133539491842omplex @ B5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_inverse
% 5.02/5.37 thf(fact_8954_divide__inverse,axiom,
% 5.02/5.37 ( divide_divide_rat
% 5.02/5.37 = ( ^ [A5: rat,B5: rat] : ( times_times_rat @ A5 @ ( inverse_inverse_rat @ B5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_inverse
% 5.02/5.37 thf(fact_8955_divide__inverse__commute,axiom,
% 5.02/5.37 ( divide_divide_real
% 5.02/5.37 = ( ^ [A5: real,B5: real] : ( times_times_real @ ( inverse_inverse_real @ B5 ) @ A5 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_inverse_commute
% 5.02/5.37 thf(fact_8956_divide__inverse__commute,axiom,
% 5.02/5.37 ( divide1717551699836669952omplex
% 5.02/5.37 = ( ^ [A5: complex,B5: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B5 ) @ A5 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_inverse_commute
% 5.02/5.37 thf(fact_8957_divide__inverse__commute,axiom,
% 5.02/5.37 ( divide_divide_rat
% 5.02/5.37 = ( ^ [A5: rat,B5: rat] : ( times_times_rat @ ( inverse_inverse_rat @ B5 ) @ A5 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_inverse_commute
% 5.02/5.37 thf(fact_8958_inverse__eq__divide,axiom,
% 5.02/5.37 ( inverse_inverse_real
% 5.02/5.37 = ( divide_divide_real @ one_one_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_eq_divide
% 5.02/5.37 thf(fact_8959_inverse__eq__divide,axiom,
% 5.02/5.37 ( invers8013647133539491842omplex
% 5.02/5.37 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_eq_divide
% 5.02/5.37 thf(fact_8960_inverse__eq__divide,axiom,
% 5.02/5.37 ( inverse_inverse_rat
% 5.02/5.37 = ( divide_divide_rat @ one_one_rat ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_eq_divide
% 5.02/5.37 thf(fact_8961_power__mult__inverse__distrib,axiom,
% 5.02/5.37 ! [X2: real,M: nat] :
% 5.02/5.37 ( ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( inverse_inverse_real @ X2 ) )
% 5.02/5.37 = ( times_times_real @ ( inverse_inverse_real @ X2 ) @ ( power_power_real @ X2 @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_mult_inverse_distrib
% 5.02/5.37 thf(fact_8962_power__mult__inverse__distrib,axiom,
% 5.02/5.37 ! [X2: complex,M: nat] :
% 5.02/5.37 ( ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( invers8013647133539491842omplex @ X2 ) )
% 5.02/5.37 = ( times_times_complex @ ( invers8013647133539491842omplex @ X2 ) @ ( power_power_complex @ X2 @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_mult_inverse_distrib
% 5.02/5.37 thf(fact_8963_power__mult__inverse__distrib,axiom,
% 5.02/5.37 ! [X2: rat,M: nat] :
% 5.02/5.37 ( ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( inverse_inverse_rat @ X2 ) )
% 5.02/5.37 = ( times_times_rat @ ( inverse_inverse_rat @ X2 ) @ ( power_power_rat @ X2 @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_mult_inverse_distrib
% 5.02/5.37 thf(fact_8964_power__mult__power__inverse__commute,axiom,
% 5.02/5.37 ! [X2: real,M: nat,N2: nat] :
% 5.02/5.37 ( ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X2 ) @ N2 ) )
% 5.02/5.37 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X2 ) @ N2 ) @ ( power_power_real @ X2 @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_mult_power_inverse_commute
% 5.02/5.37 thf(fact_8965_power__mult__power__inverse__commute,axiom,
% 5.02/5.37 ! [X2: complex,M: nat,N2: nat] :
% 5.02/5.37 ( ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X2 ) @ N2 ) )
% 5.02/5.37 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X2 ) @ N2 ) @ ( power_power_complex @ X2 @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_mult_power_inverse_commute
% 5.02/5.37 thf(fact_8966_power__mult__power__inverse__commute,axiom,
% 5.02/5.37 ! [X2: rat,M: nat,N2: nat] :
% 5.02/5.37 ( ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( power_power_rat @ ( inverse_inverse_rat @ X2 ) @ N2 ) )
% 5.02/5.37 = ( times_times_rat @ ( power_power_rat @ ( inverse_inverse_rat @ X2 ) @ N2 ) @ ( power_power_rat @ X2 @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_mult_power_inverse_commute
% 5.02/5.37 thf(fact_8967_mult__inverse__of__nat__commute,axiom,
% 5.02/5.37 ! [Xa2: nat,X2: real] :
% 5.02/5.37 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa2 ) ) @ X2 )
% 5.02/5.37 = ( times_times_real @ X2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_inverse_of_nat_commute
% 5.02/5.37 thf(fact_8968_mult__inverse__of__nat__commute,axiom,
% 5.02/5.37 ! [Xa2: nat,X2: complex] :
% 5.02/5.37 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa2 ) ) @ X2 )
% 5.02/5.37 = ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_inverse_of_nat_commute
% 5.02/5.37 thf(fact_8969_mult__inverse__of__nat__commute,axiom,
% 5.02/5.37 ! [Xa2: nat,X2: rat] :
% 5.02/5.37 ( ( times_times_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa2 ) ) @ X2 )
% 5.02/5.37 = ( times_times_rat @ X2 @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ Xa2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_inverse_of_nat_commute
% 5.02/5.37 thf(fact_8970_nonzero__abs__inverse,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.02/5.37 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_abs_inverse
% 5.02/5.37 thf(fact_8971_nonzero__abs__inverse,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.02/5.37 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_abs_inverse
% 5.02/5.37 thf(fact_8972_mult__inverse__of__int__commute,axiom,
% 5.02/5.37 ! [Xa2: int,X2: real] :
% 5.02/5.37 ( ( times_times_real @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa2 ) ) @ X2 )
% 5.02/5.37 = ( times_times_real @ X2 @ ( inverse_inverse_real @ ( ring_1_of_int_real @ Xa2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_inverse_of_int_commute
% 5.02/5.37 thf(fact_8973_mult__inverse__of__int__commute,axiom,
% 5.02/5.37 ! [Xa2: int,X2: complex] :
% 5.02/5.37 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa2 ) ) @ X2 )
% 5.02/5.37 = ( times_times_complex @ X2 @ ( invers8013647133539491842omplex @ ( ring_17405671764205052669omplex @ Xa2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_inverse_of_int_commute
% 5.02/5.37 thf(fact_8974_mult__inverse__of__int__commute,axiom,
% 5.02/5.37 ! [Xa2: int,X2: rat] :
% 5.02/5.37 ( ( times_times_rat @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa2 ) ) @ X2 )
% 5.02/5.37 = ( times_times_rat @ X2 @ ( inverse_inverse_rat @ ( ring_1_of_int_rat @ Xa2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_inverse_of_int_commute
% 5.02/5.37 thf(fact_8975_atMost__atLeast0,axiom,
% 5.02/5.37 ( set_ord_atMost_nat
% 5.02/5.37 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_atLeast0
% 5.02/5.37 thf(fact_8976_lessThan__Suc__atMost,axiom,
% 5.02/5.37 ! [K: nat] :
% 5.02/5.37 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.02/5.37 = ( set_ord_atMost_nat @ K ) ) ).
% 5.02/5.37
% 5.02/5.37 % lessThan_Suc_atMost
% 5.02/5.37 thf(fact_8977_divide__real__def,axiom,
% 5.02/5.37 ( divide_divide_real
% 5.02/5.37 = ( ^ [X: real,Y6: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y6 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_real_def
% 5.02/5.37 thf(fact_8978_atMost__Suc,axiom,
% 5.02/5.37 ! [K: nat] :
% 5.02/5.37 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.02/5.37 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_Suc
% 5.02/5.37 thf(fact_8979_not__Iic__le__Icc,axiom,
% 5.02/5.37 ! [H2: int,L3: int,H3: int] :
% 5.02/5.37 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H2 ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 5.02/5.37
% 5.02/5.37 % not_Iic_le_Icc
% 5.02/5.37 thf(fact_8980_not__Iic__le__Icc,axiom,
% 5.02/5.37 ! [H2: real,L3: real,H3: real] :
% 5.02/5.37 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H2 ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 5.02/5.37
% 5.02/5.37 % not_Iic_le_Icc
% 5.02/5.37 thf(fact_8981_prod_Otriangle__reindex__eq,axiom,
% 5.02/5.37 ! [G: nat > nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.02/5.37 @ ( collec3392354462482085612at_nat
% 5.02/5.37 @ ( produc6081775807080527818_nat_o
% 5.02/5.37 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.triangle_reindex_eq
% 5.02/5.37 thf(fact_8982_prod_Otriangle__reindex__eq,axiom,
% 5.02/5.37 ! [G: nat > nat > int,N2: nat] :
% 5.02/5.37 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.02/5.37 @ ( collec3392354462482085612at_nat
% 5.02/5.37 @ ( produc6081775807080527818_nat_o
% 5.02/5.37 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.triangle_reindex_eq
% 5.02/5.37 thf(fact_8983_le__imp__inverse__le__neg,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ A @ B )
% 5.02/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.02/5.37 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_imp_inverse_le_neg
% 5.02/5.37 thf(fact_8984_le__imp__inverse__le__neg,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.02/5.37 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_imp_inverse_le_neg
% 5.02/5.37 thf(fact_8985_inverse__le__imp__le__neg,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.02/5.37 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_le_imp_le_neg
% 5.02/5.37 thf(fact_8986_inverse__le__imp__le__neg,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.02/5.37 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_le_imp_le_neg
% 5.02/5.37 thf(fact_8987_le__imp__inverse__le,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ A @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_imp_inverse_le
% 5.02/5.37 thf(fact_8988_le__imp__inverse__le,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_eq_rat @ A @ B )
% 5.02/5.37 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.37 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_imp_inverse_le
% 5.02/5.37 thf(fact_8989_inverse__le__imp__le,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_le_imp_le
% 5.02/5.37 thf(fact_8990_inverse__le__imp__le,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.37 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_le_imp_le
% 5.02/5.37 thf(fact_8991_inverse__le__1__iff,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X2 ) @ one_one_real )
% 5.02/5.37 = ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.02/5.37 | ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_le_1_iff
% 5.02/5.37 thf(fact_8992_inverse__le__1__iff,axiom,
% 5.02/5.37 ! [X2: rat] :
% 5.02/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X2 ) @ one_one_rat )
% 5.02/5.37 = ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.02/5.37 | ( ord_less_eq_rat @ one_one_rat @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_le_1_iff
% 5.02/5.37 thf(fact_8993_one__less__inverse__iff,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X2 ) )
% 5.02/5.37 = ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 & ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_less_inverse_iff
% 5.02/5.37 thf(fact_8994_one__less__inverse__iff,axiom,
% 5.02/5.37 ! [X2: rat] :
% 5.02/5.37 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X2 ) )
% 5.02/5.37 = ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.02/5.37 & ( ord_less_rat @ X2 @ one_one_rat ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_less_inverse_iff
% 5.02/5.37 thf(fact_8995_one__less__inverse,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ A @ one_one_real )
% 5.02/5.37 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_less_inverse
% 5.02/5.37 thf(fact_8996_one__less__inverse,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.37 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.02/5.37 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_less_inverse
% 5.02/5.37 thf(fact_8997_field__class_Ofield__inverse,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.02/5.37 = one_one_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_inverse
% 5.02/5.37 thf(fact_8998_field__class_Ofield__inverse,axiom,
% 5.02/5.37 ! [A: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.02/5.37 = one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_inverse
% 5.02/5.37 thf(fact_8999_field__class_Ofield__inverse,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.02/5.37 = one_one_rat ) ) ).
% 5.02/5.37
% 5.02/5.37 % field_class.field_inverse
% 5.02/5.37 thf(fact_9000_division__ring__inverse__add,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( B != zero_zero_real )
% 5.02/5.37 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % division_ring_inverse_add
% 5.02/5.37 thf(fact_9001_division__ring__inverse__add,axiom,
% 5.02/5.37 ! [A: complex,B: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( B != zero_zero_complex )
% 5.02/5.37 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.02/5.37 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % division_ring_inverse_add
% 5.02/5.37 thf(fact_9002_division__ring__inverse__add,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( B != zero_zero_rat )
% 5.02/5.37 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % division_ring_inverse_add
% 5.02/5.37 thf(fact_9003_inverse__add,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( B != zero_zero_real )
% 5.02/5.37 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_add
% 5.02/5.37 thf(fact_9004_inverse__add,axiom,
% 5.02/5.37 ! [A: complex,B: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( B != zero_zero_complex )
% 5.02/5.37 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.02/5.37 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_add
% 5.02/5.37 thf(fact_9005_inverse__add,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( B != zero_zero_rat )
% 5.02/5.37 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_add
% 5.02/5.37 thf(fact_9006_division__ring__inverse__diff,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( B != zero_zero_real )
% 5.02/5.37 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % division_ring_inverse_diff
% 5.02/5.37 thf(fact_9007_division__ring__inverse__diff,axiom,
% 5.02/5.37 ! [A: complex,B: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( B != zero_zero_complex )
% 5.02/5.37 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.02/5.37 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % division_ring_inverse_diff
% 5.02/5.37 thf(fact_9008_division__ring__inverse__diff,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( B != zero_zero_rat )
% 5.02/5.37 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % division_ring_inverse_diff
% 5.02/5.37 thf(fact_9009_nonzero__inverse__eq__divide,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( inverse_inverse_real @ A )
% 5.02/5.37 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_eq_divide
% 5.02/5.37 thf(fact_9010_nonzero__inverse__eq__divide,axiom,
% 5.02/5.37 ! [A: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( invers8013647133539491842omplex @ A )
% 5.02/5.37 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_eq_divide
% 5.02/5.37 thf(fact_9011_nonzero__inverse__eq__divide,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( inverse_inverse_rat @ A )
% 5.02/5.37 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nonzero_inverse_eq_divide
% 5.02/5.37 thf(fact_9012_prod_Otriangle__reindex,axiom,
% 5.02/5.37 ! [G: nat > nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.02/5.37 @ ( collec3392354462482085612at_nat
% 5.02/5.37 @ ( produc6081775807080527818_nat_o
% 5.02/5.37 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.triangle_reindex
% 5.02/5.37 thf(fact_9013_prod_Otriangle__reindex,axiom,
% 5.02/5.37 ! [G: nat > nat > int,N2: nat] :
% 5.02/5.37 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.02/5.37 @ ( collec3392354462482085612at_nat
% 5.02/5.37 @ ( produc6081775807080527818_nat_o
% 5.02/5.37 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.triangle_reindex
% 5.02/5.37 thf(fact_9014_atMost__nat__numeral,axiom,
% 5.02/5.37 ! [K: num] :
% 5.02/5.37 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.02/5.37 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atMost_nat_numeral
% 5.02/5.37 thf(fact_9015_Iic__subset__Iio__iff,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.02/5.37 = ( ord_less_rat @ A @ B ) ) ).
% 5.02/5.37
% 5.02/5.37 % Iic_subset_Iio_iff
% 5.02/5.37 thf(fact_9016_Iic__subset__Iio__iff,axiom,
% 5.02/5.37 ! [A: num,B: num] :
% 5.02/5.37 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.02/5.37 = ( ord_less_num @ A @ B ) ) ).
% 5.02/5.37
% 5.02/5.37 % Iic_subset_Iio_iff
% 5.02/5.37 thf(fact_9017_Iic__subset__Iio__iff,axiom,
% 5.02/5.37 ! [A: int,B: int] :
% 5.02/5.37 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.02/5.37 = ( ord_less_int @ A @ B ) ) ).
% 5.02/5.37
% 5.02/5.37 % Iic_subset_Iio_iff
% 5.02/5.37 thf(fact_9018_Iic__subset__Iio__iff,axiom,
% 5.02/5.37 ! [A: nat,B: nat] :
% 5.02/5.37 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.02/5.37 = ( ord_less_nat @ A @ B ) ) ).
% 5.02/5.37
% 5.02/5.37 % Iic_subset_Iio_iff
% 5.02/5.37 thf(fact_9019_Iic__subset__Iio__iff,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.02/5.37 = ( ord_less_real @ A @ B ) ) ).
% 5.02/5.37
% 5.02/5.37 % Iic_subset_Iio_iff
% 5.02/5.37 thf(fact_9020_sum__choose__upper,axiom,
% 5.02/5.37 ! [M: nat,N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_choose_upper
% 5.02/5.37 thf(fact_9021_inverse__less__iff,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.02/5.37 => ( ord_less_real @ B @ A ) )
% 5.02/5.37 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.02/5.37 => ( ord_less_real @ A @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_less_iff
% 5.02/5.37 thf(fact_9022_inverse__less__iff,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.02/5.37 => ( ord_less_rat @ B @ A ) )
% 5.02/5.37 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.02/5.37 => ( ord_less_rat @ A @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_less_iff
% 5.02/5.37 thf(fact_9023_inverse__le__iff,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.02/5.37 => ( ord_less_eq_real @ B @ A ) )
% 5.02/5.37 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.02/5.37 => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_le_iff
% 5.02/5.37 thf(fact_9024_inverse__le__iff,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.02/5.37 => ( ord_less_eq_rat @ B @ A ) )
% 5.02/5.37 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.02/5.37 => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_le_iff
% 5.02/5.37 thf(fact_9025_one__le__inverse__iff,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X2 ) )
% 5.02/5.37 = ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 & ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_le_inverse_iff
% 5.02/5.37 thf(fact_9026_one__le__inverse__iff,axiom,
% 5.02/5.37 ! [X2: rat] :
% 5.02/5.37 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X2 ) )
% 5.02/5.37 = ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.02/5.37 & ( ord_less_eq_rat @ X2 @ one_one_rat ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_le_inverse_iff
% 5.02/5.37 thf(fact_9027_inverse__less__1__iff,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ ( inverse_inverse_real @ X2 ) @ one_one_real )
% 5.02/5.37 = ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.02/5.37 | ( ord_less_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_less_1_iff
% 5.02/5.37 thf(fact_9028_inverse__less__1__iff,axiom,
% 5.02/5.37 ! [X2: rat] :
% 5.02/5.37 ( ( ord_less_rat @ ( inverse_inverse_rat @ X2 ) @ one_one_rat )
% 5.02/5.37 = ( ( ord_less_eq_rat @ X2 @ zero_zero_rat )
% 5.02/5.37 | ( ord_less_rat @ one_one_rat @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_less_1_iff
% 5.02/5.37 thf(fact_9029_one__le__inverse,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.02/5.37 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_le_inverse
% 5.02/5.37 thf(fact_9030_one__le__inverse,axiom,
% 5.02/5.37 ! [A: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.02/5.37 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.02/5.37 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_le_inverse
% 5.02/5.37 thf(fact_9031_inverse__diff__inverse,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( A != zero_zero_real )
% 5.02/5.37 => ( ( B != zero_zero_real )
% 5.02/5.37 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.02/5.37 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_diff_inverse
% 5.02/5.37 thf(fact_9032_inverse__diff__inverse,axiom,
% 5.02/5.37 ! [A: complex,B: complex] :
% 5.02/5.37 ( ( A != zero_zero_complex )
% 5.02/5.37 => ( ( B != zero_zero_complex )
% 5.02/5.37 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_diff_inverse
% 5.02/5.37 thf(fact_9033_inverse__diff__inverse,axiom,
% 5.02/5.37 ! [A: rat,B: rat] :
% 5.02/5.37 ( ( A != zero_zero_rat )
% 5.02/5.37 => ( ( B != zero_zero_rat )
% 5.02/5.37 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.02/5.37 = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % inverse_diff_inverse
% 5.02/5.37 thf(fact_9034_reals__Archimedean,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ? [N: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % reals_Archimedean
% 5.02/5.37 thf(fact_9035_reals__Archimedean,axiom,
% 5.02/5.37 ! [X2: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.02/5.37 => ? [N: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) ) @ X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % reals_Archimedean
% 5.02/5.37 thf(fact_9036_forall__pos__mono__1,axiom,
% 5.02/5.37 ! [P: real > $o,E2: real] :
% 5.02/5.37 ( ! [D3: real,E: real] :
% 5.02/5.37 ( ( ord_less_real @ D3 @ E )
% 5.02/5.37 => ( ( P @ D3 )
% 5.02/5.37 => ( P @ E ) ) )
% 5.02/5.37 => ( ! [N: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.02/5.37 => ( P @ E2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % forall_pos_mono_1
% 5.02/5.37 thf(fact_9037_real__arch__inverse,axiom,
% 5.02/5.37 ! [E2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.02/5.37 = ( ? [N3: nat] :
% 5.02/5.37 ( ( N3 != zero_zero_nat )
% 5.02/5.37 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.02/5.37 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ E2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_arch_inverse
% 5.02/5.37 thf(fact_9038_forall__pos__mono,axiom,
% 5.02/5.37 ! [P: real > $o,E2: real] :
% 5.02/5.37 ( ! [D3: real,E: real] :
% 5.02/5.37 ( ( ord_less_real @ D3 @ E )
% 5.02/5.37 => ( ( P @ D3 )
% 5.02/5.37 => ( P @ E ) ) )
% 5.02/5.37 => ( ! [N: nat] :
% 5.02/5.37 ( ( N != zero_zero_nat )
% 5.02/5.37 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) ) )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.02/5.37 => ( P @ E2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % forall_pos_mono
% 5.02/5.37 thf(fact_9039_sum_OatMost__Suc__shift,axiom,
% 5.02/5.37 ! [G: nat > rat,N2: nat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.atMost_Suc_shift
% 5.02/5.37 thf(fact_9040_sum_OatMost__Suc__shift,axiom,
% 5.02/5.37 ! [G: nat > int,N2: nat] :
% 5.02/5.37 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.atMost_Suc_shift
% 5.02/5.37 thf(fact_9041_sum_OatMost__Suc__shift,axiom,
% 5.02/5.37 ! [G: nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.atMost_Suc_shift
% 5.02/5.37 thf(fact_9042_sum_OatMost__Suc__shift,axiom,
% 5.02/5.37 ! [G: nat > real,N2: nat] :
% 5.02/5.37 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.atMost_Suc_shift
% 5.02/5.37 thf(fact_9043_sum__telescope,axiom,
% 5.02/5.37 ! [F: nat > rat,I3: nat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ I3 ) )
% 5.02/5.37 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_telescope
% 5.02/5.37 thf(fact_9044_sum__telescope,axiom,
% 5.02/5.37 ! [F: nat > int,I3: nat] :
% 5.02/5.37 ( ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ I3 ) )
% 5.02/5.37 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_telescope
% 5.02/5.37 thf(fact_9045_sum__telescope,axiom,
% 5.02/5.37 ! [F: nat > real,I3: nat] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ ( F @ ( suc @ I5 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ I3 ) )
% 5.02/5.37 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_telescope
% 5.02/5.37 thf(fact_9046_polyfun__eq__coeffs,axiom,
% 5.02/5.37 ! [C: nat > complex,N2: nat,D: nat > complex] :
% 5.02/5.37 ( ( ! [X: complex] :
% 5.02/5.37 ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( D @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 5.02/5.37 = ( ! [I5: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.02/5.37 => ( ( C @ I5 )
% 5.02/5.37 = ( D @ I5 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_eq_coeffs
% 5.02/5.37 thf(fact_9047_polyfun__eq__coeffs,axiom,
% 5.02/5.37 ! [C: nat > real,N2: nat,D: nat > real] :
% 5.02/5.37 ( ( ! [X: real] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( D @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 5.02/5.37 = ( ! [I5: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.02/5.37 => ( ( C @ I5 )
% 5.02/5.37 = ( D @ I5 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_eq_coeffs
% 5.02/5.37 thf(fact_9048_bounded__imp__summable,axiom,
% 5.02/5.37 ! [A: nat > int,B4: int] :
% 5.02/5.37 ( ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N ) )
% 5.02/5.37 => ( ! [N: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N ) ) @ B4 )
% 5.02/5.37 => ( summable_int @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bounded_imp_summable
% 5.02/5.37 thf(fact_9049_bounded__imp__summable,axiom,
% 5.02/5.37 ! [A: nat > nat,B4: nat] :
% 5.02/5.37 ( ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N ) )
% 5.02/5.37 => ( ! [N: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N ) ) @ B4 )
% 5.02/5.37 => ( summable_nat @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bounded_imp_summable
% 5.02/5.37 thf(fact_9050_bounded__imp__summable,axiom,
% 5.02/5.37 ! [A: nat > real,B4: real] :
% 5.02/5.37 ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.02/5.37 => ( ! [N: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N ) ) @ B4 )
% 5.02/5.37 => ( summable_real @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bounded_imp_summable
% 5.02/5.37 thf(fact_9051_prod_OatMost__Suc__shift,axiom,
% 5.02/5.37 ! [G: nat > real,N2: nat] :
% 5.02/5.37 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.37 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups129246275422532515t_real
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.atMost_Suc_shift
% 5.02/5.37 thf(fact_9052_prod_OatMost__Suc__shift,axiom,
% 5.02/5.37 ! [G: nat > rat,N2: nat] :
% 5.02/5.37 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.37 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups73079841787564623at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.atMost_Suc_shift
% 5.02/5.37 thf(fact_9053_prod_OatMost__Suc__shift,axiom,
% 5.02/5.37 ! [G: nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.37 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.atMost_Suc_shift
% 5.02/5.37 thf(fact_9054_prod_OatMost__Suc__shift,axiom,
% 5.02/5.37 ! [G: nat > int,N2: nat] :
% 5.02/5.37 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.02/5.37 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.atMost_Suc_shift
% 5.02/5.37 thf(fact_9055_prod__int__plus__eq,axiom,
% 5.02/5.37 ! [I3: nat,J: nat] :
% 5.02/5.37 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I3 @ ( plus_plus_nat @ I3 @ J ) ) )
% 5.02/5.37 = ( groups1705073143266064639nt_int
% 5.02/5.37 @ ^ [X: int] : X
% 5.02/5.37 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I3 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I3 @ J ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod_int_plus_eq
% 5.02/5.37 thf(fact_9056_summable__exp,axiom,
% 5.02/5.37 ! [X2: complex] :
% 5.02/5.37 ( summable_complex
% 5.02/5.37 @ ^ [N3: nat] : ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri5044797733671781792omplex @ N3 ) ) @ ( power_power_complex @ X2 @ N3 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % summable_exp
% 5.02/5.37 thf(fact_9057_summable__exp,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( summable_real
% 5.02/5.37 @ ^ [N3: nat] : ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N3 ) ) @ ( power_power_real @ X2 @ N3 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % summable_exp
% 5.02/5.37 thf(fact_9058_sum_Onested__swap_H,axiom,
% 5.02/5.37 ! [A: nat > nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( groups3542108847815614940at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [J3: nat] :
% 5.02/5.37 ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.02/5.37 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.nested_swap'
% 5.02/5.37 thf(fact_9059_sum_Onested__swap_H,axiom,
% 5.02/5.37 ! [A: nat > nat > real,N2: nat] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( groups6591440286371151544t_real @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [J3: nat] :
% 5.02/5.37 ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.02/5.37 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.nested_swap'
% 5.02/5.37 thf(fact_9060_prod_Onested__swap_H,axiom,
% 5.02/5.37 ! [A: nat > nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( groups708209901874060359at_nat @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [J3: nat] :
% 5.02/5.37 ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.02/5.37 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.nested_swap'
% 5.02/5.37 thf(fact_9061_prod_Onested__swap_H,axiom,
% 5.02/5.37 ! [A: nat > nat > int,N2: nat] :
% 5.02/5.37 ( ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [I5: nat] : ( groups705719431365010083at_int @ ( A @ I5 ) @ ( set_ord_lessThan_nat @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [J3: nat] :
% 5.02/5.37 ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [I5: nat] : ( A @ I5 @ J3 )
% 5.02/5.37 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.nested_swap'
% 5.02/5.37 thf(fact_9062_sum__choose__lower,axiom,
% 5.02/5.37 ! [R2: nat,N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R2 @ K3 ) @ K3 )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( binomial @ ( suc @ ( plus_plus_nat @ R2 @ N2 ) ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_choose_lower
% 5.02/5.37 thf(fact_9063_choose__rising__sum_I1_J,axiom,
% 5.02/5.37 ! [N2: nat,M: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % choose_rising_sum(1)
% 5.02/5.37 thf(fact_9064_choose__rising__sum_I2_J,axiom,
% 5.02/5.37 ! [N2: nat,M: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 5.02/5.37
% 5.02/5.37 % choose_rising_sum(2)
% 5.02/5.37 thf(fact_9065_ex__inverse__of__nat__less,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ? [N: nat] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.02/5.37 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ex_inverse_of_nat_less
% 5.02/5.37 thf(fact_9066_ex__inverse__of__nat__less,axiom,
% 5.02/5.37 ! [X2: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ X2 )
% 5.02/5.37 => ? [N: nat] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.02/5.37 & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N ) ) @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ex_inverse_of_nat_less
% 5.02/5.37 thf(fact_9067_power__diff__conv__inverse,axiom,
% 5.02/5.37 ! [X2: real,M: nat,N2: nat] :
% 5.02/5.37 ( ( X2 != zero_zero_real )
% 5.02/5.37 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 => ( ( power_power_real @ X2 @ ( minus_minus_nat @ N2 @ M ) )
% 5.02/5.37 = ( times_times_real @ ( power_power_real @ X2 @ N2 ) @ ( power_power_real @ ( inverse_inverse_real @ X2 ) @ M ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_diff_conv_inverse
% 5.02/5.37 thf(fact_9068_power__diff__conv__inverse,axiom,
% 5.02/5.37 ! [X2: complex,M: nat,N2: nat] :
% 5.02/5.37 ( ( X2 != zero_zero_complex )
% 5.02/5.37 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 => ( ( power_power_complex @ X2 @ ( minus_minus_nat @ N2 @ M ) )
% 5.02/5.37 = ( times_times_complex @ ( power_power_complex @ X2 @ N2 ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X2 ) @ M ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_diff_conv_inverse
% 5.02/5.37 thf(fact_9069_power__diff__conv__inverse,axiom,
% 5.02/5.37 ! [X2: rat,M: nat,N2: nat] :
% 5.02/5.37 ( ( X2 != zero_zero_rat )
% 5.02/5.37 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 => ( ( power_power_rat @ X2 @ ( minus_minus_nat @ N2 @ M ) )
% 5.02/5.37 = ( times_times_rat @ ( power_power_rat @ X2 @ N2 ) @ ( power_power_rat @ ( inverse_inverse_rat @ X2 ) @ M ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % power_diff_conv_inverse
% 5.02/5.37 thf(fact_9070_zero__polynom__imp__zero__coeffs,axiom,
% 5.02/5.37 ! [C: nat > complex,N2: nat,K: nat] :
% 5.02/5.37 ( ! [W2: complex] :
% 5.02/5.37 ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ W2 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = zero_zero_complex )
% 5.02/5.37 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.37 => ( ( C @ K )
% 5.02/5.37 = zero_zero_complex ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % zero_polynom_imp_zero_coeffs
% 5.02/5.37 thf(fact_9071_zero__polynom__imp__zero__coeffs,axiom,
% 5.02/5.37 ! [C: nat > real,N2: nat,K: nat] :
% 5.02/5.37 ( ! [W2: real] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ W2 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = zero_zero_real )
% 5.02/5.37 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.02/5.37 => ( ( C @ K )
% 5.02/5.37 = zero_zero_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % zero_polynom_imp_zero_coeffs
% 5.02/5.37 thf(fact_9072_polyfun__eq__0,axiom,
% 5.02/5.37 ! [C: nat > complex,N2: nat] :
% 5.02/5.37 ( ( ! [X: complex] :
% 5.02/5.37 ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = zero_zero_complex ) )
% 5.02/5.37 = ( ! [I5: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.02/5.37 => ( ( C @ I5 )
% 5.02/5.37 = zero_zero_complex ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_eq_0
% 5.02/5.37 thf(fact_9073_polyfun__eq__0,axiom,
% 5.02/5.37 ! [C: nat > real,N2: nat] :
% 5.02/5.37 ( ( ! [X: real] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = zero_zero_real ) )
% 5.02/5.37 = ( ! [I5: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ I5 @ N2 )
% 5.02/5.37 => ( ( C @ I5 )
% 5.02/5.37 = zero_zero_real ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_eq_0
% 5.02/5.37 thf(fact_9074_sum_OatMost__shift,axiom,
% 5.02/5.37 ! [G: nat > rat,N2: nat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.atMost_shift
% 5.02/5.37 thf(fact_9075_sum_OatMost__shift,axiom,
% 5.02/5.37 ! [G: nat > int,N2: nat] :
% 5.02/5.37 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.atMost_shift
% 5.02/5.37 thf(fact_9076_sum_OatMost__shift,axiom,
% 5.02/5.37 ! [G: nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.atMost_shift
% 5.02/5.37 thf(fact_9077_sum_OatMost__shift,axiom,
% 5.02/5.37 ! [G: nat > real,N2: nat] :
% 5.02/5.37 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.atMost_shift
% 5.02/5.37 thf(fact_9078_sum__up__index__split,axiom,
% 5.02/5.37 ! [F: nat > rat,M: nat,N2: nat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_up_index_split
% 5.02/5.37 thf(fact_9079_sum__up__index__split,axiom,
% 5.02/5.37 ! [F: nat > int,M: nat,N2: nat] :
% 5.02/5.37 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_up_index_split
% 5.02/5.37 thf(fact_9080_sum__up__index__split,axiom,
% 5.02/5.37 ! [F: nat > nat,M: nat,N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_up_index_split
% 5.02/5.37 thf(fact_9081_sum__up__index__split,axiom,
% 5.02/5.37 ! [F: nat > real,M: nat,N2: nat] :
% 5.02/5.37 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_up_index_split
% 5.02/5.37 thf(fact_9082_prod_OatMost__shift,axiom,
% 5.02/5.37 ! [G: nat > real,N2: nat] :
% 5.02/5.37 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_real @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups129246275422532515t_real
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.atMost_shift
% 5.02/5.37 thf(fact_9083_prod_OatMost__shift,axiom,
% 5.02/5.37 ! [G: nat > rat,N2: nat] :
% 5.02/5.37 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups73079841787564623at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.atMost_shift
% 5.02/5.37 thf(fact_9084_prod_OatMost__shift,axiom,
% 5.02/5.37 ! [G: nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.atMost_shift
% 5.02/5.37 thf(fact_9085_prod_OatMost__shift,axiom,
% 5.02/5.37 ! [G: nat > int,N2: nat] :
% 5.02/5.37 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.02/5.37 @ ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.atMost_shift
% 5.02/5.37 thf(fact_9086_atLeast1__atMost__eq__remove0,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.02/5.37 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % atLeast1_atMost_eq_remove0
% 5.02/5.37 thf(fact_9087_gbinomial__parallel__sum,axiom,
% 5.02/5.37 ! [A: complex,N2: nat] :
% 5.02/5.37 ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % gbinomial_parallel_sum
% 5.02/5.37 thf(fact_9088_gbinomial__parallel__sum,axiom,
% 5.02/5.37 ! [A: rat,N2: nat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % gbinomial_parallel_sum
% 5.02/5.37 thf(fact_9089_gbinomial__parallel__sum,axiom,
% 5.02/5.37 ! [A: real,N2: nat] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % gbinomial_parallel_sum
% 5.02/5.37 thf(fact_9090_sum_Otriangle__reindex__eq,axiom,
% 5.02/5.37 ! [G: nat > nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.02/5.37 @ ( collec3392354462482085612at_nat
% 5.02/5.37 @ ( produc6081775807080527818_nat_o
% 5.02/5.37 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.triangle_reindex_eq
% 5.02/5.37 thf(fact_9091_sum_Otriangle__reindex__eq,axiom,
% 5.02/5.37 ! [G: nat > nat > real,N2: nat] :
% 5.02/5.37 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.02/5.37 @ ( collec3392354462482085612at_nat
% 5.02/5.37 @ ( produc6081775807080527818_nat_o
% 5.02/5.37 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.triangle_reindex_eq
% 5.02/5.37 thf(fact_9092_sum__choose__diagonal,axiom,
% 5.02/5.37 ! [M: nat,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 => ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_choose_diagonal
% 5.02/5.37 thf(fact_9093_vandermonde,axiom,
% 5.02/5.37 ! [M: nat,N2: nat,R2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R2 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ R2 ) )
% 5.02/5.37 = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % vandermonde
% 5.02/5.37 thf(fact_9094_sum__gp__basic,axiom,
% 5.02/5.37 ! [X2: complex,N2: nat] :
% 5.02/5.37 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X2 @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_gp_basic
% 5.02/5.37 thf(fact_9095_sum__gp__basic,axiom,
% 5.02/5.37 ! [X2: rat,N2: nat] :
% 5.02/5.37 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X2 @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_gp_basic
% 5.02/5.37 thf(fact_9096_sum__gp__basic,axiom,
% 5.02/5.37 ! [X2: int,N2: nat] :
% 5.02/5.37 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X2 @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_gp_basic
% 5.02/5.37 thf(fact_9097_sum__gp__basic,axiom,
% 5.02/5.37 ! [X2: real,N2: nat] :
% 5.02/5.37 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( suc @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_gp_basic
% 5.02/5.37 thf(fact_9098_exp__plus__inverse__exp,axiom,
% 5.02/5.37 ! [X2: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % exp_plus_inverse_exp
% 5.02/5.37 thf(fact_9099_polyfun__linear__factor__root,axiom,
% 5.02/5.37 ! [C: nat > complex,A: complex,N2: nat] :
% 5.02/5.37 ( ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = zero_zero_complex )
% 5.02/5.37 => ~ ! [B3: nat > complex] :
% 5.02/5.37 ~ ! [Z4: complex] :
% 5.02/5.37 ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 5.02/5.37 @ ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( B3 @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_linear_factor_root
% 5.02/5.37 thf(fact_9100_polyfun__linear__factor__root,axiom,
% 5.02/5.37 ! [C: nat > rat,A: rat,N2: nat] :
% 5.02/5.37 ( ( ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ A @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = zero_zero_rat )
% 5.02/5.37 => ~ ! [B3: nat > rat] :
% 5.02/5.37 ~ ! [Z4: rat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 5.02/5.37 @ ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_rat @ ( B3 @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_linear_factor_root
% 5.02/5.37 thf(fact_9101_polyfun__linear__factor__root,axiom,
% 5.02/5.37 ! [C: nat > int,A: int,N2: nat] :
% 5.02/5.37 ( ( ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 => ~ ! [B3: nat > int] :
% 5.02/5.37 ~ ! [Z4: int] :
% 5.02/5.37 ( ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 5.02/5.37 @ ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_int @ ( B3 @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_linear_factor_root
% 5.02/5.37 thf(fact_9102_polyfun__linear__factor__root,axiom,
% 5.02/5.37 ! [C: nat > real,A: real,N2: nat] :
% 5.02/5.37 ( ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = zero_zero_real )
% 5.02/5.37 => ~ ! [B3: nat > real] :
% 5.02/5.37 ~ ! [Z4: real] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 5.02/5.37 @ ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( B3 @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_linear_factor_root
% 5.02/5.37 thf(fact_9103_polyfun__linear__factor,axiom,
% 5.02/5.37 ! [C: nat > complex,N2: nat,A: complex] :
% 5.02/5.37 ? [B3: nat > complex] :
% 5.02/5.37 ! [Z4: complex] :
% 5.02/5.37 ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( plus_plus_complex
% 5.02/5.37 @ ( times_times_complex @ ( minus_minus_complex @ Z4 @ A )
% 5.02/5.37 @ ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( B3 @ I5 ) @ ( power_power_complex @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.02/5.37 @ ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ A @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_linear_factor
% 5.02/5.37 thf(fact_9104_polyfun__linear__factor,axiom,
% 5.02/5.37 ! [C: nat > rat,N2: nat,A: rat] :
% 5.02/5.37 ? [B3: nat > rat] :
% 5.02/5.37 ! [Z4: rat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( plus_plus_rat
% 5.02/5.37 @ ( times_times_rat @ ( minus_minus_rat @ Z4 @ A )
% 5.02/5.37 @ ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_rat @ ( B3 @ I5 ) @ ( power_power_rat @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.02/5.37 @ ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ A @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_linear_factor
% 5.02/5.37 thf(fact_9105_polyfun__linear__factor,axiom,
% 5.02/5.37 ! [C: nat > int,N2: nat,A: int] :
% 5.02/5.37 ? [B3: nat > int] :
% 5.02/5.37 ! [Z4: int] :
% 5.02/5.37 ( ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( plus_plus_int
% 5.02/5.37 @ ( times_times_int @ ( minus_minus_int @ Z4 @ A )
% 5.02/5.37 @ ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_int @ ( B3 @ I5 ) @ ( power_power_int @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.02/5.37 @ ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_int @ ( C @ I5 ) @ ( power_power_int @ A @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_linear_factor
% 5.02/5.37 thf(fact_9106_polyfun__linear__factor,axiom,
% 5.02/5.37 ! [C: nat > real,N2: nat,A: real] :
% 5.02/5.37 ? [B3: nat > real] :
% 5.02/5.37 ! [Z4: real] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( plus_plus_real
% 5.02/5.37 @ ( times_times_real @ ( minus_minus_real @ Z4 @ A )
% 5.02/5.37 @ ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( B3 @ I5 ) @ ( power_power_real @ Z4 @ I5 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.02/5.37 @ ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ A @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_linear_factor
% 5.02/5.37 thf(fact_9107_sum__power__shift,axiom,
% 5.02/5.37 ! [M: nat,N2: nat,X2: complex] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.37 = ( times_times_complex @ ( power_power_complex @ X2 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_power_shift
% 5.02/5.37 thf(fact_9108_sum__power__shift,axiom,
% 5.02/5.37 ! [M: nat,N2: nat,X2: rat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.37 = ( times_times_rat @ ( power_power_rat @ X2 @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_power_shift
% 5.02/5.37 thf(fact_9109_sum__power__shift,axiom,
% 5.02/5.37 ! [M: nat,N2: nat,X2: int] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.37 = ( times_times_int @ ( power_power_int @ X2 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_power_shift
% 5.02/5.37 thf(fact_9110_sum__power__shift,axiom,
% 5.02/5.37 ! [M: nat,N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.02/5.37 = ( times_times_real @ ( power_power_real @ X2 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X2 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum_power_shift
% 5.02/5.37 thf(fact_9111_sum_Otriangle__reindex,axiom,
% 5.02/5.37 ! [G: nat > nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.02/5.37 @ ( collec3392354462482085612at_nat
% 5.02/5.37 @ ( produc6081775807080527818_nat_o
% 5.02/5.37 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.triangle_reindex
% 5.02/5.37 thf(fact_9112_sum_Otriangle__reindex,axiom,
% 5.02/5.37 ! [G: nat > nat > real,N2: nat] :
% 5.02/5.37 ( ( groups4567486121110086003t_real @ ( produc1703576794950452218t_real @ G )
% 5.02/5.37 @ ( collec3392354462482085612at_nat
% 5.02/5.37 @ ( produc6081775807080527818_nat_o
% 5.02/5.37 @ ^ [I5: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I5 @ J3 ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( G @ I5 @ ( minus_minus_nat @ K3 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.triangle_reindex
% 5.02/5.37 thf(fact_9113_summable__Cauchy__product,axiom,
% 5.02/5.37 ! [A: nat > complex,B: nat > complex] :
% 5.02/5.37 ( ( summable_real
% 5.02/5.37 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.02/5.37 => ( ( summable_real
% 5.02/5.37 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.02/5.37 => ( summable_complex
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % summable_Cauchy_product
% 5.02/5.37 thf(fact_9114_summable__Cauchy__product,axiom,
% 5.02/5.37 ! [A: nat > real,B: nat > real] :
% 5.02/5.37 ( ( summable_real
% 5.02/5.37 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.02/5.37 => ( ( summable_real
% 5.02/5.37 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.02/5.37 => ( summable_real
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % summable_Cauchy_product
% 5.02/5.37 thf(fact_9115_choose__row__sum,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % choose_row_sum
% 5.02/5.37 thf(fact_9116_Cauchy__product,axiom,
% 5.02/5.37 ! [A: nat > complex,B: nat > complex] :
% 5.02/5.37 ( ( summable_real
% 5.02/5.37 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( A @ K3 ) ) )
% 5.02/5.37 => ( ( summable_real
% 5.02/5.37 @ ^ [K3: nat] : ( real_V1022390504157884413omplex @ ( B @ K3 ) ) )
% 5.02/5.37 => ( ( times_times_complex @ ( suminf_complex @ A ) @ ( suminf_complex @ B ) )
% 5.02/5.37 = ( suminf_complex
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Cauchy_product
% 5.02/5.37 thf(fact_9117_Cauchy__product,axiom,
% 5.02/5.37 ! [A: nat > real,B: nat > real] :
% 5.02/5.37 ( ( summable_real
% 5.02/5.37 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( A @ K3 ) ) )
% 5.02/5.37 => ( ( summable_real
% 5.02/5.37 @ ^ [K3: nat] : ( real_V7735802525324610683m_real @ ( B @ K3 ) ) )
% 5.02/5.37 => ( ( times_times_real @ ( suminf_real @ A ) @ ( suminf_real @ B ) )
% 5.02/5.37 = ( suminf_real
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( B @ ( minus_minus_nat @ K3 @ I5 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Cauchy_product
% 5.02/5.37 thf(fact_9118_binomial,axiom,
% 5.02/5.37 ! [A: nat,B: nat,N2: nat] :
% 5.02/5.37 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.02/5.37 = ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % binomial
% 5.02/5.37 thf(fact_9119_plus__inverse__ge__2,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % plus_inverse_ge_2
% 5.02/5.37 thf(fact_9120_real__inv__sqrt__pow2,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.37 = ( inverse_inverse_real @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_inv_sqrt_pow2
% 5.02/5.37 thf(fact_9121_sum_Oin__pairs__0,axiom,
% 5.02/5.37 ! [G: nat > rat,N2: nat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.in_pairs_0
% 5.02/5.37 thf(fact_9122_sum_Oin__pairs__0,axiom,
% 5.02/5.37 ! [G: nat > int,N2: nat] :
% 5.02/5.37 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.in_pairs_0
% 5.02/5.37 thf(fact_9123_sum_Oin__pairs__0,axiom,
% 5.02/5.37 ! [G: nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.in_pairs_0
% 5.02/5.37 thf(fact_9124_sum_Oin__pairs__0,axiom,
% 5.02/5.37 ! [G: nat > real,N2: nat] :
% 5.02/5.37 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sum.in_pairs_0
% 5.02/5.37 thf(fact_9125_polynomial__product,axiom,
% 5.02/5.37 ! [M: nat,A: nat > complex,N2: nat,B: nat > complex,X2: complex] :
% 5.02/5.37 ( ! [I2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M @ I2 )
% 5.02/5.37 => ( ( A @ I2 )
% 5.02/5.37 = zero_zero_complex ) )
% 5.02/5.37 => ( ! [J2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ N2 @ J2 )
% 5.02/5.37 => ( ( B @ J2 )
% 5.02/5.37 = zero_zero_complex ) )
% 5.02/5.37 => ( ( times_times_complex
% 5.02/5.37 @ ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( A @ I5 ) @ ( power_power_complex @ X2 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 @ ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X2 @ J3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [R5: nat] :
% 5.02/5.37 ( times_times_complex
% 5.02/5.37 @ ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ R5 ) )
% 5.02/5.37 @ ( power_power_complex @ X2 @ R5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polynomial_product
% 5.02/5.37 thf(fact_9126_polynomial__product,axiom,
% 5.02/5.37 ! [M: nat,A: nat > rat,N2: nat,B: nat > rat,X2: rat] :
% 5.02/5.37 ( ! [I2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M @ I2 )
% 5.02/5.37 => ( ( A @ I2 )
% 5.02/5.37 = zero_zero_rat ) )
% 5.02/5.37 => ( ! [J2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ N2 @ J2 )
% 5.02/5.37 => ( ( B @ J2 )
% 5.02/5.37 = zero_zero_rat ) )
% 5.02/5.37 => ( ( times_times_rat
% 5.02/5.37 @ ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( power_power_rat @ X2 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 @ ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X2 @ J3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [R5: nat] :
% 5.02/5.37 ( times_times_rat
% 5.02/5.37 @ ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ R5 ) )
% 5.02/5.37 @ ( power_power_rat @ X2 @ R5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polynomial_product
% 5.02/5.37 thf(fact_9127_polynomial__product,axiom,
% 5.02/5.37 ! [M: nat,A: nat > int,N2: nat,B: nat > int,X2: int] :
% 5.02/5.37 ( ! [I2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M @ I2 )
% 5.02/5.37 => ( ( A @ I2 )
% 5.02/5.37 = zero_zero_int ) )
% 5.02/5.37 => ( ! [J2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ N2 @ J2 )
% 5.02/5.37 => ( ( B @ J2 )
% 5.02/5.37 = zero_zero_int ) )
% 5.02/5.37 => ( ( times_times_int
% 5.02/5.37 @ ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_int @ ( A @ I5 ) @ ( power_power_int @ X2 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 @ ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X2 @ J3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [R5: nat] :
% 5.02/5.37 ( times_times_int
% 5.02/5.37 @ ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ R5 ) )
% 5.02/5.37 @ ( power_power_int @ X2 @ R5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polynomial_product
% 5.02/5.37 thf(fact_9128_polynomial__product,axiom,
% 5.02/5.37 ! [M: nat,A: nat > real,N2: nat,B: nat > real,X2: real] :
% 5.02/5.37 ( ! [I2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M @ I2 )
% 5.02/5.37 => ( ( A @ I2 )
% 5.02/5.37 = zero_zero_real ) )
% 5.02/5.37 => ( ! [J2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ N2 @ J2 )
% 5.02/5.37 => ( ( B @ J2 )
% 5.02/5.37 = zero_zero_real ) )
% 5.02/5.37 => ( ( times_times_real
% 5.02/5.37 @ ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( A @ I5 ) @ ( power_power_real @ X2 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 @ ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X2 @ J3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [R5: nat] :
% 5.02/5.37 ( times_times_real
% 5.02/5.37 @ ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ R5 ) )
% 5.02/5.37 @ ( power_power_real @ X2 @ R5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polynomial_product
% 5.02/5.37 thf(fact_9129_prod_Oin__pairs__0,axiom,
% 5.02/5.37 ! [G: nat > real,N2: nat] :
% 5.02/5.37 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups129246275422532515t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.in_pairs_0
% 5.02/5.37 thf(fact_9130_prod_Oin__pairs__0,axiom,
% 5.02/5.37 ! [G: nat > rat,N2: nat] :
% 5.02/5.37 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups73079841787564623at_rat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.in_pairs_0
% 5.02/5.37 thf(fact_9131_prod_Oin__pairs__0,axiom,
% 5.02/5.37 ! [G: nat > nat,N2: nat] :
% 5.02/5.37 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups708209901874060359at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.in_pairs_0
% 5.02/5.37 thf(fact_9132_prod_Oin__pairs__0,axiom,
% 5.02/5.37 ! [G: nat > int,N2: nat] :
% 5.02/5.37 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.02/5.37 = ( groups705719431365010083at_int
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % prod.in_pairs_0
% 5.02/5.37 thf(fact_9133_polyfun__eq__const,axiom,
% 5.02/5.37 ! [C: nat > complex,N2: nat,K: complex] :
% 5.02/5.37 ( ( ! [X: complex] :
% 5.02/5.37 ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ X @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = K ) )
% 5.02/5.37 = ( ( ( C @ zero_zero_nat )
% 5.02/5.37 = K )
% 5.02/5.37 & ! [X: nat] :
% 5.02/5.37 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 5.02/5.37 => ( ( C @ X )
% 5.02/5.37 = zero_zero_complex ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_eq_const
% 5.02/5.37 thf(fact_9134_polyfun__eq__const,axiom,
% 5.02/5.37 ! [C: nat > real,N2: nat,K: real] :
% 5.02/5.37 ( ( ! [X: real] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ X @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = K ) )
% 5.02/5.37 = ( ( ( C @ zero_zero_nat )
% 5.02/5.37 = K )
% 5.02/5.37 & ! [X: nat] :
% 5.02/5.37 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 5.02/5.37 => ( ( C @ X )
% 5.02/5.37 = zero_zero_real ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polyfun_eq_const
% 5.02/5.37 thf(fact_9135_gbinomial__sum__lower__neg,axiom,
% 5.02/5.37 ! [A: complex,M: nat] :
% 5.02/5.37 ( ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % gbinomial_sum_lower_neg
% 5.02/5.37 thf(fact_9136_gbinomial__sum__lower__neg,axiom,
% 5.02/5.37 ! [A: rat,M: nat] :
% 5.02/5.37 ( ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % gbinomial_sum_lower_neg
% 5.02/5.37 thf(fact_9137_gbinomial__sum__lower__neg,axiom,
% 5.02/5.37 ! [A: real,M: nat] :
% 5.02/5.37 ( ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % gbinomial_sum_lower_neg
% 5.02/5.37 thf(fact_9138_tan__cot,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X2 ) )
% 5.02/5.37 = ( inverse_inverse_real @ ( tan_real @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % tan_cot
% 5.02/5.37 thf(fact_9139_binomial__ring,axiom,
% 5.02/5.37 ! [A: complex,B: complex,N2: nat] :
% 5.02/5.37 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 5.02/5.37 = ( groups2073611262835488442omplex
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % binomial_ring
% 5.02/5.37 thf(fact_9140_binomial__ring,axiom,
% 5.02/5.37 ! [A: int,B: int,N2: nat] :
% 5.02/5.37 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.02/5.37 = ( groups3539618377306564664at_int
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % binomial_ring
% 5.02/5.37 thf(fact_9141_binomial__ring,axiom,
% 5.02/5.37 ! [A: rat,B: rat,N2: nat] :
% 5.02/5.37 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 5.02/5.37 = ( groups2906978787729119204at_rat
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % binomial_ring
% 5.02/5.37 thf(fact_9142_binomial__ring,axiom,
% 5.02/5.37 ! [A: nat,B: nat,N2: nat] :
% 5.02/5.37 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.02/5.37 = ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % binomial_ring
% 5.02/5.37 thf(fact_9143_binomial__ring,axiom,
% 5.02/5.37 ! [A: real,B: real,N2: nat] :
% 5.02/5.37 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 5.02/5.37 = ( groups6591440286371151544t_real
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % binomial_ring
% 5.02/5.37 thf(fact_9144_polynomial__product__nat,axiom,
% 5.02/5.37 ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X2: nat] :
% 5.02/5.37 ( ! [I2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M @ I2 )
% 5.02/5.37 => ( ( A @ I2 )
% 5.02/5.37 = zero_zero_nat ) )
% 5.02/5.37 => ( ! [J2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ N2 @ J2 )
% 5.02/5.37 => ( ( B @ J2 )
% 5.02/5.37 = zero_zero_nat ) )
% 5.02/5.37 => ( ( times_times_nat
% 5.02/5.37 @ ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( power_power_nat @ X2 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 @ ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X2 @ J3 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.02/5.37 = ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [R5: nat] :
% 5.02/5.37 ( times_times_nat
% 5.02/5.37 @ ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ R5 ) )
% 5.02/5.37 @ ( power_power_nat @ X2 @ R5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % polynomial_product_nat
% 5.02/5.37 thf(fact_9145_choose__square__sum,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N2 @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % choose_square_sum
% 5.02/5.37 thf(fact_9146_real__le__x__sinh,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ord_less_eq_real @ X2 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_le_x_sinh
% 5.02/5.37 thf(fact_9147_real__le__abs__sinh,axiom,
% 5.02/5.37 ! [X2: real] : ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X2 ) @ ( inverse_inverse_real @ ( exp_real @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_le_abs_sinh
% 5.02/5.37 thf(fact_9148_binomial__r__part__sum,axiom,
% 5.02/5.37 ! [M: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.02/5.37 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % binomial_r_part_sum
% 5.02/5.37 thf(fact_9149_choose__linear__sum,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [I5: nat] : ( times_times_nat @ I5 @ ( binomial @ N2 @ I5 ) )
% 5.02/5.37 @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.37 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % choose_linear_sum
% 5.02/5.37 thf(fact_9150_of__nat__id,axiom,
% 5.02/5.37 ( semiri1316708129612266289at_nat
% 5.02/5.37 = ( ^ [N3: nat] : N3 ) ) ).
% 5.02/5.37
% 5.02/5.37 % of_nat_id
% 5.02/5.37 thf(fact_9151_divide__complex__def,axiom,
% 5.02/5.37 ( divide1717551699836669952omplex
% 5.02/5.37 = ( ^ [X: complex,Y6: complex] : ( times_times_complex @ X @ ( invers8013647133539491842omplex @ Y6 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_complex_def
% 5.02/5.37 thf(fact_9152_real__scaleR__def,axiom,
% 5.02/5.37 real_V1485227260804924795R_real = times_times_real ).
% 5.02/5.37
% 5.02/5.37 % real_scaleR_def
% 5.02/5.37 thf(fact_9153_complex__scaleR,axiom,
% 5.02/5.37 ! [R2: real,A: real,B: real] :
% 5.02/5.37 ( ( real_V2046097035970521341omplex @ R2 @ ( complex2 @ A @ B ) )
% 5.02/5.37 = ( complex2 @ ( times_times_real @ R2 @ A ) @ ( times_times_real @ R2 @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % complex_scaleR
% 5.02/5.37 thf(fact_9154_complex__inverse,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.02/5.37 = ( 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 ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % complex_inverse
% 5.02/5.37 thf(fact_9155_i__even__power,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.37 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % i_even_power
% 5.02/5.37 thf(fact_9156_log__base__10__eq1,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.37 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_base_10_eq1
% 5.02/5.37 thf(fact_9157_log__one,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( log @ A @ one_one_real )
% 5.02/5.37 = zero_zero_real ) ).
% 5.02/5.37
% 5.02/5.37 % log_one
% 5.02/5.37 thf(fact_9158_norm__ii,axiom,
% 5.02/5.37 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.02/5.37 = one_one_real ) ).
% 5.02/5.37
% 5.02/5.37 % norm_ii
% 5.02/5.37 thf(fact_9159_complex__i__mult__minus,axiom,
% 5.02/5.37 ! [X2: complex] :
% 5.02/5.37 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X2 ) )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % complex_i_mult_minus
% 5.02/5.37 thf(fact_9160_log__eq__one,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( log @ A @ A )
% 5.02/5.37 = one_one_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_eq_one
% 5.02/5.37 thf(fact_9161_log__less__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.02/5.37 => ( ( ord_less_real @ ( log @ A @ X2 ) @ ( log @ A @ Y ) )
% 5.02/5.37 = ( ord_less_real @ X2 @ Y ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_less_cancel_iff
% 5.02/5.37 thf(fact_9162_log__less__one__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.02/5.37 = ( ord_less_real @ X2 @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_less_one_cancel_iff
% 5.02/5.37 thf(fact_9163_one__less__log__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.02/5.37 = ( ord_less_real @ A @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_less_log_cancel_iff
% 5.02/5.37 thf(fact_9164_log__less__zero__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.02/5.37 = ( ord_less_real @ X2 @ one_one_real ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_less_zero_cancel_iff
% 5.02/5.37 thf(fact_9165_zero__less__log__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.02/5.37 = ( ord_less_real @ one_one_real @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % zero_less_log_cancel_iff
% 5.02/5.37 thf(fact_9166_divide__numeral__i,axiom,
% 5.02/5.37 ! [Z: complex,N2: num] :
% 5.02/5.37 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N2 ) @ imaginary_unit ) )
% 5.02/5.37 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_numeral_i
% 5.02/5.37 thf(fact_9167_divide__i,axiom,
% 5.02/5.37 ! [X2: complex] :
% 5.02/5.37 ( ( divide1717551699836669952omplex @ X2 @ imaginary_unit )
% 5.02/5.37 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_i
% 5.02/5.37 thf(fact_9168_i__squared,axiom,
% 5.02/5.37 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % i_squared
% 5.02/5.37 thf(fact_9169_log__le__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ ( log @ A @ Y ) )
% 5.02/5.37 = ( ord_less_eq_real @ X2 @ Y ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_le_cancel_iff
% 5.02/5.37 thf(fact_9170_log__le__one__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ one_one_real )
% 5.02/5.37 = ( ord_less_eq_real @ X2 @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_le_one_cancel_iff
% 5.02/5.37 thf(fact_9171_one__le__log__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X2 ) )
% 5.02/5.37 = ( ord_less_eq_real @ A @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_le_log_cancel_iff
% 5.02/5.37 thf(fact_9172_log__le__zero__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( log @ A @ X2 ) @ zero_zero_real )
% 5.02/5.37 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_le_zero_cancel_iff
% 5.02/5.37 thf(fact_9173_zero__le__log__cancel__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X2 ) )
% 5.02/5.37 = ( ord_less_eq_real @ one_one_real @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % zero_le_log_cancel_iff
% 5.02/5.37 thf(fact_9174_log__pow__cancel,axiom,
% 5.02/5.37 ! [A: real,B: nat] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.02/5.37 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_pow_cancel
% 5.02/5.37 thf(fact_9175_power2__i,axiom,
% 5.02/5.37 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % power2_i
% 5.02/5.37 thf(fact_9176_complex__i__not__one,axiom,
% 5.02/5.37 imaginary_unit != one_one_complex ).
% 5.02/5.37
% 5.02/5.37 % complex_i_not_one
% 5.02/5.37 thf(fact_9177_cosh__real__ge__1,axiom,
% 5.02/5.37 ! [X2: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % cosh_real_ge_1
% 5.02/5.37 thf(fact_9178_i__times__eq__iff,axiom,
% 5.02/5.37 ! [W: complex,Z: complex] :
% 5.02/5.37 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.02/5.37 = Z )
% 5.02/5.37 = ( W
% 5.02/5.37 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % i_times_eq_iff
% 5.02/5.37 thf(fact_9179_log__ln,axiom,
% 5.02/5.37 ( ln_ln_real
% 5.02/5.37 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_ln
% 5.02/5.37 thf(fact_9180_imaginary__unit_Ocode,axiom,
% 5.02/5.37 ( imaginary_unit
% 5.02/5.37 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % imaginary_unit.code
% 5.02/5.37 thf(fact_9181_Complex__eq__i,axiom,
% 5.02/5.37 ! [X2: real,Y: real] :
% 5.02/5.37 ( ( ( complex2 @ X2 @ Y )
% 5.02/5.37 = imaginary_unit )
% 5.02/5.37 = ( ( X2 = zero_zero_real )
% 5.02/5.37 & ( Y = one_one_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Complex_eq_i
% 5.02/5.37 thf(fact_9182_i__mult__Complex,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.02/5.37 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.02/5.37
% 5.02/5.37 % i_mult_Complex
% 5.02/5.37 thf(fact_9183_Complex__mult__i,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.02/5.37 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.02/5.37
% 5.02/5.37 % Complex_mult_i
% 5.02/5.37 thf(fact_9184_log__base__change,axiom,
% 5.02/5.37 ! [A: real,B: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( log @ B @ X2 )
% 5.02/5.37 = ( divide_divide_real @ ( log @ A @ X2 ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_base_change
% 5.02/5.37 thf(fact_9185_log__of__power__eq,axiom,
% 5.02/5.37 ! [M: nat,B: real,N2: nat] :
% 5.02/5.37 ( ( ( semiri5074537144036343181t_real @ M )
% 5.02/5.37 = ( power_power_real @ B @ N2 ) )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.02/5.37 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_of_power_eq
% 5.02/5.37 thf(fact_9186_less__log__of__power,axiom,
% 5.02/5.37 ! [B: real,N2: nat,M: real] :
% 5.02/5.37 ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % less_log_of_power
% 5.02/5.37 thf(fact_9187_log__mult,axiom,
% 5.02/5.37 ! [A: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.02/5.37 => ( ( log @ A @ ( times_times_real @ X2 @ Y ) )
% 5.02/5.37 = ( plus_plus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_mult
% 5.02/5.37 thf(fact_9188_log__divide,axiom,
% 5.02/5.37 ! [A: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.02/5.37 => ( ( log @ A @ ( divide_divide_real @ X2 @ Y ) )
% 5.02/5.37 = ( minus_minus_real @ ( log @ A @ X2 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_divide
% 5.02/5.37 thf(fact_9189_le__log__of__power,axiom,
% 5.02/5.37 ! [B: real,N2: nat,M: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_log_of_power
% 5.02/5.37 thf(fact_9190_log__nat__power,axiom,
% 5.02/5.37 ! [X2: real,B: real,N2: nat] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( log @ B @ ( power_power_real @ X2 @ N2 ) )
% 5.02/5.37 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_nat_power
% 5.02/5.37 thf(fact_9191_log__inverse,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( log @ A @ ( inverse_inverse_real @ X2 ) )
% 5.02/5.37 = ( uminus_uminus_real @ ( log @ A @ X2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_inverse
% 5.02/5.37 thf(fact_9192_log2__of__power__eq,axiom,
% 5.02/5.37 ! [M: nat,N2: nat] :
% 5.02/5.37 ( ( M
% 5.02/5.37 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.37 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.02/5.37 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log2_of_power_eq
% 5.02/5.37 thf(fact_9193_log__of__power__less,axiom,
% 5.02/5.37 ! [M: nat,B: real,N2: nat] :
% 5.02/5.37 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.37 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_of_power_less
% 5.02/5.37 thf(fact_9194_log__eq__div__ln__mult__log,axiom,
% 5.02/5.37 ! [A: real,B: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.37 => ( ( B != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( log @ A @ X2 )
% 5.02/5.37 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X2 ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_eq_div_ln_mult_log
% 5.02/5.37 thf(fact_9195_log__of__power__le,axiom,
% 5.02/5.37 ! [M: nat,B: real,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.37 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_of_power_le
% 5.02/5.37 thf(fact_9196_less__log2__of__power,axiom,
% 5.02/5.37 ! [N2: nat,M: nat] :
% 5.02/5.37 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.02/5.37 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % less_log2_of_power
% 5.02/5.37 thf(fact_9197_le__log2__of__power,axiom,
% 5.02/5.37 ! [N2: nat,M: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.02/5.37 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_log2_of_power
% 5.02/5.37 thf(fact_9198_log2__of__power__less,axiom,
% 5.02/5.37 ! [M: nat,N2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.37 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.37 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log2_of_power_less
% 5.02/5.37 thf(fact_9199_cosh__ln__real,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( cosh_real @ ( ln_ln_real @ X2 ) )
% 5.02/5.37 = ( divide_divide_real @ ( plus_plus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % cosh_ln_real
% 5.02/5.37 thf(fact_9200_log2__of__power__le,axiom,
% 5.02/5.37 ! [M: nat,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.37 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.37 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log2_of_power_le
% 5.02/5.37 thf(fact_9201_log__base__10__eq2,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X2 )
% 5.02/5.37 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_base_10_eq2
% 5.02/5.37 thf(fact_9202_sinh__ln__real,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( sinh_real @ ( ln_ln_real @ X2 ) )
% 5.02/5.37 = ( divide_divide_real @ ( minus_minus_real @ X2 @ ( inverse_inverse_real @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sinh_ln_real
% 5.02/5.37 thf(fact_9203_Arg__minus__ii,axiom,
% 5.02/5.37 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.02/5.37 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Arg_minus_ii
% 5.02/5.37 thf(fact_9204_ceiling__log__nat__eq__powr__iff,axiom,
% 5.02/5.37 ! [B: nat,K: nat,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.02/5.37 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.37 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.02/5.37 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 5.02/5.37 = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.02/5.37 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ceiling_log_nat_eq_powr_iff
% 5.02/5.37 thf(fact_9205_Arg__ii,axiom,
% 5.02/5.37 ( ( arg @ imaginary_unit )
% 5.02/5.37 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Arg_ii
% 5.02/5.37 thf(fact_9206_ceiling__log2__div2,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.37 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ceiling_log2_div2
% 5.02/5.37 thf(fact_9207_ceiling__divide__eq__div__numeral,axiom,
% 5.02/5.37 ! [A: num,B: num] :
% 5.02/5.37 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.02/5.37 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ceiling_divide_eq_div_numeral
% 5.02/5.37 thf(fact_9208_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.02/5.37 ! [A: num,B: num] :
% 5.02/5.37 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.02/5.37 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ceiling_minus_divide_eq_div_numeral
% 5.02/5.37 thf(fact_9209_ceiling__log__nat__eq__if,axiom,
% 5.02/5.37 ! [B: nat,N2: nat,K: nat] :
% 5.02/5.37 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.02/5.37 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.02/5.37 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.02/5.37 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.02/5.37 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ceiling_log_nat_eq_if
% 5.02/5.37 thf(fact_9210_cis__minus__pi__half,axiom,
% 5.02/5.37 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.02/5.37
% 5.02/5.37 % cis_minus_pi_half
% 5.02/5.37 thf(fact_9211_ceiling__log__eq__powr__iff,axiom,
% 5.02/5.37 ! [X2: real,B: real,K: nat] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X2 ) )
% 5.02/5.37 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.02/5.37 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X2 )
% 5.02/5.37 & ( ord_less_eq_real @ X2 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ceiling_log_eq_powr_iff
% 5.02/5.37 thf(fact_9212_floor__log__nat__eq__powr__iff,axiom,
% 5.02/5.37 ! [B: nat,K: nat,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.02/5.37 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.02/5.37 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.02/5.37 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.37 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.02/5.37 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_log_nat_eq_powr_iff
% 5.02/5.37 thf(fact_9213_floor__log__nat__eq__if,axiom,
% 5.02/5.37 ! [B: nat,N2: nat,K: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.02/5.37 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.02/5.37 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.02/5.37 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.02/5.37 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_log_nat_eq_if
% 5.02/5.37 thf(fact_9214_powr__less__cancel__iff,axiom,
% 5.02/5.37 ! [X2: real,A: real,B: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.02/5.37 = ( ord_less_real @ A @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_less_cancel_iff
% 5.02/5.37 thf(fact_9215_norm__cis,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.02/5.37 = one_one_real ) ).
% 5.02/5.37
% 5.02/5.37 % norm_cis
% 5.02/5.37 thf(fact_9216_cis__zero,axiom,
% 5.02/5.37 ( ( cis @ zero_zero_real )
% 5.02/5.37 = one_one_complex ) ).
% 5.02/5.37
% 5.02/5.37 % cis_zero
% 5.02/5.37 thf(fact_9217_powr__eq__one__iff,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ A )
% 5.02/5.37 => ( ( ( powr_real @ A @ X2 )
% 5.02/5.37 = one_one_real )
% 5.02/5.37 = ( X2 = zero_zero_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_eq_one_iff
% 5.02/5.37 thf(fact_9218_powr__one,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( powr_real @ X2 @ one_one_real )
% 5.02/5.37 = X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_one
% 5.02/5.37 thf(fact_9219_powr__one__gt__zero__iff,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ( powr_real @ X2 @ one_one_real )
% 5.02/5.37 = X2 )
% 5.02/5.37 = ( ord_less_eq_real @ zero_zero_real @ X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_one_gt_zero_iff
% 5.02/5.37 thf(fact_9220_powr__le__cancel__iff,axiom,
% 5.02/5.37 ! [X2: real,A: real,B: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.02/5.37 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_le_cancel_iff
% 5.02/5.37 thf(fact_9221_numeral__powr__numeral__real,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.37 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % numeral_powr_numeral_real
% 5.02/5.37 thf(fact_9222_cis__pi,axiom,
% 5.02/5.37 ( ( cis @ pi )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % cis_pi
% 5.02/5.37 thf(fact_9223_powr__log__cancel,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( powr_real @ A @ ( log @ A @ X2 ) )
% 5.02/5.37 = X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_log_cancel
% 5.02/5.37 thf(fact_9224_log__powr__cancel,axiom,
% 5.02/5.37 ! [A: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 5.02/5.37 = Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_powr_cancel
% 5.02/5.37 thf(fact_9225_floor__divide__eq__div__numeral,axiom,
% 5.02/5.37 ! [A: num,B: num] :
% 5.02/5.37 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.02/5.37 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_divide_eq_div_numeral
% 5.02/5.37 thf(fact_9226_powr__numeral,axiom,
% 5.02/5.37 ! [X2: real,N2: num] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( powr_real @ X2 @ ( numeral_numeral_real @ N2 ) )
% 5.02/5.37 = ( power_power_real @ X2 @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_numeral
% 5.02/5.37 thf(fact_9227_cis__pi__half,axiom,
% 5.02/5.37 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.37 = imaginary_unit ) ).
% 5.02/5.37
% 5.02/5.37 % cis_pi_half
% 5.02/5.37 thf(fact_9228_floor__one__divide__eq__div__numeral,axiom,
% 5.02/5.37 ! [B: num] :
% 5.02/5.37 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.02/5.37 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_one_divide_eq_div_numeral
% 5.02/5.37 thf(fact_9229_cis__2pi,axiom,
% 5.02/5.37 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.02/5.37 = one_one_complex ) ).
% 5.02/5.37
% 5.02/5.37 % cis_2pi
% 5.02/5.37 thf(fact_9230_floor__minus__divide__eq__div__numeral,axiom,
% 5.02/5.37 ! [A: num,B: num] :
% 5.02/5.37 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.02/5.37 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_minus_divide_eq_div_numeral
% 5.02/5.37 thf(fact_9231_square__powr__half,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( powr_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.37 = ( abs_abs_real @ X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % square_powr_half
% 5.02/5.37 thf(fact_9232_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.02/5.37 ! [B: num] :
% 5.02/5.37 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.02/5.37 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_minus_one_divide_eq_div_numeral
% 5.02/5.37 thf(fact_9233_powr__powr,axiom,
% 5.02/5.37 ! [X2: real,A: real,B: real] :
% 5.02/5.37 ( ( powr_real @ ( powr_real @ X2 @ A ) @ B )
% 5.02/5.37 = ( powr_real @ X2 @ ( times_times_real @ A @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_powr
% 5.02/5.37 thf(fact_9234_powr__less__cancel,axiom,
% 5.02/5.37 ! [X2: real,A: real,B: real] :
% 5.02/5.37 ( ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ord_less_real @ A @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_less_cancel
% 5.02/5.37 thf(fact_9235_powr__less__mono,axiom,
% 5.02/5.37 ! [A: real,B: real,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ A @ B )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ord_less_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_less_mono
% 5.02/5.37 thf(fact_9236_powr__mono,axiom,
% 5.02/5.37 ! [A: real,B: real,X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ A @ B )
% 5.02/5.37 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ X2 @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_mono
% 5.02/5.37 thf(fact_9237_cis__mult,axiom,
% 5.02/5.37 ! [A: real,B: real] :
% 5.02/5.37 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.02/5.37 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % cis_mult
% 5.02/5.37 thf(fact_9238_gr__one__powr,axiom,
% 5.02/5.37 ! [X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.02/5.37 => ( ord_less_real @ one_one_real @ ( powr_real @ X2 @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % gr_one_powr
% 5.02/5.37 thf(fact_9239_powr__inj,axiom,
% 5.02/5.37 ! [A: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( A != one_one_real )
% 5.02/5.37 => ( ( ( powr_real @ A @ X2 )
% 5.02/5.37 = ( powr_real @ A @ Y ) )
% 5.02/5.37 = ( X2 = Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_inj
% 5.02/5.37 thf(fact_9240_powr__le1,axiom,
% 5.02/5.37 ! [A: real,X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.37 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ one_one_real ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_le1
% 5.02/5.37 thf(fact_9241_powr__mono__both,axiom,
% 5.02/5.37 ! [A: real,B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( ord_less_eq_real @ A @ B )
% 5.02/5.37 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.37 => ( ord_less_eq_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_mono_both
% 5.02/5.37 thf(fact_9242_ge__one__powr__ge__zero,axiom,
% 5.02/5.37 ! [X2: real,A: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X2 @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ge_one_powr_ge_zero
% 5.02/5.37 thf(fact_9243_powr__mult,axiom,
% 5.02/5.37 ! [X2: real,Y: real,A: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.37 => ( ( powr_real @ ( times_times_real @ X2 @ Y ) @ A )
% 5.02/5.37 = ( times_times_real @ ( powr_real @ X2 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_mult
% 5.02/5.37 thf(fact_9244_divide__powr__uminus,axiom,
% 5.02/5.37 ! [A: real,B: real,C: real] :
% 5.02/5.37 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.02/5.37 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_powr_uminus
% 5.02/5.37 thf(fact_9245_ln__powr,axiom,
% 5.02/5.37 ! [X2: real,Y: real] :
% 5.02/5.37 ( ( X2 != zero_zero_real )
% 5.02/5.37 => ( ( ln_ln_real @ ( powr_real @ X2 @ Y ) )
% 5.02/5.37 = ( times_times_real @ Y @ ( ln_ln_real @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ln_powr
% 5.02/5.37 thf(fact_9246_log__powr,axiom,
% 5.02/5.37 ! [X2: real,B: real,Y: real] :
% 5.02/5.37 ( ( X2 != zero_zero_real )
% 5.02/5.37 => ( ( log @ B @ ( powr_real @ X2 @ Y ) )
% 5.02/5.37 = ( times_times_real @ Y @ ( log @ B @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_powr
% 5.02/5.37 thf(fact_9247_floor__log__eq__powr__iff,axiom,
% 5.02/5.37 ! [X2: real,B: real,K: int] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X2 ) )
% 5.02/5.37 = K )
% 5.02/5.37 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X2 )
% 5.02/5.37 & ( ord_less_real @ X2 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_log_eq_powr_iff
% 5.02/5.37 thf(fact_9248_less__log__iff,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ Y @ ( log @ B @ X2 ) )
% 5.02/5.37 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % less_log_iff
% 5.02/5.37 thf(fact_9249_log__less__iff,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ ( log @ B @ X2 ) @ Y )
% 5.02/5.37 = ( ord_less_real @ X2 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_less_iff
% 5.02/5.37 thf(fact_9250_less__powr__iff,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ X2 @ ( powr_real @ B @ Y ) )
% 5.02/5.37 = ( ord_less_real @ ( log @ B @ X2 ) @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % less_powr_iff
% 5.02/5.37 thf(fact_9251_powr__less__iff,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X2 )
% 5.02/5.37 = ( ord_less_real @ Y @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_less_iff
% 5.02/5.37 thf(fact_9252_real__of__int__floor__add__one__gt,axiom,
% 5.02/5.37 ! [R2: real] : ( ord_less_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_of_int_floor_add_one_gt
% 5.02/5.37 thf(fact_9253_floor__eq,axiom,
% 5.02/5.37 ! [N2: int,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.02/5.37 => ( ( archim6058952711729229775r_real @ X2 )
% 5.02/5.37 = N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_eq
% 5.02/5.37 thf(fact_9254_real__of__int__floor__add__one__ge,axiom,
% 5.02/5.37 ! [R2: real] : ( ord_less_eq_real @ R2 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) @ one_one_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_of_int_floor_add_one_ge
% 5.02/5.37 thf(fact_9255_real__of__int__floor__gt__diff__one,axiom,
% 5.02/5.37 ! [R2: real] : ( ord_less_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_of_int_floor_gt_diff_one
% 5.02/5.37 thf(fact_9256_real__of__int__floor__ge__diff__one,axiom,
% 5.02/5.37 ! [R2: real] : ( ord_less_eq_real @ ( minus_minus_real @ R2 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_of_int_floor_ge_diff_one
% 5.02/5.37 thf(fact_9257_DeMoivre,axiom,
% 5.02/5.37 ! [A: real,N2: nat] :
% 5.02/5.37 ( ( power_power_complex @ ( cis @ A ) @ N2 )
% 5.02/5.37 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % DeMoivre
% 5.02/5.37 thf(fact_9258_powr__neg__one,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ one_one_real ) )
% 5.02/5.37 = ( divide_divide_real @ one_one_real @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_neg_one
% 5.02/5.37 thf(fact_9259_powr__mult__base,axiom,
% 5.02/5.37 ! [X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( times_times_real @ X2 @ ( powr_real @ X2 @ Y ) )
% 5.02/5.37 = ( powr_real @ X2 @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_mult_base
% 5.02/5.37 thf(fact_9260_le__log__iff,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X2 ) )
% 5.02/5.37 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_log_iff
% 5.02/5.37 thf(fact_9261_log__le__iff,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y )
% 5.02/5.37 = ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_le_iff
% 5.02/5.37 thf(fact_9262_le__powr__iff,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ X2 @ ( powr_real @ B @ Y ) )
% 5.02/5.37 = ( ord_less_eq_real @ ( log @ B @ X2 ) @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_powr_iff
% 5.02/5.37 thf(fact_9263_powr__le__iff,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X2 )
% 5.02/5.37 = ( ord_less_eq_real @ Y @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_le_iff
% 5.02/5.37 thf(fact_9264_floor__eq2,axiom,
% 5.02/5.37 ! [N2: int,X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ X2 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.02/5.37 => ( ( archim6058952711729229775r_real @ X2 )
% 5.02/5.37 = N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_eq2
% 5.02/5.37 thf(fact_9265_floor__divide__real__eq__div,axiom,
% 5.02/5.37 ! [B: int,A: real] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.02/5.37 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.02/5.37 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_divide_real_eq_div
% 5.02/5.37 thf(fact_9266_ln__powr__bound,axiom,
% 5.02/5.37 ! [X2: real,A: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ord_less_eq_real @ ( ln_ln_real @ X2 ) @ ( divide_divide_real @ ( powr_real @ X2 @ A ) @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ln_powr_bound
% 5.02/5.37 thf(fact_9267_ln__powr__bound2,axiom,
% 5.02/5.37 ! [X2: real,A: real] :
% 5.02/5.37 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X2 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ln_powr_bound2
% 5.02/5.37 thf(fact_9268_log__add__eq__powr,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.37 => ( ( B != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( plus_plus_real @ ( log @ B @ X2 ) @ Y )
% 5.02/5.37 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_add_eq_powr
% 5.02/5.37 thf(fact_9269_add__log__eq__powr,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.37 => ( ( B != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( plus_plus_real @ Y @ ( log @ B @ X2 ) )
% 5.02/5.37 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % add_log_eq_powr
% 5.02/5.37 thf(fact_9270_minus__log__eq__powr,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.37 => ( ( B != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( minus_minus_real @ Y @ ( log @ B @ X2 ) )
% 5.02/5.37 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % minus_log_eq_powr
% 5.02/5.37 thf(fact_9271_log__minus__eq__powr,axiom,
% 5.02/5.37 ! [B: real,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.37 => ( ( B != one_one_real )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( minus_minus_real @ ( log @ B @ X2 ) @ Y )
% 5.02/5.37 = ( log @ B @ ( times_times_real @ X2 @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_minus_eq_powr
% 5.02/5.37 thf(fact_9272_powr__half__sqrt,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.37 = ( sqrt @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_half_sqrt
% 5.02/5.37 thf(fact_9273_powr__neg__numeral,axiom,
% 5.02/5.37 ! [X2: real,N2: num] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( powr_real @ X2 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.02/5.37 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_neg_numeral
% 5.02/5.37 thf(fact_9274_floor__log2__div2,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.37 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.02/5.37 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_log2_div2
% 5.02/5.37 thf(fact_9275_bij__betw__roots__unity,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( bij_betw_nat_complex
% 5.02/5.37 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.02/5.37 @ ( set_ord_lessThan_nat @ N2 )
% 5.02/5.37 @ ( collect_complex
% 5.02/5.37 @ ^ [Z6: complex] :
% 5.02/5.37 ( ( power_power_complex @ Z6 @ N2 )
% 5.02/5.37 = one_one_complex ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bij_betw_roots_unity
% 5.02/5.37 thf(fact_9276_exp__pi__i_H,axiom,
% 5.02/5.37 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % exp_pi_i'
% 5.02/5.37 thf(fact_9277_exp__pi__i,axiom,
% 5.02/5.37 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.02/5.37 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % exp_pi_i
% 5.02/5.37 thf(fact_9278_exp__two__pi__i,axiom,
% 5.02/5.37 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.02/5.37 = one_one_complex ) ).
% 5.02/5.37
% 5.02/5.37 % exp_two_pi_i
% 5.02/5.37 thf(fact_9279_exp__two__pi__i_H,axiom,
% 5.02/5.37 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.02/5.37 = one_one_complex ) ).
% 5.02/5.37
% 5.02/5.37 % exp_two_pi_i'
% 5.02/5.37 thf(fact_9280_complex__exp__exists,axiom,
% 5.02/5.37 ! [Z: complex] :
% 5.02/5.37 ? [A4: complex,R3: real] :
% 5.02/5.37 ( Z
% 5.02/5.37 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( exp_complex @ A4 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % complex_exp_exists
% 5.02/5.37 thf(fact_9281_Complex__mult__complex__of__real,axiom,
% 5.02/5.37 ! [X2: real,Y: real,R2: real] :
% 5.02/5.37 ( ( times_times_complex @ ( complex2 @ X2 @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.02/5.37 = ( complex2 @ ( times_times_real @ X2 @ R2 ) @ ( times_times_real @ Y @ R2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Complex_mult_complex_of_real
% 5.02/5.37 thf(fact_9282_complex__of__real__mult__Complex,axiom,
% 5.02/5.37 ! [R2: real,X2: real,Y: real] :
% 5.02/5.37 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X2 @ Y ) )
% 5.02/5.37 = ( complex2 @ ( times_times_real @ R2 @ X2 ) @ ( times_times_real @ R2 @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % complex_of_real_mult_Complex
% 5.02/5.37 thf(fact_9283_Complex__add__complex__of__real,axiom,
% 5.02/5.37 ! [X2: real,Y: real,R2: real] :
% 5.02/5.37 ( ( plus_plus_complex @ ( complex2 @ X2 @ Y ) @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.02/5.37 = ( complex2 @ ( plus_plus_real @ X2 @ R2 ) @ Y ) ) ).
% 5.02/5.37
% 5.02/5.37 % Complex_add_complex_of_real
% 5.02/5.37 thf(fact_9284_complex__of__real__add__Complex,axiom,
% 5.02/5.37 ! [R2: real,X2: real,Y: real] :
% 5.02/5.37 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( complex2 @ X2 @ Y ) )
% 5.02/5.37 = ( complex2 @ ( plus_plus_real @ R2 @ X2 ) @ Y ) ) ).
% 5.02/5.37
% 5.02/5.37 % complex_of_real_add_Complex
% 5.02/5.37 thf(fact_9285_cis__conv__exp,axiom,
% 5.02/5.37 ( cis
% 5.02/5.37 = ( ^ [B5: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B5 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % cis_conv_exp
% 5.02/5.37 thf(fact_9286_i__complex__of__real,axiom,
% 5.02/5.37 ! [R2: real] :
% 5.02/5.37 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R2 ) )
% 5.02/5.37 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % i_complex_of_real
% 5.02/5.37 thf(fact_9287_complex__of__real__i,axiom,
% 5.02/5.37 ! [R2: real] :
% 5.02/5.37 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ imaginary_unit )
% 5.02/5.37 = ( complex2 @ zero_zero_real @ R2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % complex_of_real_i
% 5.02/5.37 thf(fact_9288_Complex__eq,axiom,
% 5.02/5.37 ( complex2
% 5.02/5.37 = ( ^ [A5: real,B5: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A5 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B5 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Complex_eq
% 5.02/5.37 thf(fact_9289_complex__split__polar,axiom,
% 5.02/5.37 ! [Z: complex] :
% 5.02/5.37 ? [R3: real,A4: real] :
% 5.02/5.37 ( Z
% 5.02/5.37 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A4 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A4 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % complex_split_polar
% 5.02/5.37 thf(fact_9290_cmod__unit__one,axiom,
% 5.02/5.37 ! [A: real] :
% 5.02/5.37 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.02/5.37 = one_one_real ) ).
% 5.02/5.37
% 5.02/5.37 % cmod_unit_one
% 5.02/5.37 thf(fact_9291_cmod__complex__polar,axiom,
% 5.02/5.37 ! [R2: real,A: real] :
% 5.02/5.37 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 5.02/5.37 = ( abs_abs_real @ R2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % cmod_complex_polar
% 5.02/5.37 thf(fact_9292_csqrt__ii,axiom,
% 5.02/5.37 ( ( csqrt @ imaginary_unit )
% 5.02/5.37 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % csqrt_ii
% 5.02/5.37 thf(fact_9293_arctan__def,axiom,
% 5.02/5.37 ( arctan
% 5.02/5.37 = ( ^ [Y6: real] :
% 5.02/5.37 ( the_real
% 5.02/5.37 @ ^ [X: real] :
% 5.02/5.37 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.02/5.37 & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.37 & ( ( tan_real @ X )
% 5.02/5.37 = Y6 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % arctan_def
% 5.02/5.37 thf(fact_9294_arcsin__def,axiom,
% 5.02/5.37 ( arcsin
% 5.02/5.37 = ( ^ [Y6: real] :
% 5.02/5.37 ( the_real
% 5.02/5.37 @ ^ [X: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.02/5.37 & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.37 & ( ( sin_real @ X )
% 5.02/5.37 = Y6 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % arcsin_def
% 5.02/5.37 thf(fact_9295_modulo__int__unfold,axiom,
% 5.02/5.37 ! [L: int,K: int,N2: nat,M: nat] :
% 5.02/5.37 ( ( ( ( ( sgn_sgn_int @ L )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 | ( ( sgn_sgn_int @ K )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 | ( N2 = zero_zero_nat ) )
% 5.02/5.37 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.37 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.02/5.37 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 | ( ( sgn_sgn_int @ K )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 | ( N2 = zero_zero_nat ) )
% 5.02/5.37 => ( ( ( ( sgn_sgn_int @ K )
% 5.02/5.37 = ( sgn_sgn_int @ L ) )
% 5.02/5.37 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.37 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 5.02/5.37 & ( ( ( sgn_sgn_int @ K )
% 5.02/5.37 != ( sgn_sgn_int @ L ) )
% 5.02/5.37 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.37 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.02/5.37 @ ( minus_minus_int
% 5.02/5.37 @ ( semiri1314217659103216013at_int
% 5.02/5.37 @ ( times_times_nat @ N2
% 5.02/5.37 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.37 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 5.02/5.37 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % modulo_int_unfold
% 5.02/5.37 thf(fact_9296_csqrt__eq__1,axiom,
% 5.02/5.37 ! [Z: complex] :
% 5.02/5.37 ( ( ( csqrt @ Z )
% 5.02/5.37 = one_one_complex )
% 5.02/5.37 = ( Z = one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % csqrt_eq_1
% 5.02/5.37 thf(fact_9297_csqrt__1,axiom,
% 5.02/5.37 ( ( csqrt @ one_one_complex )
% 5.02/5.37 = one_one_complex ) ).
% 5.02/5.37
% 5.02/5.37 % csqrt_1
% 5.02/5.37 thf(fact_9298_dvd__mult__sgn__iff,axiom,
% 5.02/5.37 ! [L: int,K: int,R2: int] :
% 5.02/5.37 ( ( dvd_dvd_int @ L @ ( times_times_int @ K @ ( sgn_sgn_int @ R2 ) ) )
% 5.02/5.37 = ( ( dvd_dvd_int @ L @ K )
% 5.02/5.37 | ( R2 = zero_zero_int ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % dvd_mult_sgn_iff
% 5.02/5.37 thf(fact_9299_dvd__sgn__mult__iff,axiom,
% 5.02/5.37 ! [L: int,R2: int,K: int] :
% 5.02/5.37 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ K ) )
% 5.02/5.37 = ( ( dvd_dvd_int @ L @ K )
% 5.02/5.37 | ( R2 = zero_zero_int ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % dvd_sgn_mult_iff
% 5.02/5.37 thf(fact_9300_mult__sgn__dvd__iff,axiom,
% 5.02/5.37 ! [L: int,R2: int,K: int] :
% 5.02/5.37 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R2 ) ) @ K )
% 5.02/5.37 = ( ( dvd_dvd_int @ L @ K )
% 5.02/5.37 & ( ( R2 = zero_zero_int )
% 5.02/5.37 => ( K = zero_zero_int ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mult_sgn_dvd_iff
% 5.02/5.37 thf(fact_9301_sgn__mult__dvd__iff,axiom,
% 5.02/5.37 ! [R2: int,L: int,K: int] :
% 5.02/5.37 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R2 ) @ L ) @ K )
% 5.02/5.37 = ( ( dvd_dvd_int @ L @ K )
% 5.02/5.37 & ( ( R2 = zero_zero_int )
% 5.02/5.37 => ( K = zero_zero_int ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sgn_mult_dvd_iff
% 5.02/5.37 thf(fact_9302_power2__csqrt,axiom,
% 5.02/5.37 ! [Z: complex] :
% 5.02/5.37 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.37 = Z ) ).
% 5.02/5.37
% 5.02/5.37 % power2_csqrt
% 5.02/5.37 thf(fact_9303_int__sgnE,axiom,
% 5.02/5.37 ! [K: int] :
% 5.02/5.37 ~ ! [N: nat,L4: int] :
% 5.02/5.37 ( K
% 5.02/5.37 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % int_sgnE
% 5.02/5.37 thf(fact_9304_div__eq__sgn__abs,axiom,
% 5.02/5.37 ! [K: int,L: int] :
% 5.02/5.37 ( ( ( sgn_sgn_int @ K )
% 5.02/5.37 = ( sgn_sgn_int @ L ) )
% 5.02/5.37 => ( ( divide_divide_int @ K @ L )
% 5.02/5.37 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % div_eq_sgn_abs
% 5.02/5.37 thf(fact_9305_sgn__mod,axiom,
% 5.02/5.37 ! [L: int,K: int] :
% 5.02/5.37 ( ( L != zero_zero_int )
% 5.02/5.37 => ( ~ ( dvd_dvd_int @ L @ K )
% 5.02/5.37 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 5.02/5.37 = ( sgn_sgn_int @ L ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sgn_mod
% 5.02/5.37 thf(fact_9306_zsgn__def,axiom,
% 5.02/5.37 ( sgn_sgn_int
% 5.02/5.37 = ( ^ [I5: int] : ( if_int @ ( I5 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I5 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % zsgn_def
% 5.02/5.37 thf(fact_9307_div__sgn__abs__cancel,axiom,
% 5.02/5.37 ! [V: int,K: int,L: int] :
% 5.02/5.37 ( ( V != zero_zero_int )
% 5.02/5.37 => ( ( 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 ) ) )
% 5.02/5.37 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % div_sgn_abs_cancel
% 5.02/5.37 thf(fact_9308_div__dvd__sgn__abs,axiom,
% 5.02/5.37 ! [L: int,K: int] :
% 5.02/5.37 ( ( dvd_dvd_int @ L @ K )
% 5.02/5.37 => ( ( divide_divide_int @ K @ L )
% 5.02/5.37 = ( 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 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % div_dvd_sgn_abs
% 5.02/5.37 thf(fact_9309_eucl__rel__int__remainderI,axiom,
% 5.02/5.37 ! [R2: int,L: int,K: int,Q2: int] :
% 5.02/5.37 ( ( ( sgn_sgn_int @ R2 )
% 5.02/5.37 = ( sgn_sgn_int @ L ) )
% 5.02/5.37 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ L ) )
% 5.02/5.37 => ( ( K
% 5.02/5.37 = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R2 ) )
% 5.02/5.37 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q2 @ R2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % eucl_rel_int_remainderI
% 5.02/5.37 thf(fact_9310_eucl__rel__int_Osimps,axiom,
% 5.02/5.37 ( eucl_rel_int
% 5.02/5.37 = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 5.02/5.37 ( ? [K3: int] :
% 5.02/5.37 ( ( A1 = K3 )
% 5.02/5.37 & ( A22 = zero_zero_int )
% 5.02/5.37 & ( A32
% 5.02/5.37 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.02/5.37 | ? [L2: int,K3: int,Q4: int] :
% 5.02/5.37 ( ( A1 = K3 )
% 5.02/5.37 & ( A22 = L2 )
% 5.02/5.37 & ( A32
% 5.02/5.37 = ( product_Pair_int_int @ Q4 @ zero_zero_int ) )
% 5.02/5.37 & ( L2 != zero_zero_int )
% 5.02/5.37 & ( K3
% 5.02/5.37 = ( times_times_int @ Q4 @ L2 ) ) )
% 5.02/5.37 | ? [R5: int,L2: int,K3: int,Q4: int] :
% 5.02/5.37 ( ( A1 = K3 )
% 5.02/5.37 & ( A22 = L2 )
% 5.02/5.37 & ( A32
% 5.02/5.37 = ( product_Pair_int_int @ Q4 @ R5 ) )
% 5.02/5.37 & ( ( sgn_sgn_int @ R5 )
% 5.02/5.37 = ( sgn_sgn_int @ L2 ) )
% 5.02/5.37 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 5.02/5.37 & ( K3
% 5.02/5.37 = ( plus_plus_int @ ( times_times_int @ Q4 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % eucl_rel_int.simps
% 5.02/5.37 thf(fact_9311_eucl__rel__int_Ocases,axiom,
% 5.02/5.37 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 5.02/5.37 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 5.02/5.37 => ( ( ( A23 = zero_zero_int )
% 5.02/5.37 => ( A33
% 5.02/5.37 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.02/5.37 => ( ! [Q3: int] :
% 5.02/5.37 ( ( A33
% 5.02/5.37 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.02/5.37 => ( ( A23 != zero_zero_int )
% 5.02/5.37 => ( A12
% 5.02/5.37 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.02/5.37 => ~ ! [R3: int,Q3: int] :
% 5.02/5.37 ( ( A33
% 5.02/5.37 = ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.02/5.37 => ( ( ( sgn_sgn_int @ R3 )
% 5.02/5.37 = ( sgn_sgn_int @ A23 ) )
% 5.02/5.37 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ A23 ) )
% 5.02/5.37 => ( A12
% 5.02/5.37 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R3 ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % eucl_rel_int.cases
% 5.02/5.37 thf(fact_9312_div__noneq__sgn__abs,axiom,
% 5.02/5.37 ! [L: int,K: int] :
% 5.02/5.37 ( ( L != zero_zero_int )
% 5.02/5.37 => ( ( ( sgn_sgn_int @ K )
% 5.02/5.37 != ( sgn_sgn_int @ L ) )
% 5.02/5.37 => ( ( divide_divide_int @ K @ L )
% 5.02/5.37 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.02/5.37 @ ( zero_n2684676970156552555ol_int
% 5.02/5.37 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % div_noneq_sgn_abs
% 5.02/5.37 thf(fact_9313_pi__half,axiom,
% 5.02/5.37 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.37 = ( the_real
% 5.02/5.37 @ ^ [X: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.02/5.37 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.37 & ( ( cos_real @ X )
% 5.02/5.37 = zero_zero_real ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % pi_half
% 5.02/5.37 thf(fact_9314_pi__def,axiom,
% 5.02/5.37 ( pi
% 5.02/5.37 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.02/5.37 @ ( the_real
% 5.02/5.37 @ ^ [X: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.02/5.37 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.02/5.37 & ( ( cos_real @ X )
% 5.02/5.37 = zero_zero_real ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % pi_def
% 5.02/5.37 thf(fact_9315_divide__int__unfold,axiom,
% 5.02/5.37 ! [L: int,K: int,N2: nat,M: nat] :
% 5.02/5.37 ( ( ( ( ( sgn_sgn_int @ L )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 | ( ( sgn_sgn_int @ K )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 | ( N2 = zero_zero_nat ) )
% 5.02/5.37 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.37 = zero_zero_int ) )
% 5.02/5.37 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 | ( ( sgn_sgn_int @ K )
% 5.02/5.37 = zero_zero_int )
% 5.02/5.37 | ( N2 = zero_zero_nat ) )
% 5.02/5.37 => ( ( ( ( sgn_sgn_int @ K )
% 5.02/5.37 = ( sgn_sgn_int @ L ) )
% 5.02/5.37 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.37 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 5.02/5.37 & ( ( ( sgn_sgn_int @ K )
% 5.02/5.37 != ( sgn_sgn_int @ L ) )
% 5.02/5.37 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.37 = ( uminus_uminus_int
% 5.02/5.37 @ ( semiri1314217659103216013at_int
% 5.02/5.37 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 5.02/5.37 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.37 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_int_unfold
% 5.02/5.37 thf(fact_9316_modulo__int__def,axiom,
% 5.02/5.37 ( modulo_modulo_int
% 5.02/5.37 = ( ^ [K3: int,L2: int] :
% 5.02/5.37 ( if_int @ ( L2 = zero_zero_int ) @ K3
% 5.02/5.37 @ ( if_int
% 5.02/5.37 @ ( ( sgn_sgn_int @ K3 )
% 5.02/5.37 = ( sgn_sgn_int @ L2 ) )
% 5.02/5.37 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 5.02/5.37 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.02/5.37 @ ( minus_minus_int
% 5.02/5.37 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 5.02/5.37 @ ( zero_n2684676970156552555ol_int
% 5.02/5.37 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 5.02/5.37 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % modulo_int_def
% 5.02/5.37 thf(fact_9317_divide__int__def,axiom,
% 5.02/5.37 ( divide_divide_int
% 5.02/5.37 = ( ^ [K3: int,L2: int] :
% 5.02/5.37 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 5.02/5.37 @ ( if_int
% 5.02/5.37 @ ( ( sgn_sgn_int @ K3 )
% 5.02/5.37 = ( sgn_sgn_int @ L2 ) )
% 5.02/5.37 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 5.02/5.37 @ ( uminus_uminus_int
% 5.02/5.37 @ ( semiri1314217659103216013at_int
% 5.02/5.37 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 5.02/5.37 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.37 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_int_def
% 5.02/5.37 thf(fact_9318_powr__int,axiom,
% 5.02/5.37 ! [X2: real,I3: int] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ( ord_less_eq_int @ zero_zero_int @ I3 )
% 5.02/5.37 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I3 ) )
% 5.02/5.37 = ( power_power_real @ X2 @ ( nat2 @ I3 ) ) ) )
% 5.02/5.37 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I3 )
% 5.02/5.37 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ I3 ) )
% 5.02/5.37 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ I3 ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_int
% 5.02/5.37 thf(fact_9319_nat__int,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( nat2 @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.02/5.37 = N2 ) ).
% 5.02/5.37
% 5.02/5.37 % nat_int
% 5.02/5.37 thf(fact_9320_nat__numeral,axiom,
% 5.02/5.37 ! [K: num] :
% 5.02/5.37 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.02/5.37 = ( numeral_numeral_nat @ K ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_numeral
% 5.02/5.37 thf(fact_9321_nat__of__bool,axiom,
% 5.02/5.37 ! [P: $o] :
% 5.02/5.37 ( ( nat2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.02/5.37 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_of_bool
% 5.02/5.37 thf(fact_9322_nat__1,axiom,
% 5.02/5.37 ( ( nat2 @ one_one_int )
% 5.02/5.37 = ( suc @ zero_zero_nat ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_1
% 5.02/5.37 thf(fact_9323_nat__0__iff,axiom,
% 5.02/5.37 ! [I3: int] :
% 5.02/5.37 ( ( ( nat2 @ I3 )
% 5.02/5.37 = zero_zero_nat )
% 5.02/5.37 = ( ord_less_eq_int @ I3 @ zero_zero_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_0_iff
% 5.02/5.37 thf(fact_9324_nat__le__0,axiom,
% 5.02/5.37 ! [Z: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.02/5.37 => ( ( nat2 @ Z )
% 5.02/5.37 = zero_zero_nat ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_le_0
% 5.02/5.37 thf(fact_9325_zless__nat__conj,axiom,
% 5.02/5.37 ! [W: int,Z: int] :
% 5.02/5.37 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.02/5.37 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.02/5.37 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % zless_nat_conj
% 5.02/5.37 thf(fact_9326_nat__neg__numeral,axiom,
% 5.02/5.37 ! [K: num] :
% 5.02/5.37 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.37 = zero_zero_nat ) ).
% 5.02/5.37
% 5.02/5.37 % nat_neg_numeral
% 5.02/5.37 thf(fact_9327_nat__zminus__int,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.02/5.37 = zero_zero_nat ) ).
% 5.02/5.37
% 5.02/5.37 % nat_zminus_int
% 5.02/5.37 thf(fact_9328_int__nat__eq,axiom,
% 5.02/5.37 ! [Z: int] :
% 5.02/5.37 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.02/5.37 = Z ) )
% 5.02/5.37 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.02/5.37 = zero_zero_int ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % int_nat_eq
% 5.02/5.37 thf(fact_9329_zero__less__nat__eq,axiom,
% 5.02/5.37 ! [Z: int] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.02/5.37 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.02/5.37
% 5.02/5.37 % zero_less_nat_eq
% 5.02/5.37 thf(fact_9330_diff__nat__numeral,axiom,
% 5.02/5.37 ! [V: num,V3: num] :
% 5.02/5.37 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.02/5.37 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % diff_nat_numeral
% 5.02/5.37 thf(fact_9331_nat__eq__numeral__power__cancel__iff,axiom,
% 5.02/5.37 ! [Y: int,X2: num,N2: nat] :
% 5.02/5.37 ( ( ( nat2 @ Y )
% 5.02/5.37 = ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) )
% 5.02/5.37 = ( Y
% 5.02/5.37 = ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_eq_numeral_power_cancel_iff
% 5.02/5.37 thf(fact_9332_numeral__power__eq__nat__cancel__iff,axiom,
% 5.02/5.37 ! [X2: num,N2: nat,Y: int] :
% 5.02/5.37 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 )
% 5.02/5.37 = ( nat2 @ Y ) )
% 5.02/5.37 = ( ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 )
% 5.02/5.37 = Y ) ) ).
% 5.02/5.37
% 5.02/5.37 % numeral_power_eq_nat_cancel_iff
% 5.02/5.37 thf(fact_9333_dvd__nat__abs__iff,axiom,
% 5.02/5.37 ! [N2: nat,K: int] :
% 5.02/5.37 ( ( dvd_dvd_nat @ N2 @ ( nat2 @ ( abs_abs_int @ K ) ) )
% 5.02/5.37 = ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ).
% 5.02/5.37
% 5.02/5.37 % dvd_nat_abs_iff
% 5.02/5.37 thf(fact_9334_nat__abs__dvd__iff,axiom,
% 5.02/5.37 ! [K: int,N2: nat] :
% 5.02/5.37 ( ( dvd_dvd_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ N2 )
% 5.02/5.37 = ( dvd_dvd_int @ K @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_abs_dvd_iff
% 5.02/5.37 thf(fact_9335_nat__ceiling__le__eq,axiom,
% 5.02/5.37 ! [X2: real,A: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) @ A )
% 5.02/5.37 = ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_ceiling_le_eq
% 5.02/5.37 thf(fact_9336_one__less__nat__eq,axiom,
% 5.02/5.37 ! [Z: int] :
% 5.02/5.37 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.02/5.37 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.02/5.37
% 5.02/5.37 % one_less_nat_eq
% 5.02/5.37 thf(fact_9337_nat__numeral__diff__1,axiom,
% 5.02/5.37 ! [V: num] :
% 5.02/5.37 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.02/5.37 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_numeral_diff_1
% 5.02/5.37 thf(fact_9338_nat__less__numeral__power__cancel__iff,axiom,
% 5.02/5.37 ! [A: int,X2: num,N2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) )
% 5.02/5.37 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_less_numeral_power_cancel_iff
% 5.02/5.37 thf(fact_9339_numeral__power__less__nat__cancel__iff,axiom,
% 5.02/5.37 ! [X2: num,N2: nat,A: int] :
% 5.02/5.37 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) @ ( nat2 @ A ) )
% 5.02/5.37 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ A ) ) ).
% 5.02/5.37
% 5.02/5.37 % numeral_power_less_nat_cancel_iff
% 5.02/5.37 thf(fact_9340_nat__le__numeral__power__cancel__iff,axiom,
% 5.02/5.37 ! [A: int,X2: num,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) )
% 5.02/5.37 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_le_numeral_power_cancel_iff
% 5.02/5.37 thf(fact_9341_numeral__power__le__nat__cancel__iff,axiom,
% 5.02/5.37 ! [X2: num,N2: nat,A: int] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X2 ) @ N2 ) @ ( nat2 @ A ) )
% 5.02/5.37 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X2 ) @ N2 ) @ A ) ) ).
% 5.02/5.37
% 5.02/5.37 % numeral_power_le_nat_cancel_iff
% 5.02/5.37 thf(fact_9342_nat__zero__as__int,axiom,
% 5.02/5.37 ( zero_zero_nat
% 5.02/5.37 = ( nat2 @ zero_zero_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_zero_as_int
% 5.02/5.37 thf(fact_9343_nat__numeral__as__int,axiom,
% 5.02/5.37 ( numeral_numeral_nat
% 5.02/5.37 = ( ^ [I5: num] : ( nat2 @ ( numeral_numeral_int @ I5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_numeral_as_int
% 5.02/5.37 thf(fact_9344_nat__mono,axiom,
% 5.02/5.37 ! [X2: int,Y: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ X2 @ Y )
% 5.02/5.37 => ( ord_less_eq_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_mono
% 5.02/5.37 thf(fact_9345_eq__nat__nat__iff,axiom,
% 5.02/5.37 ! [Z: int,Z7: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.02/5.37 => ( ( ( nat2 @ Z )
% 5.02/5.37 = ( nat2 @ Z7 ) )
% 5.02/5.37 = ( Z = Z7 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % eq_nat_nat_iff
% 5.02/5.37 thf(fact_9346_all__nat,axiom,
% 5.02/5.37 ( ( ^ [P3: nat > $o] :
% 5.02/5.37 ! [X7: nat] : ( P3 @ X7 ) )
% 5.02/5.37 = ( ^ [P4: nat > $o] :
% 5.02/5.37 ! [X: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.02/5.37 => ( P4 @ ( nat2 @ X ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % all_nat
% 5.02/5.37 thf(fact_9347_ex__nat,axiom,
% 5.02/5.37 ( ( ^ [P3: nat > $o] :
% 5.02/5.37 ? [X7: nat] : ( P3 @ X7 ) )
% 5.02/5.37 = ( ^ [P4: nat > $o] :
% 5.02/5.37 ? [X: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.02/5.37 & ( P4 @ ( nat2 @ X ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ex_nat
% 5.02/5.37 thf(fact_9348_nat__one__as__int,axiom,
% 5.02/5.37 ( one_one_nat
% 5.02/5.37 = ( nat2 @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_one_as_int
% 5.02/5.37 thf(fact_9349_unset__bit__nat__def,axiom,
% 5.02/5.37 ( bit_se4205575877204974255it_nat
% 5.02/5.37 = ( ^ [M6: nat,N3: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % unset_bit_nat_def
% 5.02/5.37 thf(fact_9350_nat__mask__eq,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.02/5.37 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_mask_eq
% 5.02/5.37 thf(fact_9351_nat__mono__iff,axiom,
% 5.02/5.37 ! [Z: int,W: int] :
% 5.02/5.37 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.02/5.37 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_mono_iff
% 5.02/5.37 thf(fact_9352_zless__nat__eq__int__zless,axiom,
% 5.02/5.37 ! [M: nat,Z: int] :
% 5.02/5.37 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.02/5.37 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.02/5.37
% 5.02/5.37 % zless_nat_eq_int_zless
% 5.02/5.37 thf(fact_9353_nat__le__iff,axiom,
% 5.02/5.37 ! [X2: int,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ ( nat2 @ X2 ) @ N2 )
% 5.02/5.37 = ( ord_less_eq_int @ X2 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_le_iff
% 5.02/5.37 thf(fact_9354_nat__0__le,axiom,
% 5.02/5.37 ! [Z: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.02/5.37 = Z ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_0_le
% 5.02/5.37 thf(fact_9355_int__eq__iff,axiom,
% 5.02/5.37 ! [M: nat,Z: int] :
% 5.02/5.37 ( ( ( semiri1314217659103216013at_int @ M )
% 5.02/5.37 = Z )
% 5.02/5.37 = ( ( M
% 5.02/5.37 = ( nat2 @ Z ) )
% 5.02/5.37 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % int_eq_iff
% 5.02/5.37 thf(fact_9356_nat__int__add,axiom,
% 5.02/5.37 ! [A: nat,B: nat] :
% 5.02/5.37 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.02/5.37 = ( plus_plus_nat @ A @ B ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_int_add
% 5.02/5.37 thf(fact_9357_nat__abs__mult__distrib,axiom,
% 5.02/5.37 ! [W: int,Z: int] :
% 5.02/5.37 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.02/5.37 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_abs_mult_distrib
% 5.02/5.37 thf(fact_9358_and__nat__def,axiom,
% 5.02/5.37 ( bit_se727722235901077358nd_nat
% 5.02/5.37 = ( ^ [M6: nat,N3: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % and_nat_def
% 5.02/5.37 thf(fact_9359_nat__plus__as__int,axiom,
% 5.02/5.37 ( plus_plus_nat
% 5.02/5.37 = ( ^ [A5: nat,B5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_plus_as_int
% 5.02/5.37 thf(fact_9360_or__nat__def,axiom,
% 5.02/5.37 ( bit_se1412395901928357646or_nat
% 5.02/5.37 = ( ^ [M6: nat,N3: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_nat_def
% 5.02/5.37 thf(fact_9361_nat__times__as__int,axiom,
% 5.02/5.37 ( times_times_nat
% 5.02/5.37 = ( ^ [A5: nat,B5: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_times_as_int
% 5.02/5.37 thf(fact_9362_real__nat__ceiling__ge,axiom,
% 5.02/5.37 ! [X2: real] : ( ord_less_eq_real @ X2 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_nat_ceiling_ge
% 5.02/5.37 thf(fact_9363_nat__div__as__int,axiom,
% 5.02/5.37 ( divide_divide_nat
% 5.02/5.37 = ( ^ [A5: nat,B5: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_div_as_int
% 5.02/5.37 thf(fact_9364_sgn__real__def,axiom,
% 5.02/5.37 ( sgn_sgn_real
% 5.02/5.37 = ( ^ [A5: real] : ( if_real @ ( A5 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A5 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sgn_real_def
% 5.02/5.37 thf(fact_9365_nat__less__eq__zless,axiom,
% 5.02/5.37 ! [W: int,Z: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.02/5.37 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.02/5.37 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_less_eq_zless
% 5.02/5.37 thf(fact_9366_nat__le__eq__zle,axiom,
% 5.02/5.37 ! [W: int,Z: int] :
% 5.02/5.37 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.02/5.37 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.02/5.37 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.02/5.37 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_le_eq_zle
% 5.02/5.37 thf(fact_9367_nat__eq__iff2,axiom,
% 5.02/5.37 ! [M: nat,W: int] :
% 5.02/5.37 ( ( M
% 5.02/5.37 = ( nat2 @ W ) )
% 5.02/5.37 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.02/5.37 => ( W
% 5.02/5.37 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.02/5.37 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.02/5.37 => ( M = zero_zero_nat ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_eq_iff2
% 5.02/5.37 thf(fact_9368_nat__eq__iff,axiom,
% 5.02/5.37 ! [W: int,M: nat] :
% 5.02/5.37 ( ( ( nat2 @ W )
% 5.02/5.37 = M )
% 5.02/5.37 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.02/5.37 => ( W
% 5.02/5.37 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.02/5.37 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.02/5.37 => ( M = zero_zero_nat ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_eq_iff
% 5.02/5.37 thf(fact_9369_split__nat,axiom,
% 5.02/5.37 ! [P: nat > $o,I3: int] :
% 5.02/5.37 ( ( P @ ( nat2 @ I3 ) )
% 5.02/5.37 = ( ! [N3: nat] :
% 5.02/5.37 ( ( I3
% 5.02/5.37 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.02/5.37 => ( P @ N3 ) )
% 5.02/5.37 & ( ( ord_less_int @ I3 @ zero_zero_int )
% 5.02/5.37 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % split_nat
% 5.02/5.37 thf(fact_9370_le__nat__iff,axiom,
% 5.02/5.37 ! [K: int,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.37 => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 5.02/5.37 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_nat_iff
% 5.02/5.37 thf(fact_9371_nat__add__distrib,axiom,
% 5.02/5.37 ! [Z: int,Z7: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.02/5.37 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.02/5.37 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_add_distrib
% 5.02/5.37 thf(fact_9372_nat__mult__distrib,axiom,
% 5.02/5.37 ! [Z: int,Z7: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.02/5.37 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_mult_distrib
% 5.02/5.37 thf(fact_9373_Suc__as__int,axiom,
% 5.02/5.37 ( suc
% 5.02/5.37 = ( ^ [A5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ one_one_int ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Suc_as_int
% 5.02/5.37 thf(fact_9374_nat__diff__distrib_H,axiom,
% 5.02/5.37 ! [X2: int,Y: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.37 => ( ( nat2 @ ( minus_minus_int @ X2 @ Y ) )
% 5.02/5.37 = ( minus_minus_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_diff_distrib'
% 5.02/5.37 thf(fact_9375_nat__diff__distrib,axiom,
% 5.02/5.37 ! [Z7: int,Z: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.02/5.37 => ( ( ord_less_eq_int @ Z7 @ Z )
% 5.02/5.37 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 5.02/5.37 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_diff_distrib
% 5.02/5.37 thf(fact_9376_nat__abs__triangle__ineq,axiom,
% 5.02/5.37 ! [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 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_abs_triangle_ineq
% 5.02/5.37 thf(fact_9377_nat__div__distrib,axiom,
% 5.02/5.37 ! [X2: int,Y: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.37 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y ) )
% 5.02/5.37 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_div_distrib
% 5.02/5.37 thf(fact_9378_nat__div__distrib_H,axiom,
% 5.02/5.37 ! [Y: int,X2: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.37 => ( ( nat2 @ ( divide_divide_int @ X2 @ Y ) )
% 5.02/5.37 = ( divide_divide_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_div_distrib'
% 5.02/5.37 thf(fact_9379_nat__power__eq,axiom,
% 5.02/5.37 ! [Z: int,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( nat2 @ ( power_power_int @ Z @ N2 ) )
% 5.02/5.37 = ( power_power_nat @ ( nat2 @ Z ) @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_power_eq
% 5.02/5.37 thf(fact_9380_nat__floor__neg,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ X2 @ zero_zero_real )
% 5.02/5.37 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.02/5.37 = zero_zero_nat ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_floor_neg
% 5.02/5.37 thf(fact_9381_nat__mod__distrib,axiom,
% 5.02/5.37 ! [X2: int,Y: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.37 => ( ( nat2 @ ( modulo_modulo_int @ X2 @ Y ) )
% 5.02/5.37 = ( modulo_modulo_nat @ ( nat2 @ X2 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_mod_distrib
% 5.02/5.37 thf(fact_9382_div__abs__eq__div__nat,axiom,
% 5.02/5.37 ! [K: int,L: int] :
% 5.02/5.37 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.02/5.37 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % div_abs_eq_div_nat
% 5.02/5.37 thf(fact_9383_floor__eq3,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.02/5.37 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.02/5.37 = N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_eq3
% 5.02/5.37 thf(fact_9384_le__nat__floor,axiom,
% 5.02/5.37 ! [X2: nat,A: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X2 ) @ A )
% 5.02/5.37 => ( ord_less_eq_nat @ X2 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % le_nat_floor
% 5.02/5.37 thf(fact_9385_mod__abs__eq__div__nat,axiom,
% 5.02/5.37 ! [K: int,L: int] :
% 5.02/5.37 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.02/5.37 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % mod_abs_eq_div_nat
% 5.02/5.37 thf(fact_9386_take__bit__nat__eq,axiom,
% 5.02/5.37 ! [K: int,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.37 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) )
% 5.02/5.37 = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % take_bit_nat_eq
% 5.02/5.37 thf(fact_9387_nat__take__bit__eq,axiom,
% 5.02/5.37 ! [K: int,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.37 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.02/5.37 = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_take_bit_eq
% 5.02/5.37 thf(fact_9388_bit__nat__iff,axiom,
% 5.02/5.37 ! [K: int,N2: nat] :
% 5.02/5.37 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N2 )
% 5.02/5.37 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.37 & ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bit_nat_iff
% 5.02/5.37 thf(fact_9389_nat__2,axiom,
% 5.02/5.37 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.37 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_2
% 5.02/5.37 thf(fact_9390_sgn__power__injE,axiom,
% 5.02/5.37 ! [A: real,N2: nat,X2: real,B: real] :
% 5.02/5.37 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.02/5.37 = X2 )
% 5.02/5.37 => ( ( X2
% 5.02/5.37 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 5.02/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( A = B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sgn_power_injE
% 5.02/5.37 thf(fact_9391_Suc__nat__eq__nat__zadd1,axiom,
% 5.02/5.37 ! [Z: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( ( suc @ ( nat2 @ Z ) )
% 5.02/5.37 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Suc_nat_eq_nat_zadd1
% 5.02/5.37 thf(fact_9392_nat__less__iff,axiom,
% 5.02/5.37 ! [W: int,M: nat] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.02/5.37 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.02/5.37 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_less_iff
% 5.02/5.37 thf(fact_9393_nat__mult__distrib__neg,axiom,
% 5.02/5.37 ! [Z: int,Z7: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.02/5.37 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.02/5.37 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_mult_distrib_neg
% 5.02/5.37 thf(fact_9394_nat__abs__int__diff,axiom,
% 5.02/5.37 ! [A: nat,B: nat] :
% 5.02/5.37 ( ( ( ord_less_eq_nat @ A @ B )
% 5.02/5.37 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.02/5.37 = ( minus_minus_nat @ B @ A ) ) )
% 5.02/5.37 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.02/5.37 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.02/5.37 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_abs_int_diff
% 5.02/5.37 thf(fact_9395_floor__eq4,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ X2 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.02/5.37 => ( ( nat2 @ ( archim6058952711729229775r_real @ X2 ) )
% 5.02/5.37 = N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_eq4
% 5.02/5.37 thf(fact_9396_diff__nat__eq__if,axiom,
% 5.02/5.37 ! [Z7: int,Z: int] :
% 5.02/5.37 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.02/5.37 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.02/5.37 = ( nat2 @ Z ) ) )
% 5.02/5.37 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.02/5.37 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.02/5.37 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % diff_nat_eq_if
% 5.02/5.37 thf(fact_9397_nat__dvd__iff,axiom,
% 5.02/5.37 ! [Z: int,M: nat] :
% 5.02/5.37 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.02/5.37 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.02/5.37 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.02/5.37 => ( M = zero_zero_nat ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % nat_dvd_iff
% 5.02/5.37 thf(fact_9398_floor__real__def,axiom,
% 5.02/5.37 ( archim6058952711729229775r_real
% 5.02/5.37 = ( ^ [X: real] :
% 5.02/5.37 ( the_int
% 5.02/5.37 @ ^ [Z6: int] :
% 5.02/5.37 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z6 ) @ X )
% 5.02/5.37 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_real_def
% 5.02/5.37 thf(fact_9399_even__nat__iff,axiom,
% 5.02/5.37 ! [K: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.37 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.02/5.37 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % even_nat_iff
% 5.02/5.37 thf(fact_9400_powr__real__of__int,axiom,
% 5.02/5.37 ! [X2: real,N2: int] :
% 5.02/5.37 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.02/5.37 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N2 ) )
% 5.02/5.37 = ( power_power_real @ X2 @ ( nat2 @ N2 ) ) ) )
% 5.02/5.37 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.02/5.37 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N2 ) )
% 5.02/5.37 = ( inverse_inverse_real @ ( power_power_real @ X2 @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % powr_real_of_int
% 5.02/5.37 thf(fact_9401_arctan__inverse,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( X2 != zero_zero_real )
% 5.02/5.37 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X2 ) )
% 5.02/5.37 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % arctan_inverse
% 5.02/5.37 thf(fact_9402_cis__multiple__2pi,axiom,
% 5.02/5.37 ! [N2: real] :
% 5.02/5.37 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.02/5.37 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.02/5.37 = one_one_complex ) ) ).
% 5.02/5.37
% 5.02/5.37 % cis_multiple_2pi
% 5.02/5.37 thf(fact_9403_Suc__0__xor__eq,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.02/5.37 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.37 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.37 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Suc_0_xor_eq
% 5.02/5.37 thf(fact_9404_xor__Suc__0__eq,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.02/5.37 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.37 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.37 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_Suc_0_eq
% 5.02/5.37 thf(fact_9405_horner__sum__of__bool__2__less,axiom,
% 5.02/5.37 ! [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 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % horner_sum_of_bool_2_less
% 5.02/5.37 thf(fact_9406_xor__nat__numerals_I1_J,axiom,
% 5.02/5.37 ! [Y: num] :
% 5.02/5.37 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.02/5.37 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_nat_numerals(1)
% 5.02/5.37 thf(fact_9407_xor__nat__numerals_I2_J,axiom,
% 5.02/5.37 ! [Y: num] :
% 5.02/5.37 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.02/5.37 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_nat_numerals(2)
% 5.02/5.37 thf(fact_9408_xor__nat__numerals_I3_J,axiom,
% 5.02/5.37 ! [X2: num] :
% 5.02/5.37 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.02/5.37 = ( numeral_numeral_nat @ ( bit1 @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_nat_numerals(3)
% 5.02/5.37 thf(fact_9409_xor__nat__numerals_I4_J,axiom,
% 5.02/5.37 ! [X2: num] :
% 5.02/5.37 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X2 ) ) @ ( suc @ zero_zero_nat ) )
% 5.02/5.37 = ( numeral_numeral_nat @ ( bit0 @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_nat_numerals(4)
% 5.02/5.37 thf(fact_9410_sin__times__pi__eq__0,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( ( sin_real @ ( times_times_real @ X2 @ pi ) )
% 5.02/5.37 = zero_zero_real )
% 5.02/5.37 = ( member_real @ X2 @ ring_1_Ints_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % sin_times_pi_eq_0
% 5.02/5.37 thf(fact_9411_sin__integer__2pi,axiom,
% 5.02/5.37 ! [N2: real] :
% 5.02/5.37 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.02/5.37 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.02/5.37 = zero_zero_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % sin_integer_2pi
% 5.02/5.37 thf(fact_9412_cos__integer__2pi,axiom,
% 5.02/5.37 ! [N2: real] :
% 5.02/5.37 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.02/5.37 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.02/5.37 = one_one_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % cos_integer_2pi
% 5.02/5.37 thf(fact_9413_xor__nat__unfold,axiom,
% 5.02/5.37 ( bit_se6528837805403552850or_nat
% 5.02/5.37 = ( ^ [M6: nat,N3: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N3 @ ( if_nat @ ( N3 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_nat_unfold
% 5.02/5.37 thf(fact_9414_xor__nat__rec,axiom,
% 5.02/5.37 ( bit_se6528837805403552850or_nat
% 5.02/5.37 = ( ^ [M6: nat,N3: nat] :
% 5.02/5.37 ( plus_plus_nat
% 5.02/5.37 @ ( zero_n2687167440665602831ol_nat
% 5.02/5.37 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.02/5.37 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.02/5.37 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_nat_rec
% 5.02/5.37 thf(fact_9415_floor__rat__def,axiom,
% 5.02/5.37 ( archim3151403230148437115or_rat
% 5.02/5.37 = ( ^ [X: rat] :
% 5.02/5.37 ( the_int
% 5.02/5.37 @ ^ [Z6: int] :
% 5.02/5.37 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z6 ) @ X )
% 5.02/5.37 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % floor_rat_def
% 5.02/5.37 thf(fact_9416_set__encode__def,axiom,
% 5.02/5.37 ( nat_set_encode
% 5.02/5.37 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % set_encode_def
% 5.02/5.37 thf(fact_9417_push__bit__nonnegative__int__iff,axiom,
% 5.02/5.37 ! [N2: nat,K: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.02/5.37 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.02/5.37
% 5.02/5.37 % push_bit_nonnegative_int_iff
% 5.02/5.37 thf(fact_9418_push__bit__negative__int__iff,axiom,
% 5.02/5.37 ! [N2: nat,K: int] :
% 5.02/5.37 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 5.02/5.37 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % push_bit_negative_int_iff
% 5.02/5.37 thf(fact_9419_concat__bit__of__zero__1,axiom,
% 5.02/5.37 ! [N2: nat,L: int] :
% 5.02/5.37 ( ( bit_concat_bit @ N2 @ zero_zero_int @ L )
% 5.02/5.37 = ( bit_se545348938243370406it_int @ N2 @ L ) ) ).
% 5.02/5.37
% 5.02/5.37 % concat_bit_of_zero_1
% 5.02/5.37 thf(fact_9420_xor__nonnegative__int__iff,axiom,
% 5.02/5.37 ! [K: int,L: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.02/5.37 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.02/5.37 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_nonnegative_int_iff
% 5.02/5.37 thf(fact_9421_xor__negative__int__iff,axiom,
% 5.02/5.37 ! [K: int,L: int] :
% 5.02/5.37 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.02/5.37 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.02/5.37 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_negative_int_iff
% 5.02/5.37 thf(fact_9422_set__encode__empty,axiom,
% 5.02/5.37 ( ( nat_set_encode @ bot_bot_set_nat )
% 5.02/5.37 = zero_zero_nat ) ).
% 5.02/5.37
% 5.02/5.37 % set_encode_empty
% 5.02/5.37 thf(fact_9423_push__bit__of__Suc__0,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.02/5.37 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % push_bit_of_Suc_0
% 5.02/5.37 thf(fact_9424_sgn__rat__def,axiom,
% 5.02/5.37 ( sgn_sgn_rat
% 5.02/5.37 = ( ^ [A5: rat] : ( if_rat @ ( A5 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A5 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sgn_rat_def
% 5.02/5.37 thf(fact_9425_bit__xor__int__iff,axiom,
% 5.02/5.37 ! [K: int,L: int,N2: nat] :
% 5.02/5.37 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N2 )
% 5.02/5.37 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.02/5.37 != ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bit_xor_int_iff
% 5.02/5.37 thf(fact_9426_flip__bit__int__def,axiom,
% 5.02/5.37 ( bit_se2159334234014336723it_int
% 5.02/5.37 = ( ^ [N3: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % flip_bit_int_def
% 5.02/5.37 thf(fact_9427_obtain__pos__sum,axiom,
% 5.02/5.37 ! [R2: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ R2 )
% 5.02/5.37 => ~ ! [S: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ S )
% 5.02/5.37 => ! [T3: rat] :
% 5.02/5.37 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 5.02/5.37 => ( R2
% 5.02/5.37 != ( plus_plus_rat @ S @ T3 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % obtain_pos_sum
% 5.02/5.37 thf(fact_9428_push__bit__nat__eq,axiom,
% 5.02/5.37 ! [N2: nat,K: int] :
% 5.02/5.37 ( ( bit_se547839408752420682it_nat @ N2 @ ( nat2 @ K ) )
% 5.02/5.37 = ( nat2 @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % push_bit_nat_eq
% 5.02/5.37 thf(fact_9429_XOR__lower,axiom,
% 5.02/5.37 ! [X2: int,Y: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.37 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % XOR_lower
% 5.02/5.37 thf(fact_9430_set__bit__nat__def,axiom,
% 5.02/5.37 ( bit_se7882103937844011126it_nat
% 5.02/5.37 = ( ^ [M6: nat,N3: nat] : ( bit_se1412395901928357646or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % set_bit_nat_def
% 5.02/5.37 thf(fact_9431_flip__bit__nat__def,axiom,
% 5.02/5.37 ( bit_se2161824704523386999it_nat
% 5.02/5.37 = ( ^ [M6: nat,N3: nat] : ( bit_se6528837805403552850or_nat @ N3 @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % flip_bit_nat_def
% 5.02/5.37 thf(fact_9432_bit__push__bit__iff__int,axiom,
% 5.02/5.37 ! [M: nat,K: int,N2: nat] :
% 5.02/5.37 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 5.02/5.37 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bit_push_bit_iff_int
% 5.02/5.37 thf(fact_9433_xor__nat__def,axiom,
% 5.02/5.37 ( bit_se6528837805403552850or_nat
% 5.02/5.37 = ( ^ [M6: nat,N3: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_nat_def
% 5.02/5.37 thf(fact_9434_bit__push__bit__iff__nat,axiom,
% 5.02/5.37 ! [M: nat,Q2: nat,N2: nat] :
% 5.02/5.37 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N2 )
% 5.02/5.37 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.37 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bit_push_bit_iff_nat
% 5.02/5.37 thf(fact_9435_concat__bit__eq,axiom,
% 5.02/5.37 ( bit_concat_bit
% 5.02/5.37 = ( ^ [N3: nat,K3: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N3 @ K3 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % concat_bit_eq
% 5.02/5.37 thf(fact_9436_concat__bit__def,axiom,
% 5.02/5.37 ( bit_concat_bit
% 5.02/5.37 = ( ^ [N3: nat,K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N3 @ K3 ) @ ( bit_se545348938243370406it_int @ N3 @ L2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % concat_bit_def
% 5.02/5.37 thf(fact_9437_set__bit__int__def,axiom,
% 5.02/5.37 ( bit_se7879613467334960850it_int
% 5.02/5.37 = ( ^ [N3: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % set_bit_int_def
% 5.02/5.37 thf(fact_9438_push__bit__int__def,axiom,
% 5.02/5.37 ( bit_se545348938243370406it_int
% 5.02/5.37 = ( ^ [N3: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % push_bit_int_def
% 5.02/5.37 thf(fact_9439_push__bit__nat__def,axiom,
% 5.02/5.37 ( bit_se547839408752420682it_nat
% 5.02/5.37 = ( ^ [N3: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % push_bit_nat_def
% 5.02/5.37 thf(fact_9440_push__bit__minus__one,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.37 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % push_bit_minus_one
% 5.02/5.37 thf(fact_9441_XOR__upper,axiom,
% 5.02/5.37 ! [X2: int,N2: nat,Y: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.37 => ( ( ord_less_int @ X2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.37 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.02/5.37 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X2 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % XOR_upper
% 5.02/5.37 thf(fact_9442_xor__int__rec,axiom,
% 5.02/5.37 ( bit_se6526347334894502574or_int
% 5.02/5.37 = ( ^ [K3: int,L2: int] :
% 5.02/5.37 ( plus_plus_int
% 5.02/5.37 @ ( zero_n2684676970156552555ol_int
% 5.02/5.37 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.02/5.37 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.02/5.37 @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_int_rec
% 5.02/5.37 thf(fact_9443_xor__int__unfold,axiom,
% 5.02/5.37 ( bit_se6526347334894502574or_int
% 5.02/5.37 = ( ^ [K3: int,L2: int] :
% 5.02/5.37 ( if_int
% 5.02/5.37 @ ( K3
% 5.02/5.37 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.37 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 5.02/5.37 @ ( if_int
% 5.02/5.37 @ ( L2
% 5.02/5.37 = ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.37 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.02/5.37 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_int_unfold
% 5.02/5.37 thf(fact_9444_set__encode__insert,axiom,
% 5.02/5.37 ! [A3: set_nat,N2: nat] :
% 5.02/5.37 ( ( finite_finite_nat @ A3 )
% 5.02/5.37 => ( ~ ( member_nat @ N2 @ A3 )
% 5.02/5.37 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A3 ) )
% 5.02/5.37 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A3 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % set_encode_insert
% 5.02/5.37 thf(fact_9445_rat__inverse__code,axiom,
% 5.02/5.37 ! [P2: rat] :
% 5.02/5.37 ( ( quotient_of @ ( inverse_inverse_rat @ P2 ) )
% 5.02/5.37 = ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [A5: int,B5: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B5 ) @ ( abs_abs_int @ A5 ) ) )
% 5.02/5.37 @ ( quotient_of @ P2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_inverse_code
% 5.02/5.37 thf(fact_9446_normalize__negative,axiom,
% 5.02/5.37 ! [Q2: int,P2: int] :
% 5.02/5.37 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.02/5.37 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.02/5.37 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P2 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % normalize_negative
% 5.02/5.37 thf(fact_9447_set__vebt__finite,axiom,
% 5.02/5.37 ! [T2: vEBT_VEBT,N2: nat] :
% 5.02/5.37 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 5.02/5.37 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % set_vebt_finite
% 5.02/5.37 thf(fact_9448_not__negative__int__iff,axiom,
% 5.02/5.37 ! [K: int] :
% 5.02/5.37 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.02/5.37 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.02/5.37
% 5.02/5.37 % not_negative_int_iff
% 5.02/5.37 thf(fact_9449_not__nonnegative__int__iff,axiom,
% 5.02/5.37 ! [K: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.02/5.37 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % not_nonnegative_int_iff
% 5.02/5.37 thf(fact_9450_quotient__of__number_I3_J,axiom,
% 5.02/5.37 ! [K: num] :
% 5.02/5.37 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.02/5.37 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % quotient_of_number(3)
% 5.02/5.37 thf(fact_9451_normalize__denom__zero,axiom,
% 5.02/5.37 ! [P2: int] :
% 5.02/5.37 ( ( normalize @ ( product_Pair_int_int @ P2 @ zero_zero_int ) )
% 5.02/5.37 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % normalize_denom_zero
% 5.02/5.37 thf(fact_9452_rat__one__code,axiom,
% 5.02/5.37 ( ( quotient_of @ one_one_rat )
% 5.02/5.37 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_one_code
% 5.02/5.37 thf(fact_9453_rat__zero__code,axiom,
% 5.02/5.37 ( ( quotient_of @ zero_zero_rat )
% 5.02/5.37 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_zero_code
% 5.02/5.37 thf(fact_9454_quotient__of__number_I5_J,axiom,
% 5.02/5.37 ! [K: num] :
% 5.02/5.37 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.02/5.37 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % quotient_of_number(5)
% 5.02/5.37 thf(fact_9455_quotient__of__number_I4_J,axiom,
% 5.02/5.37 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.02/5.37 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % quotient_of_number(4)
% 5.02/5.37 thf(fact_9456_or__minus__minus__numerals,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.37 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_minus_minus_numerals
% 5.02/5.37 thf(fact_9457_and__minus__minus__numerals,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.37 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % and_minus_minus_numerals
% 5.02/5.37 thf(fact_9458_finite__M__bounded__by__nat,axiom,
% 5.02/5.37 ! [P: nat > $o,I3: nat] :
% 5.02/5.37 ( finite_finite_nat
% 5.02/5.37 @ ( collect_nat
% 5.02/5.37 @ ^ [K3: nat] :
% 5.02/5.37 ( ( P @ K3 )
% 5.02/5.37 & ( ord_less_nat @ K3 @ I3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_M_bounded_by_nat
% 5.02/5.37 thf(fact_9459_finite__less__ub,axiom,
% 5.02/5.37 ! [F: nat > nat,U: nat] :
% 5.02/5.37 ( ! [N: nat] : ( ord_less_eq_nat @ N @ ( F @ N ) )
% 5.02/5.37 => ( finite_finite_nat
% 5.02/5.37 @ ( collect_nat
% 5.02/5.37 @ ^ [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ U ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_less_ub
% 5.02/5.37 thf(fact_9460_divide__rat__def,axiom,
% 5.02/5.37 ( divide_divide_rat
% 5.02/5.37 = ( ^ [Q4: rat,R5: rat] : ( times_times_rat @ Q4 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % divide_rat_def
% 5.02/5.37 thf(fact_9461_finite__nat__set__iff__bounded__le,axiom,
% 5.02/5.37 ( finite_finite_nat
% 5.02/5.37 = ( ^ [N9: set_nat] :
% 5.02/5.37 ? [M6: nat] :
% 5.02/5.37 ! [X: nat] :
% 5.02/5.37 ( ( member_nat @ X @ N9 )
% 5.02/5.37 => ( ord_less_eq_nat @ X @ M6 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_nat_set_iff_bounded_le
% 5.02/5.37 thf(fact_9462_finite__nat__set__iff__bounded,axiom,
% 5.02/5.37 ( finite_finite_nat
% 5.02/5.37 = ( ^ [N9: set_nat] :
% 5.02/5.37 ? [M6: nat] :
% 5.02/5.37 ! [X: nat] :
% 5.02/5.37 ( ( member_nat @ X @ N9 )
% 5.02/5.37 => ( ord_less_nat @ X @ M6 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_nat_set_iff_bounded
% 5.02/5.37 thf(fact_9463_bounded__nat__set__is__finite,axiom,
% 5.02/5.37 ! [N4: set_nat,N2: nat] :
% 5.02/5.37 ( ! [X5: nat] :
% 5.02/5.37 ( ( member_nat @ X5 @ N4 )
% 5.02/5.37 => ( ord_less_nat @ X5 @ N2 ) )
% 5.02/5.37 => ( finite_finite_nat @ N4 ) ) ).
% 5.02/5.37
% 5.02/5.37 % bounded_nat_set_is_finite
% 5.02/5.37 thf(fact_9464_diff__rat__def,axiom,
% 5.02/5.37 ( minus_minus_rat
% 5.02/5.37 = ( ^ [Q4: rat,R5: rat] : ( plus_plus_rat @ Q4 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % diff_rat_def
% 5.02/5.37 thf(fact_9465_bit__not__int__iff,axiom,
% 5.02/5.37 ! [K: int,N2: nat] :
% 5.02/5.37 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N2 )
% 5.02/5.37 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bit_not_int_iff
% 5.02/5.37 thf(fact_9466_or__int__def,axiom,
% 5.02/5.37 ( bit_se1409905431419307370or_int
% 5.02/5.37 = ( ^ [K3: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_int_def
% 5.02/5.37 thf(fact_9467_rat__divide__code,axiom,
% 5.02/5.37 ! [P2: rat,Q2: rat] :
% 5.02/5.37 ( ( quotient_of @ ( divide_divide_rat @ P2 @ Q2 ) )
% 5.02/5.37 = ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [A5: int,C2: int] :
% 5.02/5.37 ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [B5: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C2 @ B5 ) ) )
% 5.02/5.37 @ ( quotient_of @ Q2 ) )
% 5.02/5.37 @ ( quotient_of @ P2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_divide_code
% 5.02/5.37 thf(fact_9468_rat__times__code,axiom,
% 5.02/5.37 ! [P2: rat,Q2: rat] :
% 5.02/5.37 ( ( quotient_of @ ( times_times_rat @ P2 @ Q2 ) )
% 5.02/5.37 = ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [A5: int,C2: int] :
% 5.02/5.37 ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [B5: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B5 ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.02/5.37 @ ( quotient_of @ Q2 ) )
% 5.02/5.37 @ ( quotient_of @ P2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_times_code
% 5.02/5.37 thf(fact_9469_set__encode__inf,axiom,
% 5.02/5.37 ! [A3: set_nat] :
% 5.02/5.37 ( ~ ( finite_finite_nat @ A3 )
% 5.02/5.37 => ( ( nat_set_encode @ A3 )
% 5.02/5.37 = zero_zero_nat ) ) ).
% 5.02/5.37
% 5.02/5.37 % set_encode_inf
% 5.02/5.37 thf(fact_9470_not__int__def,axiom,
% 5.02/5.37 ( bit_ri7919022796975470100ot_int
% 5.02/5.37 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % not_int_def
% 5.02/5.37 thf(fact_9471_and__not__numerals_I1_J,axiom,
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.02/5.37 = zero_zero_int ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(1)
% 5.02/5.37 thf(fact_9472_or__not__numerals_I1_J,axiom,
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.02/5.37 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(1)
% 5.02/5.37 thf(fact_9473_rat__plus__code,axiom,
% 5.02/5.37 ! [P2: rat,Q2: rat] :
% 5.02/5.37 ( ( quotient_of @ ( plus_plus_rat @ P2 @ Q2 ) )
% 5.02/5.37 = ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [A5: int,C2: int] :
% 5.02/5.37 ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [B5: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ B5 @ C2 ) ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.02/5.37 @ ( quotient_of @ Q2 ) )
% 5.02/5.37 @ ( quotient_of @ P2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_plus_code
% 5.02/5.37 thf(fact_9474_rat__minus__code,axiom,
% 5.02/5.37 ! [P2: rat,Q2: rat] :
% 5.02/5.37 ( ( quotient_of @ ( minus_minus_rat @ P2 @ Q2 ) )
% 5.02/5.37 = ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [A5: int,C2: int] :
% 5.02/5.37 ( produc4245557441103728435nt_int
% 5.02/5.37 @ ^ [B5: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ B5 @ C2 ) ) @ ( times_times_int @ C2 @ D2 ) ) )
% 5.02/5.37 @ ( quotient_of @ Q2 ) )
% 5.02/5.37 @ ( quotient_of @ P2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_minus_code
% 5.02/5.37 thf(fact_9475_unset__bit__int__def,axiom,
% 5.02/5.37 ( bit_se4203085406695923979it_int
% 5.02/5.37 = ( ^ [N3: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N3 @ one_one_int ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % unset_bit_int_def
% 5.02/5.37 thf(fact_9476_xor__int__def,axiom,
% 5.02/5.37 ( bit_se6526347334894502574or_int
% 5.02/5.37 = ( ^ [K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % xor_int_def
% 5.02/5.37 thf(fact_9477_finite__divisors__nat,axiom,
% 5.02/5.37 ! [M: nat] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.37 => ( finite_finite_nat
% 5.02/5.37 @ ( collect_nat
% 5.02/5.37 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_divisors_nat
% 5.02/5.37 thf(fact_9478_quotient__of__denom__pos,axiom,
% 5.02/5.37 ! [R2: rat,P2: int,Q2: int] :
% 5.02/5.37 ( ( ( quotient_of @ R2 )
% 5.02/5.37 = ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.02/5.37 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % quotient_of_denom_pos
% 5.02/5.37 thf(fact_9479_subset__eq__atLeast0__atMost__finite,axiom,
% 5.02/5.37 ! [N4: set_nat,N2: nat] :
% 5.02/5.37 ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.37 => ( finite_finite_nat @ N4 ) ) ).
% 5.02/5.37
% 5.02/5.37 % subset_eq_atLeast0_atMost_finite
% 5.02/5.37 thf(fact_9480_not__int__div__2,axiom,
% 5.02/5.37 ! [K: int] :
% 5.02/5.37 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.37 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % not_int_div_2
% 5.02/5.37 thf(fact_9481_even__not__iff__int,axiom,
% 5.02/5.37 ! [K: int] :
% 5.02/5.37 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.02/5.37 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % even_not_iff_int
% 5.02/5.37 thf(fact_9482_and__not__numerals_I2_J,axiom,
% 5.02/5.37 ! [N2: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.37 = one_one_int ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(2)
% 5.02/5.37 thf(fact_9483_and__not__numerals_I4_J,axiom,
% 5.02/5.37 ! [M: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.02/5.37 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(4)
% 5.02/5.37 thf(fact_9484_or__not__numerals_I2_J,axiom,
% 5.02/5.37 ! [N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.37 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(2)
% 5.02/5.37 thf(fact_9485_or__not__numerals_I4_J,axiom,
% 5.02/5.37 ! [M: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.02/5.37 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(4)
% 5.02/5.37 thf(fact_9486_bit__minus__int__iff,axiom,
% 5.02/5.37 ! [K: int,N2: nat] :
% 5.02/5.37 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N2 )
% 5.02/5.37 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % bit_minus_int_iff
% 5.02/5.37 thf(fact_9487_int__numeral__or__not__num__neg,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % int_numeral_or_not_num_neg
% 5.02/5.37 thf(fact_9488_int__numeral__not__or__num__neg,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.37 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % int_numeral_not_or_num_neg
% 5.02/5.37 thf(fact_9489_numeral__or__not__num__eq,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) )
% 5.02/5.37 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % numeral_or_not_num_eq
% 5.02/5.37 thf(fact_9490_and__not__numerals_I5_J,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.37 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(5)
% 5.02/5.37 thf(fact_9491_and__not__numerals_I7_J,axiom,
% 5.02/5.37 ! [M: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.02/5.37 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(7)
% 5.02/5.37 thf(fact_9492_or__not__numerals_I3_J,axiom,
% 5.02/5.37 ! [N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.37 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(3)
% 5.02/5.37 thf(fact_9493_and__not__numerals_I3_J,axiom,
% 5.02/5.37 ! [N2: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.37 = zero_zero_int ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(3)
% 5.02/5.37 thf(fact_9494_or__not__numerals_I7_J,axiom,
% 5.02/5.37 ! [M: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.02/5.37 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(7)
% 5.02/5.37 thf(fact_9495_normalize__denom__pos,axiom,
% 5.02/5.37 ! [R2: product_prod_int_int,P2: int,Q2: int] :
% 5.02/5.37 ( ( ( normalize @ R2 )
% 5.02/5.37 = ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.02/5.37 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % normalize_denom_pos
% 5.02/5.37 thf(fact_9496_normalize__crossproduct,axiom,
% 5.02/5.37 ! [Q2: int,S2: int,P2: int,R2: int] :
% 5.02/5.37 ( ( Q2 != zero_zero_int )
% 5.02/5.37 => ( ( S2 != zero_zero_int )
% 5.02/5.37 => ( ( ( normalize @ ( product_Pair_int_int @ P2 @ Q2 ) )
% 5.02/5.37 = ( normalize @ ( product_Pair_int_int @ R2 @ S2 ) ) )
% 5.02/5.37 => ( ( times_times_int @ P2 @ S2 )
% 5.02/5.37 = ( times_times_int @ R2 @ Q2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % normalize_crossproduct
% 5.02/5.37 thf(fact_9497_and__not__numerals_I6_J,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.37 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(6)
% 5.02/5.37 thf(fact_9498_and__not__numerals_I9_J,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.37 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(9)
% 5.02/5.37 thf(fact_9499_or__not__numerals_I6_J,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.37 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(6)
% 5.02/5.37 thf(fact_9500_rat__less__code,axiom,
% 5.02/5.37 ( ord_less_rat
% 5.02/5.37 = ( ^ [P6: rat,Q4: rat] :
% 5.02/5.37 ( produc4947309494688390418_int_o
% 5.02/5.37 @ ^ [A5: int,C2: int] :
% 5.02/5.37 ( produc4947309494688390418_int_o
% 5.02/5.37 @ ^ [B5: int,D2: int] : ( ord_less_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C2 @ B5 ) )
% 5.02/5.37 @ ( quotient_of @ Q4 ) )
% 5.02/5.37 @ ( quotient_of @ P6 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_less_code
% 5.02/5.37 thf(fact_9501_rat__floor__code,axiom,
% 5.02/5.37 ( archim3151403230148437115or_rat
% 5.02/5.37 = ( ^ [P6: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P6 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_floor_code
% 5.02/5.37 thf(fact_9502_rat__less__eq__code,axiom,
% 5.02/5.37 ( ord_less_eq_rat
% 5.02/5.37 = ( ^ [P6: rat,Q4: rat] :
% 5.02/5.37 ( produc4947309494688390418_int_o
% 5.02/5.37 @ ^ [A5: int,C2: int] :
% 5.02/5.37 ( produc4947309494688390418_int_o
% 5.02/5.37 @ ^ [B5: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C2 @ B5 ) )
% 5.02/5.37 @ ( quotient_of @ Q4 ) )
% 5.02/5.37 @ ( quotient_of @ P6 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % rat_less_eq_code
% 5.02/5.37 thf(fact_9503_even__set__encode__iff,axiom,
% 5.02/5.37 ! [A3: set_nat] :
% 5.02/5.37 ( ( finite_finite_nat @ A3 )
% 5.02/5.37 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A3 ) )
% 5.02/5.37 = ( ~ ( member_nat @ zero_zero_nat @ A3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % even_set_encode_iff
% 5.02/5.37 thf(fact_9504_or__not__numerals_I5_J,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.37 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(5)
% 5.02/5.37 thf(fact_9505_and__not__numerals_I8_J,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.37 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % and_not_numerals(8)
% 5.02/5.37 thf(fact_9506_or__not__numerals_I9_J,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.37 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(9)
% 5.02/5.37 thf(fact_9507_or__not__numerals_I8_J,axiom,
% 5.02/5.37 ! [M: num,N2: num] :
% 5.02/5.37 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.37 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % or_not_numerals(8)
% 5.02/5.37 thf(fact_9508_not__int__rec,axiom,
% 5.02/5.37 ( bit_ri7919022796975470100ot_int
% 5.02/5.37 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % not_int_rec
% 5.02/5.37 thf(fact_9509_finite__Collect__le__nat,axiom,
% 5.02/5.37 ! [K: nat] :
% 5.02/5.37 ( finite_finite_nat
% 5.02/5.37 @ ( collect_nat
% 5.02/5.37 @ ^ [N3: nat] : ( ord_less_eq_nat @ N3 @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_Collect_le_nat
% 5.02/5.37 thf(fact_9510_finite__Collect__less__nat,axiom,
% 5.02/5.37 ! [K: nat] :
% 5.02/5.37 ( finite_finite_nat
% 5.02/5.37 @ ( collect_nat
% 5.02/5.37 @ ^ [N3: nat] : ( ord_less_nat @ N3 @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_Collect_less_nat
% 5.02/5.37 thf(fact_9511_finite__interval__int1,axiom,
% 5.02/5.37 ! [A: int,B: int] :
% 5.02/5.37 ( finite_finite_int
% 5.02/5.37 @ ( collect_int
% 5.02/5.37 @ ^ [I5: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ A @ I5 )
% 5.02/5.37 & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_interval_int1
% 5.02/5.37 thf(fact_9512_finite__interval__int4,axiom,
% 5.02/5.37 ! [A: int,B: int] :
% 5.02/5.37 ( finite_finite_int
% 5.02/5.37 @ ( collect_int
% 5.02/5.37 @ ^ [I5: int] :
% 5.02/5.37 ( ( ord_less_int @ A @ I5 )
% 5.02/5.37 & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_interval_int4
% 5.02/5.37 thf(fact_9513_finite__interval__int3,axiom,
% 5.02/5.37 ! [A: int,B: int] :
% 5.02/5.37 ( finite_finite_int
% 5.02/5.37 @ ( collect_int
% 5.02/5.37 @ ^ [I5: int] :
% 5.02/5.37 ( ( ord_less_int @ A @ I5 )
% 5.02/5.37 & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_interval_int3
% 5.02/5.37 thf(fact_9514_finite__interval__int2,axiom,
% 5.02/5.37 ! [A: int,B: int] :
% 5.02/5.37 ( finite_finite_int
% 5.02/5.37 @ ( collect_int
% 5.02/5.37 @ ^ [I5: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ A @ I5 )
% 5.02/5.37 & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_interval_int2
% 5.02/5.37 thf(fact_9515_finite__nth__roots,axiom,
% 5.02/5.37 ! [N2: nat,C: complex] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( finite3207457112153483333omplex
% 5.02/5.37 @ ( collect_complex
% 5.02/5.37 @ ^ [Z6: complex] :
% 5.02/5.37 ( ( power_power_complex @ Z6 @ N2 )
% 5.02/5.37 = C ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_nth_roots
% 5.02/5.37 thf(fact_9516_finite__divisors__int,axiom,
% 5.02/5.37 ! [I3: int] :
% 5.02/5.37 ( ( I3 != zero_zero_int )
% 5.02/5.37 => ( finite_finite_int
% 5.02/5.37 @ ( collect_int
% 5.02/5.37 @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ I3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % finite_divisors_int
% 5.02/5.37 thf(fact_9517_quotient__of__int,axiom,
% 5.02/5.37 ! [A: int] :
% 5.02/5.37 ( ( quotient_of @ ( of_int @ A ) )
% 5.02/5.37 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.02/5.37
% 5.02/5.37 % quotient_of_int
% 5.02/5.37 thf(fact_9518_bij__betw__nth__root__unity,axiom,
% 5.02/5.37 ! [C: complex,N2: nat] :
% 5.02/5.37 ( ( C != zero_zero_complex )
% 5.02/5.37 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 5.02/5.37 @ ( collect_complex
% 5.02/5.37 @ ^ [Z6: complex] :
% 5.02/5.37 ( ( power_power_complex @ Z6 @ N2 )
% 5.02/5.37 = one_one_complex ) )
% 5.02/5.37 @ ( collect_complex
% 5.02/5.37 @ ^ [Z6: complex] :
% 5.02/5.37 ( ( power_power_complex @ Z6 @ N2 )
% 5.02/5.37 = C ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % bij_betw_nth_root_unity
% 5.02/5.37 thf(fact_9519_Frct__code__post_I5_J,axiom,
% 5.02/5.37 ! [K: num] :
% 5.02/5.37 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.02/5.37 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Frct_code_post(5)
% 5.02/5.37 thf(fact_9520_real__root__Suc__0,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( root @ ( suc @ zero_zero_nat ) @ X2 )
% 5.02/5.37 = X2 ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_Suc_0
% 5.02/5.37 thf(fact_9521_root__0,axiom,
% 5.02/5.37 ! [X2: real] :
% 5.02/5.37 ( ( root @ zero_zero_nat @ X2 )
% 5.02/5.37 = zero_zero_real ) ).
% 5.02/5.37
% 5.02/5.37 % root_0
% 5.02/5.37 thf(fact_9522_real__root__eq__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ( root @ N2 @ X2 )
% 5.02/5.37 = ( root @ N2 @ Y ) )
% 5.02/5.37 = ( X2 = Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_eq_iff
% 5.02/5.37 thf(fact_9523_real__root__eq__0__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ( root @ N2 @ X2 )
% 5.02/5.37 = zero_zero_real )
% 5.02/5.37 = ( X2 = zero_zero_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_eq_0_iff
% 5.02/5.37 thf(fact_9524_real__root__less__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ ( root @ N2 @ X2 ) @ ( root @ N2 @ Y ) )
% 5.02/5.37 = ( ord_less_real @ X2 @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_less_iff
% 5.02/5.37 thf(fact_9525_real__root__le__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( root @ N2 @ X2 ) @ ( root @ N2 @ Y ) )
% 5.02/5.37 = ( ord_less_eq_real @ X2 @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_le_iff
% 5.02/5.37 thf(fact_9526_real__root__eq__1__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ( root @ N2 @ X2 )
% 5.02/5.37 = one_one_real )
% 5.02/5.37 = ( X2 = one_one_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_eq_1_iff
% 5.02/5.37 thf(fact_9527_real__root__one,axiom,
% 5.02/5.37 ! [N2: nat] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( root @ N2 @ one_one_real )
% 5.02/5.37 = one_one_real ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_one
% 5.02/5.37 thf(fact_9528_real__root__lt__0__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ ( root @ N2 @ X2 ) @ zero_zero_real )
% 5.02/5.37 = ( ord_less_real @ X2 @ zero_zero_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_lt_0_iff
% 5.02/5.37 thf(fact_9529_real__root__gt__0__iff,axiom,
% 5.02/5.37 ! [N2: nat,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.02/5.37 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_gt_0_iff
% 5.02/5.37 thf(fact_9530_real__root__le__0__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( root @ N2 @ X2 ) @ zero_zero_real )
% 5.02/5.37 = ( ord_less_eq_real @ X2 @ zero_zero_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_le_0_iff
% 5.02/5.37 thf(fact_9531_real__root__ge__0__iff,axiom,
% 5.02/5.37 ! [N2: nat,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.02/5.37 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_ge_0_iff
% 5.02/5.37 thf(fact_9532_real__root__lt__1__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ ( root @ N2 @ X2 ) @ one_one_real )
% 5.02/5.37 = ( ord_less_real @ X2 @ one_one_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_lt_1_iff
% 5.02/5.37 thf(fact_9533_real__root__gt__1__iff,axiom,
% 5.02/5.37 ! [N2: nat,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.02/5.37 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_gt_1_iff
% 5.02/5.37 thf(fact_9534_real__root__le__1__iff,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ ( root @ N2 @ X2 ) @ one_one_real )
% 5.02/5.37 = ( ord_less_eq_real @ X2 @ one_one_real ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_le_1_iff
% 5.02/5.37 thf(fact_9535_real__root__ge__1__iff,axiom,
% 5.02/5.37 ! [N2: nat,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.02/5.37 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_ge_1_iff
% 5.02/5.37 thf(fact_9536_real__root__pow__pos2,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( power_power_real @ ( root @ N2 @ X2 ) @ N2 )
% 5.02/5.37 = X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_pow_pos2
% 5.02/5.37 thf(fact_9537_real__root__mult__exp,axiom,
% 5.02/5.37 ! [M: nat,N2: nat,X2: real] :
% 5.02/5.37 ( ( root @ ( times_times_nat @ M @ N2 ) @ X2 )
% 5.02/5.37 = ( root @ M @ ( root @ N2 @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_mult_exp
% 5.02/5.37 thf(fact_9538_real__root__mult,axiom,
% 5.02/5.37 ! [N2: nat,X2: real,Y: real] :
% 5.02/5.37 ( ( root @ N2 @ ( times_times_real @ X2 @ Y ) )
% 5.02/5.37 = ( times_times_real @ ( root @ N2 @ X2 ) @ ( root @ N2 @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_mult
% 5.02/5.37 thf(fact_9539_real__root__less__mono,axiom,
% 5.02/5.37 ! [N2: nat,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ X2 @ Y )
% 5.02/5.37 => ( ord_less_real @ ( root @ N2 @ X2 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_less_mono
% 5.02/5.37 thf(fact_9540_real__root__le__mono,axiom,
% 5.02/5.37 ! [N2: nat,X2: real,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ X2 @ Y )
% 5.02/5.37 => ( ord_less_eq_real @ ( root @ N2 @ X2 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_le_mono
% 5.02/5.37 thf(fact_9541_real__root__power,axiom,
% 5.02/5.37 ! [N2: nat,X2: real,K: nat] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( root @ N2 @ ( power_power_real @ X2 @ K ) )
% 5.02/5.37 = ( power_power_real @ ( root @ N2 @ X2 ) @ K ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_power
% 5.02/5.37 thf(fact_9542_real__root__abs,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( root @ N2 @ ( abs_abs_real @ X2 ) )
% 5.02/5.37 = ( abs_abs_real @ ( root @ N2 @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_abs
% 5.02/5.37 thf(fact_9543_sgn__root,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( sgn_sgn_real @ ( root @ N2 @ X2 ) )
% 5.02/5.37 = ( sgn_sgn_real @ X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sgn_root
% 5.02/5.37 thf(fact_9544_real__root__gt__zero,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_gt_zero
% 5.02/5.37 thf(fact_9545_real__root__strict__decreasing,axiom,
% 5.02/5.37 ! [N2: nat,N4: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_nat @ N2 @ N4 )
% 5.02/5.37 => ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ord_less_real @ ( root @ N4 @ X2 ) @ ( root @ N2 @ X2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_strict_decreasing
% 5.02/5.37 thf(fact_9546_sqrt__def,axiom,
% 5.02/5.37 ( sqrt
% 5.02/5.37 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % sqrt_def
% 5.02/5.37 thf(fact_9547_root__abs__power,axiom,
% 5.02/5.37 ! [N2: nat,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 5.02/5.37 = ( abs_abs_real @ Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % root_abs_power
% 5.02/5.37 thf(fact_9548_real__root__pos__pos,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X2 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_pos_pos
% 5.02/5.37 thf(fact_9549_real__root__strict__increasing,axiom,
% 5.02/5.37 ! [N2: nat,N4: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_nat @ N2 @ N4 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.37 => ( ord_less_real @ ( root @ N2 @ X2 ) @ ( root @ N4 @ X2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_strict_increasing
% 5.02/5.37 thf(fact_9550_real__root__decreasing,axiom,
% 5.02/5.37 ! [N2: nat,N4: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.02/5.37 => ( ( ord_less_eq_real @ one_one_real @ X2 )
% 5.02/5.37 => ( ord_less_eq_real @ ( root @ N4 @ X2 ) @ ( root @ N2 @ X2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_decreasing
% 5.02/5.37 thf(fact_9551_real__root__pow__pos,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( power_power_real @ ( root @ N2 @ X2 ) @ N2 )
% 5.02/5.37 = X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_pow_pos
% 5.02/5.37 thf(fact_9552_real__root__pos__unique,axiom,
% 5.02/5.37 ! [N2: nat,Y: real,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.02/5.37 => ( ( ( power_power_real @ Y @ N2 )
% 5.02/5.37 = X2 )
% 5.02/5.37 => ( ( root @ N2 @ X2 )
% 5.02/5.37 = Y ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_pos_unique
% 5.02/5.37 thf(fact_9553_real__root__power__cancel,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( root @ N2 @ ( power_power_real @ X2 @ N2 ) )
% 5.02/5.37 = X2 ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_power_cancel
% 5.02/5.37 thf(fact_9554_odd__real__root__power__cancel,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.37 => ( ( root @ N2 @ ( power_power_real @ X2 @ N2 ) )
% 5.02/5.37 = X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % odd_real_root_power_cancel
% 5.02/5.37 thf(fact_9555_odd__real__root__unique,axiom,
% 5.02/5.37 ! [N2: nat,Y: real,X2: real] :
% 5.02/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.37 => ( ( ( power_power_real @ Y @ N2 )
% 5.02/5.37 = X2 )
% 5.02/5.37 => ( ( root @ N2 @ X2 )
% 5.02/5.37 = Y ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % odd_real_root_unique
% 5.02/5.37 thf(fact_9556_odd__real__root__pow,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.37 => ( ( power_power_real @ ( root @ N2 @ X2 ) @ N2 )
% 5.02/5.37 = X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % odd_real_root_pow
% 5.02/5.37 thf(fact_9557_Frct__code__post_I1_J,axiom,
% 5.02/5.37 ! [A: int] :
% 5.02/5.37 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.02/5.37 = zero_zero_rat ) ).
% 5.02/5.37
% 5.02/5.37 % Frct_code_post(1)
% 5.02/5.37 thf(fact_9558_Frct__code__post_I2_J,axiom,
% 5.02/5.37 ! [A: int] :
% 5.02/5.37 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.02/5.37 = zero_zero_rat ) ).
% 5.02/5.37
% 5.02/5.37 % Frct_code_post(2)
% 5.02/5.37 thf(fact_9559_real__root__increasing,axiom,
% 5.02/5.37 ! [N2: nat,N4: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.02/5.37 => ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.37 => ( ord_less_eq_real @ ( root @ N2 @ X2 ) @ ( root @ N4 @ X2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % real_root_increasing
% 5.02/5.37 thf(fact_9560_Frct__code__post_I3_J,axiom,
% 5.02/5.37 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.02/5.37 = one_one_rat ) ).
% 5.02/5.37
% 5.02/5.37 % Frct_code_post(3)
% 5.02/5.37 thf(fact_9561_root__sgn__power,axiom,
% 5.02/5.37 ! [N2: nat,Y: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 5.02/5.37 = Y ) ) ).
% 5.02/5.37
% 5.02/5.37 % root_sgn_power
% 5.02/5.37 thf(fact_9562_sgn__power__root,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X2 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X2 ) ) @ N2 ) )
% 5.02/5.37 = X2 ) ) ).
% 5.02/5.37
% 5.02/5.37 % sgn_power_root
% 5.02/5.37 thf(fact_9563_ln__root,axiom,
% 5.02/5.37 ! [N2: nat,B: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.37 => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 5.02/5.37 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ln_root
% 5.02/5.37 thf(fact_9564_log__root,axiom,
% 5.02/5.37 ! [N2: nat,A: real,B: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.02/5.37 => ( ( log @ B @ ( root @ N2 @ A ) )
% 5.02/5.37 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_root
% 5.02/5.37 thf(fact_9565_log__base__root,axiom,
% 5.02/5.37 ! [N2: nat,B: real,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.02/5.37 => ( ( log @ ( root @ N2 @ B ) @ X2 )
% 5.02/5.37 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X2 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % log_base_root
% 5.02/5.37 thf(fact_9566_split__root,axiom,
% 5.02/5.37 ! [P: real > $o,N2: nat,X2: real] :
% 5.02/5.37 ( ( P @ ( root @ N2 @ X2 ) )
% 5.02/5.37 = ( ( ( N2 = zero_zero_nat )
% 5.02/5.37 => ( P @ zero_zero_real ) )
% 5.02/5.37 & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ! [Y6: real] :
% 5.02/5.37 ( ( ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N2 ) )
% 5.02/5.37 = X2 )
% 5.02/5.37 => ( P @ Y6 ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % split_root
% 5.02/5.37 thf(fact_9567_Frct__code__post_I4_J,axiom,
% 5.02/5.37 ! [K: num] :
% 5.02/5.37 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.02/5.37 = ( numeral_numeral_rat @ K ) ) ).
% 5.02/5.37
% 5.02/5.37 % Frct_code_post(4)
% 5.02/5.37 thf(fact_9568_root__powr__inverse,axiom,
% 5.02/5.37 ! [N2: nat,X2: real] :
% 5.02/5.37 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.37 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.37 => ( ( root @ N2 @ X2 )
% 5.02/5.37 = ( powr_real @ X2 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % root_powr_inverse
% 5.02/5.37 thf(fact_9569_Frct__code__post_I6_J,axiom,
% 5.02/5.37 ! [K: num,L: num] :
% 5.02/5.37 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 5.02/5.37 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Frct_code_post(6)
% 5.02/5.37 thf(fact_9570_infinite__int__iff__unbounded,axiom,
% 5.02/5.37 ! [S3: set_int] :
% 5.02/5.37 ( ( ~ ( finite_finite_int @ S3 ) )
% 5.02/5.37 = ( ! [M6: int] :
% 5.02/5.37 ? [N3: int] :
% 5.02/5.37 ( ( ord_less_int @ M6 @ ( abs_abs_int @ N3 ) )
% 5.02/5.37 & ( member_int @ N3 @ S3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % infinite_int_iff_unbounded
% 5.02/5.37 thf(fact_9571_infinite__int__iff__unbounded__le,axiom,
% 5.02/5.37 ! [S3: set_int] :
% 5.02/5.37 ( ( ~ ( finite_finite_int @ S3 ) )
% 5.02/5.37 = ( ! [M6: int] :
% 5.02/5.37 ? [N3: int] :
% 5.02/5.37 ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N3 ) )
% 5.02/5.37 & ( member_int @ N3 @ S3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % infinite_int_iff_unbounded_le
% 5.02/5.37 thf(fact_9572_infinite__nat__iff__unbounded,axiom,
% 5.02/5.37 ! [S3: set_nat] :
% 5.02/5.37 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.02/5.37 = ( ! [M6: nat] :
% 5.02/5.37 ? [N3: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M6 @ N3 )
% 5.02/5.37 & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % infinite_nat_iff_unbounded
% 5.02/5.37 thf(fact_9573_unbounded__k__infinite,axiom,
% 5.02/5.37 ! [K: nat,S3: set_nat] :
% 5.02/5.37 ( ! [M3: nat] :
% 5.02/5.37 ( ( ord_less_nat @ K @ M3 )
% 5.02/5.37 => ? [N8: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M3 @ N8 )
% 5.02/5.37 & ( member_nat @ N8 @ S3 ) ) )
% 5.02/5.37 => ~ ( finite_finite_nat @ S3 ) ) ).
% 5.02/5.37
% 5.02/5.37 % unbounded_k_infinite
% 5.02/5.37 thf(fact_9574_infinite__nat__iff__unbounded__le,axiom,
% 5.02/5.37 ! [S3: set_nat] :
% 5.02/5.37 ( ( ~ ( finite_finite_nat @ S3 ) )
% 5.02/5.37 = ( ! [M6: nat] :
% 5.02/5.37 ? [N3: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M6 @ N3 )
% 5.02/5.37 & ( member_nat @ N3 @ S3 ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % infinite_nat_iff_unbounded_le
% 5.02/5.37 thf(fact_9575_valid__eq2,axiom,
% 5.02/5.37 ! [T2: vEBT_VEBT,D: nat] :
% 5.02/5.37 ( ( vEBT_VEBT_valid @ T2 @ D )
% 5.02/5.37 => ( vEBT_invar_vebt @ T2 @ D ) ) ).
% 5.02/5.37
% 5.02/5.37 % valid_eq2
% 5.02/5.37 thf(fact_9576_valid__eq,axiom,
% 5.02/5.37 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.02/5.37
% 5.02/5.37 % valid_eq
% 5.02/5.37 thf(fact_9577_valid__eq1,axiom,
% 5.02/5.37 ! [T2: vEBT_VEBT,D: nat] :
% 5.02/5.37 ( ( vEBT_invar_vebt @ T2 @ D )
% 5.02/5.37 => ( vEBT_VEBT_valid @ T2 @ D ) ) ).
% 5.02/5.37
% 5.02/5.37 % valid_eq1
% 5.02/5.37 thf(fact_9578_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.02/5.37 ! [Uu: $o,Uv: $o,D: nat] :
% 5.02/5.37 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.02/5.37 = ( D = one_one_nat ) ) ).
% 5.02/5.37
% 5.02/5.37 % VEBT_internal.valid'.simps(1)
% 5.02/5.37 thf(fact_9579_Sum__Ico__nat,axiom,
% 5.02/5.37 ! [M: nat,N2: nat] :
% 5.02/5.37 ( ( groups3542108847815614940at_nat
% 5.02/5.37 @ ^ [X: nat] : X
% 5.02/5.37 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.02/5.37 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Sum_Ico_nat
% 5.02/5.37 thf(fact_9580_VEBT_Osize_I3_J,axiom,
% 5.02/5.37 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.02/5.37 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.02/5.37 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % VEBT.size(3)
% 5.02/5.37 thf(fact_9581_Cauchy__iff2,axiom,
% 5.02/5.37 ( topolo4055970368930404560y_real
% 5.02/5.37 = ( ^ [X4: nat > real] :
% 5.02/5.37 ! [J3: nat] :
% 5.02/5.37 ? [M8: nat] :
% 5.02/5.37 ! [M6: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M8 @ M6 )
% 5.02/5.37 => ! [N3: nat] :
% 5.02/5.37 ( ( ord_less_eq_nat @ M8 @ N3 )
% 5.02/5.37 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X4 @ M6 ) @ ( X4 @ N3 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % Cauchy_iff2
% 5.02/5.37 thf(fact_9582_atLeastLessThan__singleton,axiom,
% 5.02/5.37 ! [M: nat] :
% 5.02/5.37 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.02/5.37 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.02/5.37
% 5.02/5.37 % atLeastLessThan_singleton
% 5.02/5.37 thf(fact_9583_ex__nat__less__eq,axiom,
% 5.02/5.37 ! [N2: nat,P: nat > $o] :
% 5.02/5.37 ( ( ? [M6: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M6 @ N2 )
% 5.02/5.37 & ( P @ M6 ) ) )
% 5.02/5.37 = ( ? [X: nat] :
% 5.02/5.37 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.37 & ( P @ X ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % ex_nat_less_eq
% 5.02/5.37 thf(fact_9584_all__nat__less__eq,axiom,
% 5.02/5.37 ! [N2: nat,P: nat > $o] :
% 5.02/5.37 ( ( ! [M6: nat] :
% 5.02/5.37 ( ( ord_less_nat @ M6 @ N2 )
% 5.02/5.37 => ( P @ M6 ) ) )
% 5.02/5.37 = ( ! [X: nat] :
% 5.02/5.37 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.37 => ( P @ X ) ) ) ) ).
% 5.02/5.37
% 5.02/5.37 % all_nat_less_eq
% 5.02/5.37 thf(fact_9585_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.02/5.37 ! [L: nat,U: nat] :
% 5.02/5.37 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.02/5.37 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastLessThanSuc_atLeastAtMost
% 5.02/5.38 thf(fact_9586_lessThan__atLeast0,axiom,
% 5.02/5.38 ( set_ord_lessThan_nat
% 5.02/5.38 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % lessThan_atLeast0
% 5.02/5.38 thf(fact_9587_atLeastLessThan0,axiom,
% 5.02/5.38 ! [M: nat] :
% 5.02/5.38 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.02/5.38 = bot_bot_set_nat ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastLessThan0
% 5.02/5.38 thf(fact_9588_atLeast0__lessThan__Suc,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.02/5.38 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeast0_lessThan_Suc
% 5.02/5.38 thf(fact_9589_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.02/5.38 ! [N4: set_nat,N2: nat] :
% 5.02/5.38 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.38 => ( finite_finite_nat @ N4 ) ) ).
% 5.02/5.38
% 5.02/5.38 % subset_eq_atLeast0_lessThan_finite
% 5.02/5.38 thf(fact_9590_atLeastLessThanSuc,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.38 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.02/5.38 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.38 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.02/5.38 = bot_bot_set_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastLessThanSuc
% 5.02/5.38 thf(fact_9591_prod__Suc__fact,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.38 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % prod_Suc_fact
% 5.02/5.38 thf(fact_9592_prod__Suc__Suc__fact,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.02/5.38 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % prod_Suc_Suc_fact
% 5.02/5.38 thf(fact_9593_atLeastLessThan__nat__numeral,axiom,
% 5.02/5.38 ! [M: nat,K: num] :
% 5.02/5.38 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.02/5.38 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.02/5.38 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.02/5.38 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.02/5.38 = bot_bot_set_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastLessThan_nat_numeral
% 5.02/5.38 thf(fact_9594_atLeast1__lessThan__eq__remove0,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.02/5.38 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeast1_lessThan_eq_remove0
% 5.02/5.38 thf(fact_9595_sum__power2,axiom,
% 5.02/5.38 ! [K: nat] :
% 5.02/5.38 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.02/5.38 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % sum_power2
% 5.02/5.38 thf(fact_9596_Chebyshev__sum__upper__nat,axiom,
% 5.02/5.38 ! [N2: nat,A: nat > nat,B: nat > nat] :
% 5.02/5.38 ( ! [I2: nat,J2: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.02/5.38 => ( ( ord_less_nat @ J2 @ N2 )
% 5.02/5.38 => ( ord_less_eq_nat @ ( A @ I2 ) @ ( A @ J2 ) ) ) )
% 5.02/5.38 => ( ! [I2: nat,J2: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ I2 @ J2 )
% 5.02/5.38 => ( ( ord_less_nat @ J2 @ N2 )
% 5.02/5.38 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I2 ) ) ) )
% 5.02/5.38 => ( ord_less_eq_nat
% 5.02/5.38 @ ( times_times_nat @ N2
% 5.02/5.38 @ ( groups3542108847815614940at_nat
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( B @ I5 ) )
% 5.02/5.38 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 5.02/5.38 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Chebyshev_sum_upper_nat
% 5.02/5.38 thf(fact_9597_finite__atLeastZeroLessThan__int,axiom,
% 5.02/5.38 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % finite_atLeastZeroLessThan_int
% 5.02/5.38 thf(fact_9598_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.02/5.38 ! [L: int,U: int] :
% 5.02/5.38 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 5.02/5.38 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.02/5.38 thf(fact_9599_VEBT_Osize__gen_I1_J,axiom,
% 5.02/5.38 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.02/5.38 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.02/5.38 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT.size_gen(1)
% 5.02/5.38 thf(fact_9600_Code__Target__Int_Opositive__def,axiom,
% 5.02/5.38 code_Target_positive = numeral_numeral_int ).
% 5.02/5.38
% 5.02/5.38 % Code_Target_Int.positive_def
% 5.02/5.38 thf(fact_9601_VEBT_Osize__gen_I2_J,axiom,
% 5.02/5.38 ! [X21: $o,X222: $o] :
% 5.02/5.38 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.02/5.38 = zero_zero_nat ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT.size_gen(2)
% 5.02/5.38 thf(fact_9602_divmod__step__integer__def,axiom,
% 5.02/5.38 ( unique4921790084139445826nteger
% 5.02/5.38 = ( ^ [L2: num] :
% 5.02/5.38 ( produc6916734918728496179nteger
% 5.02/5.38 @ ^ [Q4: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R5 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % divmod_step_integer_def
% 5.02/5.38 thf(fact_9603_csqrt_Osimps_I1_J,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( re @ ( csqrt @ Z ) )
% 5.02/5.38 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % csqrt.simps(1)
% 5.02/5.38 thf(fact_9604_sgn__integer__code,axiom,
% 5.02/5.38 ( sgn_sgn_Code_integer
% 5.02/5.38 = ( ^ [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 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sgn_integer_code
% 5.02/5.38 thf(fact_9605_times__integer__code_I1_J,axiom,
% 5.02/5.38 ! [K: code_integer] :
% 5.02/5.38 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.02/5.38 = zero_z3403309356797280102nteger ) ).
% 5.02/5.38
% 5.02/5.38 % times_integer_code(1)
% 5.02/5.38 thf(fact_9606_times__integer__code_I2_J,axiom,
% 5.02/5.38 ! [L: code_integer] :
% 5.02/5.38 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 5.02/5.38 = zero_z3403309356797280102nteger ) ).
% 5.02/5.38
% 5.02/5.38 % times_integer_code(2)
% 5.02/5.38 thf(fact_9607_plus__integer__code_I1_J,axiom,
% 5.02/5.38 ! [K: code_integer] :
% 5.02/5.38 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.02/5.38 = K ) ).
% 5.02/5.38
% 5.02/5.38 % plus_integer_code(1)
% 5.02/5.38 thf(fact_9608_plus__integer__code_I2_J,axiom,
% 5.02/5.38 ! [L: code_integer] :
% 5.02/5.38 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L )
% 5.02/5.38 = L ) ).
% 5.02/5.38
% 5.02/5.38 % plus_integer_code(2)
% 5.02/5.38 thf(fact_9609_one__complex_Osimps_I1_J,axiom,
% 5.02/5.38 ( ( re @ one_one_complex )
% 5.02/5.38 = one_one_real ) ).
% 5.02/5.38
% 5.02/5.38 % one_complex.simps(1)
% 5.02/5.38 thf(fact_9610_plus__complex_Osimps_I1_J,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( re @ ( plus_plus_complex @ X2 @ Y ) )
% 5.02/5.38 = ( plus_plus_real @ ( re @ X2 ) @ ( re @ Y ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % plus_complex.simps(1)
% 5.02/5.38 thf(fact_9611_scaleR__complex_Osimps_I1_J,axiom,
% 5.02/5.38 ! [R2: real,X2: complex] :
% 5.02/5.38 ( ( re @ ( real_V2046097035970521341omplex @ R2 @ X2 ) )
% 5.02/5.38 = ( times_times_real @ R2 @ ( re @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % scaleR_complex.simps(1)
% 5.02/5.38 thf(fact_9612_zero__natural_Orsp,axiom,
% 5.02/5.38 zero_zero_nat = zero_zero_nat ).
% 5.02/5.38
% 5.02/5.38 % zero_natural.rsp
% 5.02/5.38 thf(fact_9613_zero__integer_Orsp,axiom,
% 5.02/5.38 zero_zero_int = zero_zero_int ).
% 5.02/5.38
% 5.02/5.38 % zero_integer.rsp
% 5.02/5.38 thf(fact_9614_one__integer_Orsp,axiom,
% 5.02/5.38 one_one_int = one_one_int ).
% 5.02/5.38
% 5.02/5.38 % one_integer.rsp
% 5.02/5.38 thf(fact_9615_one__natural_Orsp,axiom,
% 5.02/5.38 one_one_nat = one_one_nat ).
% 5.02/5.38
% 5.02/5.38 % one_natural.rsp
% 5.02/5.38 thf(fact_9616_cmod__plus__Re__le__0__iff,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.02/5.38 = ( ( re @ Z )
% 5.02/5.38 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % cmod_plus_Re_le_0_iff
% 5.02/5.38 thf(fact_9617_cos__n__Re__cis__pow__n,axiom,
% 5.02/5.38 ! [N2: nat,A: real] :
% 5.02/5.38 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) )
% 5.02/5.38 = ( re @ ( power_power_complex @ ( cis @ A ) @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % cos_n_Re_cis_pow_n
% 5.02/5.38 thf(fact_9618_csqrt_Ocode,axiom,
% 5.02/5.38 ( csqrt
% 5.02/5.38 = ( ^ [Z6: complex] :
% 5.02/5.38 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.38 @ ( times_times_real
% 5.02/5.38 @ ( if_real
% 5.02/5.38 @ ( ( im @ Z6 )
% 5.02/5.38 = zero_zero_real )
% 5.02/5.38 @ one_one_real
% 5.02/5.38 @ ( sgn_sgn_real @ ( im @ Z6 ) ) )
% 5.02/5.38 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z6 ) @ ( re @ Z6 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % csqrt.code
% 5.02/5.38 thf(fact_9619_csqrt_Osimps_I2_J,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( im @ ( csqrt @ Z ) )
% 5.02/5.38 = ( times_times_real
% 5.02/5.38 @ ( if_real
% 5.02/5.38 @ ( ( im @ Z )
% 5.02/5.38 = zero_zero_real )
% 5.02/5.38 @ one_one_real
% 5.02/5.38 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.02/5.38 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % csqrt.simps(2)
% 5.02/5.38 thf(fact_9620_integer__of__int__code,axiom,
% 5.02/5.38 ( code_integer_of_int
% 5.02/5.38 = ( ^ [K3: int] :
% 5.02/5.38 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.02/5.38 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.02/5.38 @ ( if_Code_integer
% 5.02/5.38 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.02/5.38 = zero_zero_int )
% 5.02/5.38 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % integer_of_int_code
% 5.02/5.38 thf(fact_9621_Im__i__times,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.02/5.38 = ( re @ Z ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_i_times
% 5.02/5.38 thf(fact_9622_Re__i__times,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.02/5.38 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_i_times
% 5.02/5.38 thf(fact_9623_csqrt__minus,axiom,
% 5.02/5.38 ! [X2: complex] :
% 5.02/5.38 ( ( ( ord_less_real @ ( im @ X2 ) @ zero_zero_real )
% 5.02/5.38 | ( ( ( im @ X2 )
% 5.02/5.38 = zero_zero_real )
% 5.02/5.38 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X2 ) ) ) )
% 5.02/5.38 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X2 ) )
% 5.02/5.38 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % csqrt_minus
% 5.02/5.38 thf(fact_9624_csqrt__of__real__nonpos,axiom,
% 5.02/5.38 ! [X2: complex] :
% 5.02/5.38 ( ( ( im @ X2 )
% 5.02/5.38 = zero_zero_real )
% 5.02/5.38 => ( ( ord_less_eq_real @ ( re @ X2 ) @ zero_zero_real )
% 5.02/5.38 => ( ( csqrt @ X2 )
% 5.02/5.38 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X2 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % csqrt_of_real_nonpos
% 5.02/5.38 thf(fact_9625_divide__integer_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: int,X2: int] :
% 5.02/5.38 ( ( divide6298287555418463151nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.02/5.38 = ( code_integer_of_int @ ( divide_divide_int @ Xa2 @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % divide_integer.abs_eq
% 5.02/5.38 thf(fact_9626_less__integer_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: int,X2: int] :
% 5.02/5.38 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.02/5.38 = ( ord_less_int @ Xa2 @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_integer.abs_eq
% 5.02/5.38 thf(fact_9627_zero__integer__def,axiom,
% 5.02/5.38 ( zero_z3403309356797280102nteger
% 5.02/5.38 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % zero_integer_def
% 5.02/5.38 thf(fact_9628_imaginary__unit_Osimps_I2_J,axiom,
% 5.02/5.38 ( ( im @ imaginary_unit )
% 5.02/5.38 = one_one_real ) ).
% 5.02/5.38
% 5.02/5.38 % imaginary_unit.simps(2)
% 5.02/5.38 thf(fact_9629_one__complex_Osimps_I2_J,axiom,
% 5.02/5.38 ( ( im @ one_one_complex )
% 5.02/5.38 = zero_zero_real ) ).
% 5.02/5.38
% 5.02/5.38 % one_complex.simps(2)
% 5.02/5.38 thf(fact_9630_plus__integer_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: int,X2: int] :
% 5.02/5.38 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.02/5.38 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % plus_integer.abs_eq
% 5.02/5.38 thf(fact_9631_times__integer_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: int,X2: int] :
% 5.02/5.38 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.02/5.38 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % times_integer.abs_eq
% 5.02/5.38 thf(fact_9632_one__integer__def,axiom,
% 5.02/5.38 ( one_one_Code_integer
% 5.02/5.38 = ( code_integer_of_int @ one_one_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % one_integer_def
% 5.02/5.38 thf(fact_9633_less__eq__integer_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: int,X2: int] :
% 5.02/5.38 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X2 ) )
% 5.02/5.38 = ( ord_less_eq_int @ Xa2 @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_eq_integer.abs_eq
% 5.02/5.38 thf(fact_9634_plus__complex_Osimps_I2_J,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( im @ ( plus_plus_complex @ X2 @ Y ) )
% 5.02/5.38 = ( plus_plus_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % plus_complex.simps(2)
% 5.02/5.38 thf(fact_9635_scaleR__complex_Osimps_I2_J,axiom,
% 5.02/5.38 ! [R2: real,X2: complex] :
% 5.02/5.38 ( ( im @ ( real_V2046097035970521341omplex @ R2 @ X2 ) )
% 5.02/5.38 = ( times_times_real @ R2 @ ( im @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % scaleR_complex.simps(2)
% 5.02/5.38 thf(fact_9636_times__complex_Osimps_I2_J,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( im @ ( times_times_complex @ X2 @ Y ) )
% 5.02/5.38 = ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % times_complex.simps(2)
% 5.02/5.38 thf(fact_9637_times__complex_Osimps_I1_J,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( re @ ( times_times_complex @ X2 @ Y ) )
% 5.02/5.38 = ( minus_minus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( im @ Y ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % times_complex.simps(1)
% 5.02/5.38 thf(fact_9638_plus__complex_Ocode,axiom,
% 5.02/5.38 ( plus_plus_complex
% 5.02/5.38 = ( ^ [X: complex,Y6: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X ) @ ( re @ Y6 ) ) @ ( plus_plus_real @ ( im @ X ) @ ( im @ Y6 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % plus_complex.code
% 5.02/5.38 thf(fact_9639_scaleR__complex_Ocode,axiom,
% 5.02/5.38 ( real_V2046097035970521341omplex
% 5.02/5.38 = ( ^ [R5: real,X: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X ) ) @ ( times_times_real @ R5 @ ( im @ X ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % scaleR_complex.code
% 5.02/5.38 thf(fact_9640_cmod__le,axiom,
% 5.02/5.38 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % cmod_le
% 5.02/5.38 thf(fact_9641_sin__n__Im__cis__pow__n,axiom,
% 5.02/5.38 ! [N2: nat,A: real] :
% 5.02/5.38 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) )
% 5.02/5.38 = ( im @ ( power_power_complex @ ( cis @ A ) @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sin_n_Im_cis_pow_n
% 5.02/5.38 thf(fact_9642_Re__exp,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( re @ ( exp_complex @ Z ) )
% 5.02/5.38 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_exp
% 5.02/5.38 thf(fact_9643_Im__exp,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( im @ ( exp_complex @ Z ) )
% 5.02/5.38 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_exp
% 5.02/5.38 thf(fact_9644_complex__eq,axiom,
% 5.02/5.38 ! [A: complex] :
% 5.02/5.38 ( A
% 5.02/5.38 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_eq
% 5.02/5.38 thf(fact_9645_times__complex_Ocode,axiom,
% 5.02/5.38 ( times_times_complex
% 5.02/5.38 = ( ^ [X: complex,Y6: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y6 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y6 ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y6 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % times_complex.code
% 5.02/5.38 thf(fact_9646_exp__eq__polar,axiom,
% 5.02/5.38 ( exp_complex
% 5.02/5.38 = ( ^ [Z6: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z6 ) ) ) @ ( cis @ ( im @ Z6 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % exp_eq_polar
% 5.02/5.38 thf(fact_9647_cmod__power2,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.38 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % cmod_power2
% 5.02/5.38 thf(fact_9648_Im__power2,axiom,
% 5.02/5.38 ! [X2: complex] :
% 5.02/5.38 ( ( im @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.38 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X2 ) ) @ ( im @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_power2
% 5.02/5.38 thf(fact_9649_Re__power2,axiom,
% 5.02/5.38 ! [X2: complex] :
% 5.02/5.38 ( ( re @ ( power_power_complex @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.38 = ( minus_minus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_power2
% 5.02/5.38 thf(fact_9650_complex__eq__0,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( Z = zero_zero_complex )
% 5.02/5.38 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.38 = zero_zero_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_eq_0
% 5.02/5.38 thf(fact_9651_norm__complex__def,axiom,
% 5.02/5.38 ( real_V1022390504157884413omplex
% 5.02/5.38 = ( ^ [Z6: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z6 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % norm_complex_def
% 5.02/5.38 thf(fact_9652_inverse__complex_Osimps_I1_J,axiom,
% 5.02/5.38 ! [X2: complex] :
% 5.02/5.38 ( ( re @ ( invers8013647133539491842omplex @ X2 ) )
% 5.02/5.38 = ( divide_divide_real @ ( re @ X2 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % inverse_complex.simps(1)
% 5.02/5.38 thf(fact_9653_complex__neq__0,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( Z != zero_zero_complex )
% 5.02/5.38 = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_neq_0
% 5.02/5.38 thf(fact_9654_Re__divide,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( re @ ( divide1717551699836669952omplex @ X2 @ Y ) )
% 5.02/5.38 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X2 ) @ ( 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 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_divide
% 5.02/5.38 thf(fact_9655_csqrt__unique,axiom,
% 5.02/5.38 ! [W: complex,Z: complex] :
% 5.02/5.38 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.02/5.38 = Z )
% 5.02/5.38 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.02/5.38 | ( ( ( re @ W )
% 5.02/5.38 = zero_zero_real )
% 5.02/5.38 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.02/5.38 => ( ( csqrt @ Z )
% 5.02/5.38 = W ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % csqrt_unique
% 5.02/5.38 thf(fact_9656_csqrt__square,axiom,
% 5.02/5.38 ! [B: complex] :
% 5.02/5.38 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.02/5.38 | ( ( ( re @ B )
% 5.02/5.38 = zero_zero_real )
% 5.02/5.38 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.02/5.38 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.38 = B ) ) ).
% 5.02/5.38
% 5.02/5.38 % csqrt_square
% 5.02/5.38 thf(fact_9657_inverse__complex_Osimps_I2_J,axiom,
% 5.02/5.38 ! [X2: complex] :
% 5.02/5.38 ( ( im @ ( invers8013647133539491842omplex @ X2 ) )
% 5.02/5.38 = ( 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 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % inverse_complex.simps(2)
% 5.02/5.38 thf(fact_9658_Im__divide,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( im @ ( divide1717551699836669952omplex @ X2 @ Y ) )
% 5.02/5.38 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X2 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X2 ) @ ( 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 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_divide
% 5.02/5.38 thf(fact_9659_complex__abs__le__norm,axiom,
% 5.02/5.38 ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_abs_le_norm
% 5.02/5.38 thf(fact_9660_complex__unit__circle,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( Z != zero_zero_complex )
% 5.02/5.38 => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.38 = one_one_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_unit_circle
% 5.02/5.38 thf(fact_9661_inverse__complex_Ocode,axiom,
% 5.02/5.38 ( invers8013647133539491842omplex
% 5.02/5.38 = ( ^ [X: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % inverse_complex.code
% 5.02/5.38 thf(fact_9662_Complex__divide,axiom,
% 5.02/5.38 ( divide1717551699836669952omplex
% 5.02/5.38 = ( ^ [X: complex,Y6: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( im @ X ) @ ( 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 @ X ) @ ( re @ Y6 ) ) @ ( times_times_real @ ( re @ X ) @ ( 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 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Complex_divide
% 5.02/5.38 thf(fact_9663_Im__Reals__divide,axiom,
% 5.02/5.38 ! [R2: complex,Z: complex] :
% 5.02/5.38 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.02/5.38 => ( ( im @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.02/5.38 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R2 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_Reals_divide
% 5.02/5.38 thf(fact_9664_Re__Reals__divide,axiom,
% 5.02/5.38 ! [R2: complex,Z: complex] :
% 5.02/5.38 ( ( member_complex @ R2 @ real_V2521375963428798218omplex )
% 5.02/5.38 => ( ( re @ ( divide1717551699836669952omplex @ R2 @ Z ) )
% 5.02/5.38 = ( divide_divide_real @ ( times_times_real @ ( re @ R2 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_Reals_divide
% 5.02/5.38 thf(fact_9665_imaginary__eq__real__iff,axiom,
% 5.02/5.38 ! [Y: complex,X2: complex] :
% 5.02/5.38 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.02/5.38 => ( ( member_complex @ X2 @ real_V2521375963428798218omplex )
% 5.02/5.38 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 5.02/5.38 = X2 )
% 5.02/5.38 = ( ( X2 = zero_zero_complex )
% 5.02/5.38 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % imaginary_eq_real_iff
% 5.02/5.38 thf(fact_9666_real__eq__imaginary__iff,axiom,
% 5.02/5.38 ! [Y: complex,X2: complex] :
% 5.02/5.38 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.02/5.38 => ( ( member_complex @ X2 @ real_V2521375963428798218omplex )
% 5.02/5.38 => ( ( X2
% 5.02/5.38 = ( times_times_complex @ imaginary_unit @ Y ) )
% 5.02/5.38 = ( ( X2 = zero_zero_complex )
% 5.02/5.38 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % real_eq_imaginary_iff
% 5.02/5.38 thf(fact_9667_complex__mult__cnj,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.02/5.38 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_mult_cnj
% 5.02/5.38 thf(fact_9668_integer__of__num_I3_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( code_integer_of_num @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.02/5.38
% 5.02/5.38 % integer_of_num(3)
% 5.02/5.38 thf(fact_9669_int__of__integer__code,axiom,
% 5.02/5.38 ( code_int_of_integer
% 5.02/5.38 = ( ^ [K3: code_integer] :
% 5.02/5.38 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.02/5.38 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.02/5.38 @ ( produc1553301316500091796er_int
% 5.02/5.38 @ ^ [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 ) )
% 5.02/5.38 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % int_of_integer_code
% 5.02/5.38 thf(fact_9670_complex__cnj__mult,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( cnj @ ( times_times_complex @ X2 @ Y ) )
% 5.02/5.38 = ( times_times_complex @ ( cnj @ X2 ) @ ( cnj @ Y ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_cnj_mult
% 5.02/5.38 thf(fact_9671_complex__cnj__one__iff,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( ( cnj @ Z )
% 5.02/5.38 = one_one_complex )
% 5.02/5.38 = ( Z = one_one_complex ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_cnj_one_iff
% 5.02/5.38 thf(fact_9672_complex__cnj__one,axiom,
% 5.02/5.38 ( ( cnj @ one_one_complex )
% 5.02/5.38 = one_one_complex ) ).
% 5.02/5.38
% 5.02/5.38 % complex_cnj_one
% 5.02/5.38 thf(fact_9673_complex__cnj__add,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( cnj @ ( plus_plus_complex @ X2 @ Y ) )
% 5.02/5.38 = ( plus_plus_complex @ ( cnj @ X2 ) @ ( cnj @ Y ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_cnj_add
% 5.02/5.38 thf(fact_9674_zero__integer_Orep__eq,axiom,
% 5.02/5.38 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 5.02/5.38 = zero_zero_int ) ).
% 5.02/5.38
% 5.02/5.38 % zero_integer.rep_eq
% 5.02/5.38 thf(fact_9675_int__of__integer__numeral,axiom,
% 5.02/5.38 ! [K: num] :
% 5.02/5.38 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.02/5.38 = ( numeral_numeral_int @ K ) ) ).
% 5.02/5.38
% 5.02/5.38 % int_of_integer_numeral
% 5.02/5.38 thf(fact_9676_plus__integer_Orep__eq,axiom,
% 5.02/5.38 ! [X2: code_integer,Xa2: code_integer] :
% 5.02/5.38 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X2 @ Xa2 ) )
% 5.02/5.38 = ( plus_plus_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % plus_integer.rep_eq
% 5.02/5.38 thf(fact_9677_times__integer_Orep__eq,axiom,
% 5.02/5.38 ! [X2: code_integer,Xa2: code_integer] :
% 5.02/5.38 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X2 @ Xa2 ) )
% 5.02/5.38 = ( times_times_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % times_integer.rep_eq
% 5.02/5.38 thf(fact_9678_one__integer_Orep__eq,axiom,
% 5.02/5.38 ( ( code_int_of_integer @ one_one_Code_integer )
% 5.02/5.38 = one_one_int ) ).
% 5.02/5.38
% 5.02/5.38 % one_integer.rep_eq
% 5.02/5.38 thf(fact_9679_divide__integer_Orep__eq,axiom,
% 5.02/5.38 ! [X2: code_integer,Xa2: code_integer] :
% 5.02/5.38 ( ( code_int_of_integer @ ( divide6298287555418463151nteger @ X2 @ Xa2 ) )
% 5.02/5.38 = ( divide_divide_int @ ( code_int_of_integer @ X2 ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % divide_integer.rep_eq
% 5.02/5.38 thf(fact_9680_complex__In__mult__cnj__zero,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.02/5.38 = zero_zero_real ) ).
% 5.02/5.38
% 5.02/5.38 % complex_In_mult_cnj_zero
% 5.02/5.38 thf(fact_9681_less__integer_Orep__eq,axiom,
% 5.02/5.38 ( ord_le6747313008572928689nteger
% 5.02/5.38 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_integer.rep_eq
% 5.02/5.38 thf(fact_9682_integer__less__iff,axiom,
% 5.02/5.38 ( ord_le6747313008572928689nteger
% 5.02/5.38 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % integer_less_iff
% 5.02/5.38 thf(fact_9683_less__eq__integer_Orep__eq,axiom,
% 5.02/5.38 ( ord_le3102999989581377725nteger
% 5.02/5.38 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_eq_integer.rep_eq
% 5.02/5.38 thf(fact_9684_integer__less__eq__iff,axiom,
% 5.02/5.38 ( ord_le3102999989581377725nteger
% 5.02/5.38 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % integer_less_eq_iff
% 5.02/5.38 thf(fact_9685_Re__complex__div__eq__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.38 = zero_zero_real )
% 5.02/5.38 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.02/5.38 = zero_zero_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_complex_div_eq_0
% 5.02/5.38 thf(fact_9686_Im__complex__div__eq__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.02/5.38 = zero_zero_real )
% 5.02/5.38 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.02/5.38 = zero_zero_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_complex_div_eq_0
% 5.02/5.38 thf(fact_9687_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.02/5.38 ( real_V1022390504157884413omplex
% 5.02/5.38 = ( ^ [Z6: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z6 @ ( cnj @ Z6 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_mod_sqrt_Re_mult_cnj
% 5.02/5.38 thf(fact_9688_integer__of__num__triv_I1_J,axiom,
% 5.02/5.38 ( ( code_integer_of_num @ one )
% 5.02/5.38 = one_one_Code_integer ) ).
% 5.02/5.38
% 5.02/5.38 % integer_of_num_triv(1)
% 5.02/5.38 thf(fact_9689_Re__complex__div__gt__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.02/5.38 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_complex_div_gt_0
% 5.02/5.38 thf(fact_9690_Re__complex__div__lt__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.02/5.38 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_complex_div_lt_0
% 5.02/5.38 thf(fact_9691_Re__complex__div__ge__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.02/5.38 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_complex_div_ge_0
% 5.02/5.38 thf(fact_9692_Re__complex__div__le__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.02/5.38 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % Re_complex_div_le_0
% 5.02/5.38 thf(fact_9693_Im__complex__div__gt__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.02/5.38 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_complex_div_gt_0
% 5.02/5.38 thf(fact_9694_Im__complex__div__lt__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.02/5.38 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_complex_div_lt_0
% 5.02/5.38 thf(fact_9695_Im__complex__div__ge__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.02/5.38 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_complex_div_ge_0
% 5.02/5.38 thf(fact_9696_Im__complex__div__le__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.02/5.38 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % Im_complex_div_le_0
% 5.02/5.38 thf(fact_9697_integer__of__num_I2_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % integer_of_num(2)
% 5.02/5.38 thf(fact_9698_complex__mod__mult__cnj,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.02/5.38 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_mod_mult_cnj
% 5.02/5.38 thf(fact_9699_complex__div__gt__0,axiom,
% 5.02/5.38 ! [A: complex,B: complex] :
% 5.02/5.38 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.02/5.38 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.02/5.38 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.02/5.38 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_div_gt_0
% 5.02/5.38 thf(fact_9700_integer__of__num__triv_I2_J,axiom,
% 5.02/5.38 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.02/5.38 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % integer_of_num_triv(2)
% 5.02/5.38 thf(fact_9701_complex__norm__square,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.02/5.38 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_norm_square
% 5.02/5.38 thf(fact_9702_complex__add__cnj,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.02/5.38 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_add_cnj
% 5.02/5.38 thf(fact_9703_complex__diff__cnj,axiom,
% 5.02/5.38 ! [Z: complex] :
% 5.02/5.38 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.02/5.38 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_diff_cnj
% 5.02/5.38 thf(fact_9704_complex__div__cnj,axiom,
% 5.02/5.38 ( divide1717551699836669952omplex
% 5.02/5.38 = ( ^ [A5: complex,B5: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A5 @ ( cnj @ B5 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % complex_div_cnj
% 5.02/5.38 thf(fact_9705_cnj__add__mult__eq__Re,axiom,
% 5.02/5.38 ! [Z: complex,W: complex] :
% 5.02/5.38 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.02/5.38 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % cnj_add_mult_eq_Re
% 5.02/5.38 thf(fact_9706_num__of__integer__code,axiom,
% 5.02/5.38 ( code_num_of_integer
% 5.02/5.38 = ( ^ [K3: code_integer] :
% 5.02/5.38 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.02/5.38 @ ( produc7336495610019696514er_num
% 5.02/5.38 @ ^ [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 ) )
% 5.02/5.38 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % num_of_integer_code
% 5.02/5.38 thf(fact_9707_nat__of__integer__code,axiom,
% 5.02/5.38 ( code_nat_of_integer
% 5.02/5.38 = ( ^ [K3: code_integer] :
% 5.02/5.38 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.02/5.38 @ ( produc1555791787009142072er_nat
% 5.02/5.38 @ ^ [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 ) )
% 5.02/5.38 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat_of_integer_code
% 5.02/5.38 thf(fact_9708_bit__cut__integer__def,axiom,
% 5.02/5.38 ( code_bit_cut_integer
% 5.02/5.38 = ( ^ [K3: code_integer] :
% 5.02/5.38 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.02/5.38 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bit_cut_integer_def
% 5.02/5.38 thf(fact_9709_nat__of__integer__non__positive,axiom,
% 5.02/5.38 ! [K: code_integer] :
% 5.02/5.38 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.02/5.38 => ( ( code_nat_of_integer @ K )
% 5.02/5.38 = zero_zero_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat_of_integer_non_positive
% 5.02/5.38 thf(fact_9710_nat__of__integer__code__post_I1_J,axiom,
% 5.02/5.38 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 5.02/5.38 = zero_zero_nat ) ).
% 5.02/5.38
% 5.02/5.38 % nat_of_integer_code_post(1)
% 5.02/5.38 thf(fact_9711_nat__of__integer__code__post_I3_J,axiom,
% 5.02/5.38 ! [K: num] :
% 5.02/5.38 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.02/5.38 = ( numeral_numeral_nat @ K ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat_of_integer_code_post(3)
% 5.02/5.38 thf(fact_9712_nat__of__integer__code__post_I2_J,axiom,
% 5.02/5.38 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.02/5.38 = one_one_nat ) ).
% 5.02/5.38
% 5.02/5.38 % nat_of_integer_code_post(2)
% 5.02/5.38 thf(fact_9713_bit__cut__integer__code,axiom,
% 5.02/5.38 ( code_bit_cut_integer
% 5.02/5.38 = ( ^ [K3: code_integer] :
% 5.02/5.38 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.02/5.38 @ ( produc9125791028180074456eger_o
% 5.02/5.38 @ ^ [R5: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 5.02/5.38 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bit_cut_integer_code
% 5.02/5.38 thf(fact_9714_card__Collect__less__nat,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( finite_card_nat
% 5.02/5.38 @ ( collect_nat
% 5.02/5.38 @ ^ [I5: nat] : ( ord_less_nat @ I5 @ N2 ) ) )
% 5.02/5.38 = N2 ) ).
% 5.02/5.38
% 5.02/5.38 % card_Collect_less_nat
% 5.02/5.38 thf(fact_9715_card__atMost,axiom,
% 5.02/5.38 ! [U: nat] :
% 5.02/5.38 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.02/5.38 = ( suc @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_atMost
% 5.02/5.38 thf(fact_9716_card__Collect__le__nat,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( finite_card_nat
% 5.02/5.38 @ ( collect_nat
% 5.02/5.38 @ ^ [I5: nat] : ( ord_less_eq_nat @ I5 @ N2 ) ) )
% 5.02/5.38 = ( suc @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_Collect_le_nat
% 5.02/5.38 thf(fact_9717_card__atLeastAtMost,axiom,
% 5.02/5.38 ! [L: nat,U: nat] :
% 5.02/5.38 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.02/5.38 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_atLeastAtMost
% 5.02/5.38 thf(fact_9718_card__atLeastAtMost__int,axiom,
% 5.02/5.38 ! [L: int,U: int] :
% 5.02/5.38 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.02/5.38 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_atLeastAtMost_int
% 5.02/5.38 thf(fact_9719_card__less,axiom,
% 5.02/5.38 ! [M7: set_nat,I3: nat] :
% 5.02/5.38 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.02/5.38 => ( ( finite_card_nat
% 5.02/5.38 @ ( collect_nat
% 5.02/5.38 @ ^ [K3: nat] :
% 5.02/5.38 ( ( member_nat @ K3 @ M7 )
% 5.02/5.38 & ( ord_less_nat @ K3 @ ( suc @ I3 ) ) ) ) )
% 5.02/5.38 != zero_zero_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_less
% 5.02/5.38 thf(fact_9720_card__less__Suc,axiom,
% 5.02/5.38 ! [M7: set_nat,I3: nat] :
% 5.02/5.38 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.02/5.38 => ( ( suc
% 5.02/5.38 @ ( finite_card_nat
% 5.02/5.38 @ ( collect_nat
% 5.02/5.38 @ ^ [K3: nat] :
% 5.02/5.38 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.02/5.38 & ( ord_less_nat @ K3 @ I3 ) ) ) ) )
% 5.02/5.38 = ( finite_card_nat
% 5.02/5.38 @ ( collect_nat
% 5.02/5.38 @ ^ [K3: nat] :
% 5.02/5.38 ( ( member_nat @ K3 @ M7 )
% 5.02/5.38 & ( ord_less_nat @ K3 @ ( suc @ I3 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_less_Suc
% 5.02/5.38 thf(fact_9721_card__less__Suc2,axiom,
% 5.02/5.38 ! [M7: set_nat,I3: nat] :
% 5.02/5.38 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.02/5.38 => ( ( finite_card_nat
% 5.02/5.38 @ ( collect_nat
% 5.02/5.38 @ ^ [K3: nat] :
% 5.02/5.38 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.02/5.38 & ( ord_less_nat @ K3 @ I3 ) ) ) )
% 5.02/5.38 = ( finite_card_nat
% 5.02/5.38 @ ( collect_nat
% 5.02/5.38 @ ^ [K3: nat] :
% 5.02/5.38 ( ( member_nat @ K3 @ M7 )
% 5.02/5.38 & ( ord_less_nat @ K3 @ ( suc @ I3 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_less_Suc2
% 5.02/5.38 thf(fact_9722_card__atLeastZeroLessThan__int,axiom,
% 5.02/5.38 ! [U: int] :
% 5.02/5.38 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.02/5.38 = ( nat2 @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_atLeastZeroLessThan_int
% 5.02/5.38 thf(fact_9723_subset__card__intvl__is__intvl,axiom,
% 5.02/5.38 ! [A3: set_nat,K: nat] :
% 5.02/5.38 ( ( ord_less_eq_set_nat @ A3 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A3 ) ) ) )
% 5.02/5.38 => ( A3
% 5.02/5.38 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A3 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % subset_card_intvl_is_intvl
% 5.02/5.38 thf(fact_9724_subset__eq__atLeast0__lessThan__card,axiom,
% 5.02/5.38 ! [N4: set_nat,N2: nat] :
% 5.02/5.38 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.02/5.38 => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % subset_eq_atLeast0_lessThan_card
% 5.02/5.38 thf(fact_9725_card__sum__le__nat__sum,axiom,
% 5.02/5.38 ! [S3: set_nat] :
% 5.02/5.38 ( ord_less_eq_nat
% 5.02/5.38 @ ( groups3542108847815614940at_nat
% 5.02/5.38 @ ^ [X: nat] : X
% 5.02/5.38 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 5.02/5.38 @ ( groups3542108847815614940at_nat
% 5.02/5.38 @ ^ [X: nat] : X
% 5.02/5.38 @ S3 ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_sum_le_nat_sum
% 5.02/5.38 thf(fact_9726_card__nth__roots,axiom,
% 5.02/5.38 ! [C: complex,N2: nat] :
% 5.02/5.38 ( ( C != zero_zero_complex )
% 5.02/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( finite_card_complex
% 5.02/5.38 @ ( collect_complex
% 5.02/5.38 @ ^ [Z6: complex] :
% 5.02/5.38 ( ( power_power_complex @ Z6 @ N2 )
% 5.02/5.38 = C ) ) )
% 5.02/5.38 = N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_nth_roots
% 5.02/5.38 thf(fact_9727_card__roots__unity__eq,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( finite_card_complex
% 5.02/5.38 @ ( collect_complex
% 5.02/5.38 @ ^ [Z6: complex] :
% 5.02/5.38 ( ( power_power_complex @ Z6 @ N2 )
% 5.02/5.38 = one_one_complex ) ) )
% 5.02/5.38 = N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_roots_unity_eq
% 5.02/5.38 thf(fact_9728_divmod__integer__code,axiom,
% 5.02/5.38 ( code_divmod_integer
% 5.02/5.38 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.02/5.38 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.02/5.38 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.02/5.38 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.02/5.38 @ ( produc6916734918728496179nteger
% 5.02/5.38 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S4 ) ) )
% 5.02/5.38 @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 5.02/5.38 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.02/5.38 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.02/5.38 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.02/5.38 @ ( produc6916734918728496179nteger
% 5.02/5.38 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S4 ) ) )
% 5.02/5.38 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % divmod_integer_code
% 5.02/5.38 thf(fact_9729_bezw__0,axiom,
% 5.02/5.38 ! [X2: nat] :
% 5.02/5.38 ( ( bezw @ X2 @ zero_zero_nat )
% 5.02/5.38 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezw_0
% 5.02/5.38 thf(fact_9730_nat_Odisc__eq__case_I1_J,axiom,
% 5.02/5.38 ! [Nat: nat] :
% 5.02/5.38 ( ( Nat = zero_zero_nat )
% 5.02/5.38 = ( case_nat_o @ $true
% 5.02/5.38 @ ^ [Uu3: nat] : $false
% 5.02/5.38 @ Nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat.disc_eq_case(1)
% 5.02/5.38 thf(fact_9731_nat_Odisc__eq__case_I2_J,axiom,
% 5.02/5.38 ! [Nat: nat] :
% 5.02/5.38 ( ( Nat != zero_zero_nat )
% 5.02/5.38 = ( case_nat_o @ $false
% 5.02/5.38 @ ^ [Uu3: nat] : $true
% 5.02/5.38 @ Nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat.disc_eq_case(2)
% 5.02/5.38 thf(fact_9732_less__eq__nat_Osimps_I2_J,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.02/5.38 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_eq_nat.simps(2)
% 5.02/5.38 thf(fact_9733_max__Suc1,axiom,
% 5.02/5.38 ! [N2: nat,M: nat] :
% 5.02/5.38 ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 5.02/5.38 = ( case_nat_nat @ ( suc @ N2 )
% 5.02/5.38 @ ^ [M4: nat] : ( suc @ ( ord_max_nat @ N2 @ M4 ) )
% 5.02/5.38 @ M ) ) ).
% 5.02/5.38
% 5.02/5.38 % max_Suc1
% 5.02/5.38 thf(fact_9734_max__Suc2,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 5.02/5.38 = ( case_nat_nat @ ( suc @ N2 )
% 5.02/5.38 @ ^ [M4: nat] : ( suc @ ( ord_max_nat @ M4 @ N2 ) )
% 5.02/5.38 @ M ) ) ).
% 5.02/5.38
% 5.02/5.38 % max_Suc2
% 5.02/5.38 thf(fact_9735_diff__Suc,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.02/5.38 = ( case_nat_nat @ zero_zero_nat
% 5.02/5.38 @ ^ [K3: nat] : K3
% 5.02/5.38 @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % diff_Suc
% 5.02/5.38 thf(fact_9736_binomial__def,axiom,
% 5.02/5.38 ( binomial
% 5.02/5.38 = ( ^ [N3: nat,K3: nat] :
% 5.02/5.38 ( finite_card_set_nat
% 5.02/5.38 @ ( collect_set_nat
% 5.02/5.38 @ ^ [K7: set_nat] :
% 5.02/5.38 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N3 ) ) )
% 5.02/5.38 & ( ( finite_card_nat @ K7 )
% 5.02/5.38 = K3 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % binomial_def
% 5.02/5.38 thf(fact_9737_prod__decode__aux_Osimps,axiom,
% 5.02/5.38 ( nat_prod_decode_aux
% 5.02/5.38 = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % prod_decode_aux.simps
% 5.02/5.38 thf(fact_9738_pred__def,axiom,
% 5.02/5.38 ( pred
% 5.02/5.38 = ( case_nat_nat @ zero_zero_nat
% 5.02/5.38 @ ^ [X24: nat] : X24 ) ) ).
% 5.02/5.38
% 5.02/5.38 % pred_def
% 5.02/5.38 thf(fact_9739_prod__decode__aux_Oelims,axiom,
% 5.02/5.38 ! [X2: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.02/5.38 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % prod_decode_aux.elims
% 5.02/5.38 thf(fact_9740_Suc__0__div__numeral,axiom,
% 5.02/5.38 ! [K: num] :
% 5.02/5.38 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.02/5.38 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Suc_0_div_numeral
% 5.02/5.38 thf(fact_9741_drop__bit__numeral__minus__bit1,axiom,
% 5.02/5.38 ! [L: num,K: num] :
% 5.02/5.38 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.02/5.38 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_numeral_minus_bit1
% 5.02/5.38 thf(fact_9742_Suc__0__mod__numeral,axiom,
% 5.02/5.38 ! [K: num] :
% 5.02/5.38 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.02/5.38 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Suc_0_mod_numeral
% 5.02/5.38 thf(fact_9743_drop__bit__nonnegative__int__iff,axiom,
% 5.02/5.38 ! [N2: nat,K: int] :
% 5.02/5.38 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) )
% 5.02/5.38 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_nonnegative_int_iff
% 5.02/5.38 thf(fact_9744_drop__bit__negative__int__iff,axiom,
% 5.02/5.38 ! [N2: nat,K: int] :
% 5.02/5.38 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 5.02/5.38 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_negative_int_iff
% 5.02/5.38 thf(fact_9745_drop__bit__minus__one,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.02/5.38 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_minus_one
% 5.02/5.38 thf(fact_9746_fst__divmod__nat,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 5.02/5.38 = ( divide_divide_nat @ M @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % fst_divmod_nat
% 5.02/5.38 thf(fact_9747_snd__divmod__nat,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 5.02/5.38 = ( modulo_modulo_nat @ M @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % snd_divmod_nat
% 5.02/5.38 thf(fact_9748_drop__bit__Suc__minus__bit0,axiom,
% 5.02/5.38 ! [N2: nat,K: num] :
% 5.02/5.38 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.02/5.38 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_Suc_minus_bit0
% 5.02/5.38 thf(fact_9749_drop__bit__numeral__minus__bit0,axiom,
% 5.02/5.38 ! [L: num,K: num] :
% 5.02/5.38 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.02/5.38 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_numeral_minus_bit0
% 5.02/5.38 thf(fact_9750_drop__bit__Suc__minus__bit1,axiom,
% 5.02/5.38 ! [N2: nat,K: num] :
% 5.02/5.38 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.02/5.38 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_Suc_minus_bit1
% 5.02/5.38 thf(fact_9751_drop__bit__push__bit__int,axiom,
% 5.02/5.38 ! [M: nat,N2: nat,K: int] :
% 5.02/5.38 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.02/5.38 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N2 @ M ) @ K ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_push_bit_int
% 5.02/5.38 thf(fact_9752_drop__bit__int__def,axiom,
% 5.02/5.38 ( bit_se8568078237143864401it_int
% 5.02/5.38 = ( ^ [N3: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_int_def
% 5.02/5.38 thf(fact_9753_drop__bit__of__Suc__0,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.02/5.38 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_of_Suc_0
% 5.02/5.38 thf(fact_9754_drop__bit__nat__eq,axiom,
% 5.02/5.38 ! [N2: nat,K: int] :
% 5.02/5.38 ( ( bit_se8570568707652914677it_nat @ N2 @ ( nat2 @ K ) )
% 5.02/5.38 = ( nat2 @ ( bit_se8568078237143864401it_int @ N2 @ K ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_nat_eq
% 5.02/5.38 thf(fact_9755_quotient__of__denom__pos_H,axiom,
% 5.02/5.38 ! [R2: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % quotient_of_denom_pos'
% 5.02/5.38 thf(fact_9756_bezw__non__0,axiom,
% 5.02/5.38 ! [Y: nat,X2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.02/5.38 => ( ( bezw @ X2 @ Y )
% 5.02/5.38 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Y ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezw_non_0
% 5.02/5.38 thf(fact_9757_bezw_Oelims,axiom,
% 5.02/5.38 ! [X2: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.02/5.38 ( ( ( bezw @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.02/5.38 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezw.elims
% 5.02/5.38 thf(fact_9758_bezw_Osimps,axiom,
% 5.02/5.38 ( bezw
% 5.02/5.38 = ( ^ [X: 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 @ X @ Y6 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X @ Y6 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y6 @ ( modulo_modulo_nat @ X @ Y6 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y6 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezw.simps
% 5.02/5.38 thf(fact_9759_drop__bit__nat__def,axiom,
% 5.02/5.38 ( bit_se8570568707652914677it_nat
% 5.02/5.38 = ( ^ [N3: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % drop_bit_nat_def
% 5.02/5.38 thf(fact_9760_rat__sgn__code,axiom,
% 5.02/5.38 ! [P2: rat] :
% 5.02/5.38 ( ( quotient_of @ ( sgn_sgn_rat @ P2 ) )
% 5.02/5.38 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P2 ) ) ) @ one_one_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % rat_sgn_code
% 5.02/5.38 thf(fact_9761_minus__one__mod__numeral,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % minus_one_mod_numeral
% 5.02/5.38 thf(fact_9762_one__mod__minus__numeral,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % one_mod_minus_numeral
% 5.02/5.38 thf(fact_9763_minus__numeral__mod__numeral,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % minus_numeral_mod_numeral
% 5.02/5.38 thf(fact_9764_numeral__mod__minus__numeral,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % numeral_mod_minus_numeral
% 5.02/5.38 thf(fact_9765_Divides_Oadjust__mod__def,axiom,
% 5.02/5.38 ( adjust_mod
% 5.02/5.38 = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Divides.adjust_mod_def
% 5.02/5.38 thf(fact_9766_bezw_Opelims,axiom,
% 5.02/5.38 ! [X2: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.02/5.38 ( ( ( bezw @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.02/5.38 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.02/5.38 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X2 @ Xa2 ) ) ) ) ) ) ) )
% 5.02/5.38 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezw.pelims
% 5.02/5.38 thf(fact_9767_normalize__def,axiom,
% 5.02/5.38 ( normalize
% 5.02/5.38 = ( ^ [P6: product_prod_int_int] :
% 5.02/5.38 ( 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 ) ) ) )
% 5.02/5.38 @ ( if_Pro3027730157355071871nt_int
% 5.02/5.38 @ ( ( product_snd_int_int @ P6 )
% 5.02/5.38 = zero_zero_int )
% 5.02/5.38 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.02/5.38 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % normalize_def
% 5.02/5.38 thf(fact_9768_gcd__1__int,axiom,
% 5.02/5.38 ! [M: int] :
% 5.02/5.38 ( ( gcd_gcd_int @ M @ one_one_int )
% 5.02/5.38 = one_one_int ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_1_int
% 5.02/5.38 thf(fact_9769_gcd__pos__int,axiom,
% 5.02/5.38 ! [M: int,N2: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N2 ) )
% 5.02/5.38 = ( ( M != zero_zero_int )
% 5.02/5.38 | ( N2 != zero_zero_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_pos_int
% 5.02/5.38 thf(fact_9770_gcd__neg__numeral__2__int,axiom,
% 5.02/5.38 ! [X2: int,N2: num] :
% 5.02/5.38 ( ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( gcd_gcd_int @ X2 @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_neg_numeral_2_int
% 5.02/5.38 thf(fact_9771_gcd__neg__numeral__1__int,axiom,
% 5.02/5.38 ! [N2: num,X2: int] :
% 5.02/5.38 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ X2 )
% 5.02/5.38 = ( gcd_gcd_int @ ( numeral_numeral_int @ N2 ) @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_neg_numeral_1_int
% 5.02/5.38 thf(fact_9772_gcd__0__int,axiom,
% 5.02/5.38 ! [X2: int] :
% 5.02/5.38 ( ( gcd_gcd_int @ X2 @ zero_zero_int )
% 5.02/5.38 = ( abs_abs_int @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_0_int
% 5.02/5.38 thf(fact_9773_gcd__0__left__int,axiom,
% 5.02/5.38 ! [X2: int] :
% 5.02/5.38 ( ( gcd_gcd_int @ zero_zero_int @ X2 )
% 5.02/5.38 = ( abs_abs_int @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_0_left_int
% 5.02/5.38 thf(fact_9774_gcd__ge__0__int,axiom,
% 5.02/5.38 ! [X2: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X2 @ Y ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_ge_0_int
% 5.02/5.38 thf(fact_9775_bezout__int,axiom,
% 5.02/5.38 ! [X2: int,Y: int] :
% 5.02/5.38 ? [U3: int,V2: int] :
% 5.02/5.38 ( ( plus_plus_int @ ( times_times_int @ U3 @ X2 ) @ ( times_times_int @ V2 @ Y ) )
% 5.02/5.38 = ( gcd_gcd_int @ X2 @ Y ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezout_int
% 5.02/5.38 thf(fact_9776_gcd__mult__distrib__int,axiom,
% 5.02/5.38 ! [K: int,M: int,N2: int] :
% 5.02/5.38 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N2 ) )
% 5.02/5.38 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_mult_distrib_int
% 5.02/5.38 thf(fact_9777_gcd__le2__int,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_le2_int
% 5.02/5.38 thf(fact_9778_gcd__le1__int,axiom,
% 5.02/5.38 ! [A: int,B: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ A )
% 5.02/5.38 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_le1_int
% 5.02/5.38 thf(fact_9779_gcd__cases__int,axiom,
% 5.02/5.38 ! [X2: int,Y: int,P: int > $o] :
% 5.02/5.38 ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.38 => ( P @ ( gcd_gcd_int @ X2 @ Y ) ) ) )
% 5.02/5.38 => ( ( ( ord_less_eq_int @ zero_zero_int @ X2 )
% 5.02/5.38 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.02/5.38 => ( P @ ( gcd_gcd_int @ X2 @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.02/5.38 => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.02/5.38 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.02/5.38 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ Y ) ) ) )
% 5.02/5.38 => ( ( ( ord_less_eq_int @ X2 @ zero_zero_int )
% 5.02/5.38 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.02/5.38 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X2 ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.02/5.38 => ( P @ ( gcd_gcd_int @ X2 @ Y ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_cases_int
% 5.02/5.38 thf(fact_9780_gcd__unique__int,axiom,
% 5.02/5.38 ! [D: int,A: int,B: int] :
% 5.02/5.38 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.02/5.38 & ( dvd_dvd_int @ D @ A )
% 5.02/5.38 & ( dvd_dvd_int @ D @ B )
% 5.02/5.38 & ! [E3: int] :
% 5.02/5.38 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.02/5.38 & ( dvd_dvd_int @ E3 @ B ) )
% 5.02/5.38 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.02/5.38 = ( D
% 5.02/5.38 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_unique_int
% 5.02/5.38 thf(fact_9781_gcd__non__0__int,axiom,
% 5.02/5.38 ! [Y: int,X2: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ Y )
% 5.02/5.38 => ( ( gcd_gcd_int @ X2 @ Y )
% 5.02/5.38 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X2 @ Y ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_non_0_int
% 5.02/5.38 thf(fact_9782_gcd__code__int,axiom,
% 5.02/5.38 ( gcd_gcd_int
% 5.02/5.38 = ( ^ [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 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_code_int
% 5.02/5.38 thf(fact_9783_nat__descend__induct,axiom,
% 5.02/5.38 ! [N2: nat,P: nat > $o,M: nat] :
% 5.02/5.38 ( ! [K2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ N2 @ K2 )
% 5.02/5.38 => ( P @ K2 ) )
% 5.02/5.38 => ( ! [K2: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.02/5.38 => ( ! [I: nat] :
% 5.02/5.38 ( ( ord_less_nat @ K2 @ I )
% 5.02/5.38 => ( P @ I ) )
% 5.02/5.38 => ( P @ K2 ) ) )
% 5.02/5.38 => ( P @ M ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat_descend_induct
% 5.02/5.38 thf(fact_9784_prod__decode__aux_Opelims,axiom,
% 5.02/5.38 ! [X2: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.02/5.38 ( ( ( nat_prod_decode_aux @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.02/5.38 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X2 @ Xa2 ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_nat @ Xa2 @ X2 )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( nat_prod_decode_aux @ ( suc @ X2 ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X2 ) ) ) ) ) )
% 5.02/5.38 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % prod_decode_aux.pelims
% 5.02/5.38 thf(fact_9785_finite__enumerate,axiom,
% 5.02/5.38 ! [S3: set_nat] :
% 5.02/5.38 ( ( finite_finite_nat @ S3 )
% 5.02/5.38 => ? [R3: nat > nat] :
% 5.02/5.38 ( ( strict1292158309912662752at_nat @ R3 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S3 ) ) )
% 5.02/5.38 & ! [N8: nat] :
% 5.02/5.38 ( ( ord_less_nat @ N8 @ ( finite_card_nat @ S3 ) )
% 5.02/5.38 => ( member_nat @ ( R3 @ N8 ) @ S3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % finite_enumerate
% 5.02/5.38 thf(fact_9786_gcd__0__left__nat,axiom,
% 5.02/5.38 ! [X2: nat] :
% 5.02/5.38 ( ( gcd_gcd_nat @ zero_zero_nat @ X2 )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_0_left_nat
% 5.02/5.38 thf(fact_9787_gcd__0__nat,axiom,
% 5.02/5.38 ! [X2: nat] :
% 5.02/5.38 ( ( gcd_gcd_nat @ X2 @ zero_zero_nat )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_0_nat
% 5.02/5.38 thf(fact_9788_gcd__nat_Oright__neutral,axiom,
% 5.02/5.38 ! [A: nat] :
% 5.02/5.38 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 5.02/5.38 = A ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_nat.right_neutral
% 5.02/5.38 thf(fact_9789_gcd__nat_Oneutr__eq__iff,axiom,
% 5.02/5.38 ! [A: nat,B: nat] :
% 5.02/5.38 ( ( zero_zero_nat
% 5.02/5.38 = ( gcd_gcd_nat @ A @ B ) )
% 5.02/5.38 = ( ( A = zero_zero_nat )
% 5.02/5.38 & ( B = zero_zero_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_nat.neutr_eq_iff
% 5.02/5.38 thf(fact_9790_gcd__nat_Oleft__neutral,axiom,
% 5.02/5.38 ! [A: nat] :
% 5.02/5.38 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 5.02/5.38 = A ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_nat.left_neutral
% 5.02/5.38 thf(fact_9791_gcd__nat_Oeq__neutr__iff,axiom,
% 5.02/5.38 ! [A: nat,B: nat] :
% 5.02/5.38 ( ( ( gcd_gcd_nat @ A @ B )
% 5.02/5.38 = zero_zero_nat )
% 5.02/5.38 = ( ( A = zero_zero_nat )
% 5.02/5.38 & ( B = zero_zero_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_nat.eq_neutr_iff
% 5.02/5.38 thf(fact_9792_gcd__1__nat,axiom,
% 5.02/5.38 ! [M: nat] :
% 5.02/5.38 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.02/5.38 = one_one_nat ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_1_nat
% 5.02/5.38 thf(fact_9793_gcd__Suc__0,axiom,
% 5.02/5.38 ! [M: nat] :
% 5.02/5.38 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.02/5.38 = ( suc @ zero_zero_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_Suc_0
% 5.02/5.38 thf(fact_9794_gcd__pos__nat,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N2 ) )
% 5.02/5.38 = ( ( M != zero_zero_nat )
% 5.02/5.38 | ( N2 != zero_zero_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_pos_nat
% 5.02/5.38 thf(fact_9795_gcd__mult__distrib__nat,axiom,
% 5.02/5.38 ! [K: nat,M: nat,N2: nat] :
% 5.02/5.38 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N2 ) )
% 5.02/5.38 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_mult_distrib_nat
% 5.02/5.38 thf(fact_9796_gcd__le2__nat,axiom,
% 5.02/5.38 ! [B: nat,A: nat] :
% 5.02/5.38 ( ( B != zero_zero_nat )
% 5.02/5.38 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_le2_nat
% 5.02/5.38 thf(fact_9797_gcd__le1__nat,axiom,
% 5.02/5.38 ! [A: nat,B: nat] :
% 5.02/5.38 ( ( A != zero_zero_nat )
% 5.02/5.38 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_le1_nat
% 5.02/5.38 thf(fact_9798_gcd__diff1__nat,axiom,
% 5.02/5.38 ! [N2: nat,M: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ N2 @ M )
% 5.02/5.38 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 )
% 5.02/5.38 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_diff1_nat
% 5.02/5.38 thf(fact_9799_gcd__diff2__nat,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.38 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N2 @ M ) @ N2 )
% 5.02/5.38 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_diff2_nat
% 5.02/5.38 thf(fact_9800_gcd__nat_Oelims,axiom,
% 5.02/5.38 ! [X2: nat,Xa2: nat,Y: nat] :
% 5.02/5.38 ( ( ( gcd_gcd_nat @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.38 => ( Y = X2 ) )
% 5.02/5.38 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_nat.elims
% 5.02/5.38 thf(fact_9801_gcd__nat_Osimps,axiom,
% 5.02/5.38 ( gcd_gcd_nat
% 5.02/5.38 = ( ^ [X: nat,Y6: nat] : ( if_nat @ ( Y6 = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y6 @ ( modulo_modulo_nat @ X @ Y6 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_nat.simps
% 5.02/5.38 thf(fact_9802_gcd__non__0__nat,axiom,
% 5.02/5.38 ! [Y: nat,X2: nat] :
% 5.02/5.38 ( ( Y != zero_zero_nat )
% 5.02/5.38 => ( ( gcd_gcd_nat @ X2 @ Y )
% 5.02/5.38 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X2 @ Y ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_non_0_nat
% 5.02/5.38 thf(fact_9803_bezout__nat,axiom,
% 5.02/5.38 ! [A: nat,B: nat] :
% 5.02/5.38 ( ( A != zero_zero_nat )
% 5.02/5.38 => ? [X5: nat,Y3: nat] :
% 5.02/5.38 ( ( times_times_nat @ A @ X5 )
% 5.02/5.38 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezout_nat
% 5.02/5.38 thf(fact_9804_bezout__gcd__nat_H,axiom,
% 5.02/5.38 ! [B: nat,A: nat] :
% 5.02/5.38 ? [X5: nat,Y3: nat] :
% 5.02/5.38 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X5 ) )
% 5.02/5.38 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.02/5.38 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.02/5.38 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X5 ) )
% 5.02/5.38 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.02/5.38 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezout_gcd_nat'
% 5.02/5.38 thf(fact_9805_bezw__aux,axiom,
% 5.02/5.38 ! [X2: nat,Y: nat] :
% 5.02/5.38 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X2 @ Y ) )
% 5.02/5.38 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X2 @ Y ) ) @ ( semiri1314217659103216013at_int @ X2 ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X2 @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % bezw_aux
% 5.02/5.38 thf(fact_9806_gcd__nat_Opelims,axiom,
% 5.02/5.38 ! [X2: nat,Xa2: nat,Y: nat] :
% 5.02/5.38 ( ( ( gcd_gcd_nat @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) )
% 5.02/5.38 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.02/5.38 => ( Y = X2 ) )
% 5.02/5.38 & ( ( Xa2 != zero_zero_nat )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X2 @ Xa2 ) ) ) ) )
% 5.02/5.38 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X2 @ Xa2 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_nat.pelims
% 5.02/5.38 thf(fact_9807_card__greaterThanLessThan__int,axiom,
% 5.02/5.38 ! [L: int,U: int] :
% 5.02/5.38 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 5.02/5.38 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_greaterThanLessThan_int
% 5.02/5.38 thf(fact_9808_xor__minus__numerals_I1_J,axiom,
% 5.02/5.38 ! [N2: num,K: int] :
% 5.02/5.38 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ K )
% 5.02/5.38 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N2 @ one ) @ K ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_minus_numerals(1)
% 5.02/5.38 thf(fact_9809_xor__minus__numerals_I2_J,axiom,
% 5.02/5.38 ! [K: int,N2: num] :
% 5.02/5.38 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_minus_numerals(2)
% 5.02/5.38 thf(fact_9810_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.02/5.38 ! [L: int,U: int] :
% 5.02/5.38 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.02/5.38 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.02/5.38 thf(fact_9811_sub__BitM__One__eq,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 5.02/5.38 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sub_BitM_One_eq
% 5.02/5.38 thf(fact_9812_card__greaterThanLessThan,axiom,
% 5.02/5.38 ! [L: nat,U: nat] :
% 5.02/5.38 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.02/5.38 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_greaterThanLessThan
% 5.02/5.38 thf(fact_9813_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.02/5.38 ! [L: nat,U: nat] :
% 5.02/5.38 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.02/5.38 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastSucLessThan_greaterThanLessThan
% 5.02/5.38 thf(fact_9814_tanh__real__bounds,axiom,
% 5.02/5.38 ! [X2: real] : ( member_real @ ( tanh_real @ X2 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % tanh_real_bounds
% 5.02/5.38 thf(fact_9815_Suc__funpow,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( compow_nat_nat @ N2 @ suc )
% 5.02/5.38 = ( plus_plus_nat @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % Suc_funpow
% 5.02/5.38 thf(fact_9816_divmod__integer__eq__cases,axiom,
% 5.02/5.38 ( code_divmod_integer
% 5.02/5.38 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.02/5.38 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.02/5.38 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.02/5.38 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 5.02/5.38 @ ( if_Pro6119634080678213985nteger
% 5.02/5.38 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.02/5.38 = ( sgn_sgn_Code_integer @ L2 ) )
% 5.02/5.38 @ ( code_divmod_abs @ K3 @ L2 )
% 5.02/5.38 @ ( produc6916734918728496179nteger
% 5.02/5.38 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S4 ) ) )
% 5.02/5.38 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % divmod_integer_eq_cases
% 5.02/5.38 thf(fact_9817_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.02/5.38 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] : ( ord_less_eq_nat @ Y6 @ X )
% 5.02/5.38 @ ^ [X: nat,Y6: nat] : ( ord_less_nat @ Y6 @ X ) ) ).
% 5.02/5.38
% 5.02/5.38 % max_nat.semilattice_neutr_order_axioms
% 5.02/5.38 thf(fact_9818_card_Ocomp__fun__commute__on,axiom,
% 5.02/5.38 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.02/5.38 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.02/5.38
% 5.02/5.38 % card.comp_fun_commute_on
% 5.02/5.38 thf(fact_9819_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.02/5.38 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.02/5.38 @ ^ [M6: nat,N3: nat] :
% 5.02/5.38 ( ( dvd_dvd_nat @ M6 @ N3 )
% 5.02/5.38 & ( M6 != N3 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % gcd_nat.semilattice_neutr_order_axioms
% 5.02/5.38 thf(fact_9820_Sup__nat__empty,axiom,
% 5.02/5.38 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.02/5.38 = zero_zero_nat ) ).
% 5.02/5.38
% 5.02/5.38 % Sup_nat_empty
% 5.02/5.38 thf(fact_9821_Code__Target__Int_Onegative__def,axiom,
% 5.02/5.38 ( code_Target_negative
% 5.02/5.38 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % Code_Target_Int.negative_def
% 5.02/5.38 thf(fact_9822_times__int_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.02/5.38 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.02/5.38 = ( abs_Integ
% 5.02/5.38 @ ( produc27273713700761075at_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc2626176000494625587at_nat
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y6 @ U2 ) ) ) )
% 5.02/5.38 @ Xa2
% 5.02/5.38 @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % times_int.abs_eq
% 5.02/5.38 thf(fact_9823_int_Oabs__induct,axiom,
% 5.02/5.38 ! [P: int > $o,X2: int] :
% 5.02/5.38 ( ! [Y3: product_prod_nat_nat] : ( P @ ( abs_Integ @ Y3 ) )
% 5.02/5.38 => ( P @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % int.abs_induct
% 5.02/5.38 thf(fact_9824_eq__Abs__Integ,axiom,
% 5.02/5.38 ! [Z: int] :
% 5.02/5.38 ~ ! [X5: nat,Y3: nat] :
% 5.02/5.38 ( Z
% 5.02/5.38 != ( abs_Integ @ ( product_Pair_nat_nat @ X5 @ Y3 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % eq_Abs_Integ
% 5.02/5.38 thf(fact_9825_nat_Oabs__eq,axiom,
% 5.02/5.38 ! [X2: product_prod_nat_nat] :
% 5.02/5.38 ( ( nat2 @ ( abs_Integ @ X2 ) )
% 5.02/5.38 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat.abs_eq
% 5.02/5.38 thf(fact_9826_zero__int__def,axiom,
% 5.02/5.38 ( zero_zero_int
% 5.02/5.38 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % zero_int_def
% 5.02/5.38 thf(fact_9827_int__def,axiom,
% 5.02/5.38 ( semiri1314217659103216013at_int
% 5.02/5.38 = ( ^ [N3: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N3 @ zero_zero_nat ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % int_def
% 5.02/5.38 thf(fact_9828_uminus__int_Oabs__eq,axiom,
% 5.02/5.38 ! [X2: product_prod_nat_nat] :
% 5.02/5.38 ( ( uminus_uminus_int @ ( abs_Integ @ X2 ) )
% 5.02/5.38 = ( abs_Integ
% 5.02/5.38 @ ( produc2626176000494625587at_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X )
% 5.02/5.38 @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % uminus_int.abs_eq
% 5.02/5.38 thf(fact_9829_one__int__def,axiom,
% 5.02/5.38 ( one_one_int
% 5.02/5.38 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % one_int_def
% 5.02/5.38 thf(fact_9830_less__int_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.02/5.38 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.02/5.38 = ( produc8739625826339149834_nat_o
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) )
% 5.02/5.38 @ Xa2
% 5.02/5.38 @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_int.abs_eq
% 5.02/5.38 thf(fact_9831_less__eq__int_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.02/5.38 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.02/5.38 = ( produc8739625826339149834_nat_o
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) )
% 5.02/5.38 @ Xa2
% 5.02/5.38 @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_eq_int.abs_eq
% 5.02/5.38 thf(fact_9832_plus__int_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.02/5.38 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.02/5.38 = ( abs_Integ
% 5.02/5.38 @ ( produc27273713700761075at_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc2626176000494625587at_nat
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) )
% 5.02/5.38 @ Xa2
% 5.02/5.38 @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % plus_int.abs_eq
% 5.02/5.38 thf(fact_9833_minus__int_Oabs__eq,axiom,
% 5.02/5.38 ! [Xa2: product_prod_nat_nat,X2: product_prod_nat_nat] :
% 5.02/5.38 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X2 ) )
% 5.02/5.38 = ( abs_Integ
% 5.02/5.38 @ ( produc27273713700761075at_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc2626176000494625587at_nat
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y6 @ U2 ) ) )
% 5.02/5.38 @ Xa2
% 5.02/5.38 @ X2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % minus_int.abs_eq
% 5.02/5.38 thf(fact_9834_Gcd__remove0__nat,axiom,
% 5.02/5.38 ! [M7: set_nat] :
% 5.02/5.38 ( ( finite_finite_nat @ M7 )
% 5.02/5.38 => ( ( gcd_Gcd_nat @ M7 )
% 5.02/5.38 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M7 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Gcd_remove0_nat
% 5.02/5.38 thf(fact_9835_Gcd__nat__eq__one,axiom,
% 5.02/5.38 ! [N4: set_nat] :
% 5.02/5.38 ( ( member_nat @ one_one_nat @ N4 )
% 5.02/5.38 => ( ( gcd_Gcd_nat @ N4 )
% 5.02/5.38 = one_one_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % Gcd_nat_eq_one
% 5.02/5.38 thf(fact_9836_less__eq__int_Orep__eq,axiom,
% 5.02/5.38 ( ord_less_eq_int
% 5.02/5.38 = ( ^ [X: int,Xa4: int] :
% 5.02/5.38 ( produc8739625826339149834_nat_o
% 5.02/5.38 @ ^ [Y6: nat,Z6: nat] :
% 5.02/5.38 ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y6 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 5.02/5.38 @ ( rep_Integ @ X )
% 5.02/5.38 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_eq_int.rep_eq
% 5.02/5.38 thf(fact_9837_less__int_Orep__eq,axiom,
% 5.02/5.38 ( ord_less_int
% 5.02/5.38 = ( ^ [X: int,Xa4: int] :
% 5.02/5.38 ( produc8739625826339149834_nat_o
% 5.02/5.38 @ ^ [Y6: nat,Z6: nat] :
% 5.02/5.38 ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y6 @ V4 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 5.02/5.38 @ ( rep_Integ @ X )
% 5.02/5.38 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_int.rep_eq
% 5.02/5.38 thf(fact_9838_Gcd__int__greater__eq__0,axiom,
% 5.02/5.38 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.02/5.38
% 5.02/5.38 % Gcd_int_greater_eq_0
% 5.02/5.38 thf(fact_9839_nat_Orep__eq,axiom,
% 5.02/5.38 ( nat2
% 5.02/5.38 = ( ^ [X: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat.rep_eq
% 5.02/5.38 thf(fact_9840_prod__encode__def,axiom,
% 5.02/5.38 ( nat_prod_encode
% 5.02/5.38 = ( produc6842872674320459806at_nat
% 5.02/5.38 @ ^ [M6: nat,N3: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N3 ) ) @ M6 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % prod_encode_def
% 5.02/5.38 thf(fact_9841_uminus__int__def,axiom,
% 5.02/5.38 ( uminus_uminus_int
% 5.02/5.38 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.02/5.38 @ ( produc2626176000494625587at_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] : ( product_Pair_nat_nat @ Y6 @ X ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % uminus_int_def
% 5.02/5.38 thf(fact_9842_le__prod__encode__2,axiom,
% 5.02/5.38 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % le_prod_encode_2
% 5.02/5.38 thf(fact_9843_le__prod__encode__1,axiom,
% 5.02/5.38 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % le_prod_encode_1
% 5.02/5.38 thf(fact_9844_prod__encode__prod__decode__aux,axiom,
% 5.02/5.38 ! [K: nat,M: nat] :
% 5.02/5.38 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.02/5.38 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.02/5.38
% 5.02/5.38 % prod_encode_prod_decode_aux
% 5.02/5.38 thf(fact_9845_times__int__def,axiom,
% 5.02/5.38 ( times_times_int
% 5.02/5.38 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.02/5.38 @ ( produc27273713700761075at_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc2626176000494625587at_nat
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y6 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y6 @ U2 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % times_int_def
% 5.02/5.38 thf(fact_9846_minus__int__def,axiom,
% 5.02/5.38 ( minus_minus_int
% 5.02/5.38 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.02/5.38 @ ( produc27273713700761075at_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc2626176000494625587at_nat
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y6 @ U2 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % minus_int_def
% 5.02/5.38 thf(fact_9847_plus__int__def,axiom,
% 5.02/5.38 ( plus_plus_int
% 5.02/5.38 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.02/5.38 @ ( produc27273713700761075at_nat
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc2626176000494625587at_nat
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y6 @ V4 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % plus_int_def
% 5.02/5.38 thf(fact_9848_num__of__nat_Osimps_I2_J,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.02/5.38 = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.02/5.38 = one ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % num_of_nat.simps(2)
% 5.02/5.38 thf(fact_9849_num__of__nat__numeral__eq,axiom,
% 5.02/5.38 ! [Q2: num] :
% 5.02/5.38 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.02/5.38 = Q2 ) ).
% 5.02/5.38
% 5.02/5.38 % num_of_nat_numeral_eq
% 5.02/5.38 thf(fact_9850_num__of__nat_Osimps_I1_J,axiom,
% 5.02/5.38 ( ( num_of_nat @ zero_zero_nat )
% 5.02/5.38 = one ) ).
% 5.02/5.38
% 5.02/5.38 % num_of_nat.simps(1)
% 5.02/5.38 thf(fact_9851_numeral__num__of__nat,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 5.02/5.38 = N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % numeral_num_of_nat
% 5.02/5.38 thf(fact_9852_num__of__nat__One,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 5.02/5.38 => ( ( num_of_nat @ N2 )
% 5.02/5.38 = one ) ) ).
% 5.02/5.38
% 5.02/5.38 % num_of_nat_One
% 5.02/5.38 thf(fact_9853_num__of__nat__double,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 5.02/5.38 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % num_of_nat_double
% 5.02/5.38 thf(fact_9854_num__of__nat__plus__distrib,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.02/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.02/5.38 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % num_of_nat_plus_distrib
% 5.02/5.38 thf(fact_9855_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.02/5.38 ! [N2: nat,J: nat,I3: nat] :
% 5.02/5.38 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I3 ) ) )
% 5.02/5.38 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I3 @ J ) ) @ N2 )
% 5.02/5.38 = ( suc @ ( plus_plus_nat @ I3 @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nth_sorted_list_of_set_greaterThanLessThan
% 5.02/5.38 thf(fact_9856_pow_Osimps_I3_J,axiom,
% 5.02/5.38 ! [X2: num,Y: num] :
% 5.02/5.38 ( ( pow @ X2 @ ( bit1 @ Y ) )
% 5.02/5.38 = ( times_times_num @ ( sqr @ ( pow @ X2 @ Y ) ) @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % pow.simps(3)
% 5.02/5.38 thf(fact_9857_sqr_Osimps_I1_J,axiom,
% 5.02/5.38 ( ( sqr @ one )
% 5.02/5.38 = one ) ).
% 5.02/5.38
% 5.02/5.38 % sqr.simps(1)
% 5.02/5.38 thf(fact_9858_sqr_Osimps_I2_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( sqr @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sqr.simps(2)
% 5.02/5.38 thf(fact_9859_sqr__conv__mult,axiom,
% 5.02/5.38 ( sqr
% 5.02/5.38 = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sqr_conv_mult
% 5.02/5.38 thf(fact_9860_pow_Osimps_I2_J,axiom,
% 5.02/5.38 ! [X2: num,Y: num] :
% 5.02/5.38 ( ( pow @ X2 @ ( bit0 @ Y ) )
% 5.02/5.38 = ( sqr @ ( pow @ X2 @ Y ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % pow.simps(2)
% 5.02/5.38 thf(fact_9861_sqr_Osimps_I3_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( sqr @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sqr.simps(3)
% 5.02/5.38 thf(fact_9862_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.02/5.38 ! [N2: nat,J: nat,I3: nat] :
% 5.02/5.38 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I3 ) )
% 5.02/5.38 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I3 @ J ) ) @ N2 )
% 5.02/5.38 = ( suc @ ( plus_plus_nat @ I3 @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nth_sorted_list_of_set_greaterThanAtMost
% 5.02/5.38 thf(fact_9863_image__minus__const__atLeastLessThan__nat,axiom,
% 5.02/5.38 ! [C: nat,Y: nat,X2: nat] :
% 5.02/5.38 ( ( ( ord_less_nat @ C @ Y )
% 5.02/5.38 => ( ( image_nat_nat
% 5.02/5.38 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.02/5.38 @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 5.02/5.38 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X2 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_nat @ C @ Y )
% 5.02/5.38 => ( ( ( ord_less_nat @ X2 @ Y )
% 5.02/5.38 => ( ( image_nat_nat
% 5.02/5.38 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.02/5.38 @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 5.02/5.38 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.02/5.38 & ( ~ ( ord_less_nat @ X2 @ Y )
% 5.02/5.38 => ( ( image_nat_nat
% 5.02/5.38 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.02/5.38 @ ( set_or4665077453230672383an_nat @ X2 @ Y ) )
% 5.02/5.38 = bot_bot_set_nat ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % image_minus_const_atLeastLessThan_nat
% 5.02/5.38 thf(fact_9864_rat__floor__lemma,axiom,
% 5.02/5.38 ! [A: int,B: int] :
% 5.02/5.38 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.02/5.38 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % rat_floor_lemma
% 5.02/5.38 thf(fact_9865_bij__betw__Suc,axiom,
% 5.02/5.38 ! [M7: set_nat,N4: set_nat] :
% 5.02/5.38 ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 5.02/5.38 = ( ( image_nat_nat @ suc @ M7 )
% 5.02/5.38 = N4 ) ) ).
% 5.02/5.38
% 5.02/5.38 % bij_betw_Suc
% 5.02/5.38 thf(fact_9866_image__Suc__atLeastAtMost,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I3 @ J ) )
% 5.02/5.38 = ( set_or1269000886237332187st_nat @ ( suc @ I3 ) @ ( suc @ J ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % image_Suc_atLeastAtMost
% 5.02/5.38 thf(fact_9867_image__Suc__atLeastLessThan,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I3 @ J ) )
% 5.02/5.38 = ( set_or4665077453230672383an_nat @ ( suc @ I3 ) @ ( suc @ J ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % image_Suc_atLeastLessThan
% 5.02/5.38 thf(fact_9868_mult__rat,axiom,
% 5.02/5.38 ! [A: int,B: int,C: int,D: int] :
% 5.02/5.38 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.02/5.38 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % mult_rat
% 5.02/5.38 thf(fact_9869_divide__rat,axiom,
% 5.02/5.38 ! [A: int,B: int,C: int,D: int] :
% 5.02/5.38 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.02/5.38 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % divide_rat
% 5.02/5.38 thf(fact_9870_floor__Fract,axiom,
% 5.02/5.38 ! [A: int,B: int] :
% 5.02/5.38 ( ( archim3151403230148437115or_rat @ ( fract @ A @ B ) )
% 5.02/5.38 = ( divide_divide_int @ A @ B ) ) ).
% 5.02/5.38
% 5.02/5.38 % floor_Fract
% 5.02/5.38 thf(fact_9871_less__rat,axiom,
% 5.02/5.38 ! [B: int,D: int,A: int,C: int] :
% 5.02/5.38 ( ( B != zero_zero_int )
% 5.02/5.38 => ( ( D != zero_zero_int )
% 5.02/5.38 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.02/5.38 = ( 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 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_rat
% 5.02/5.38 thf(fact_9872_add__rat,axiom,
% 5.02/5.38 ! [B: int,D: int,A: int,C: int] :
% 5.02/5.38 ( ( B != zero_zero_int )
% 5.02/5.38 => ( ( D != zero_zero_int )
% 5.02/5.38 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.02/5.38 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % add_rat
% 5.02/5.38 thf(fact_9873_le__rat,axiom,
% 5.02/5.38 ! [B: int,D: int,A: int,C: int] :
% 5.02/5.38 ( ( B != zero_zero_int )
% 5.02/5.38 => ( ( D != zero_zero_int )
% 5.02/5.38 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.02/5.38 = ( 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 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % le_rat
% 5.02/5.38 thf(fact_9874_diff__rat,axiom,
% 5.02/5.38 ! [B: int,D: int,A: int,C: int] :
% 5.02/5.38 ( ( B != zero_zero_int )
% 5.02/5.38 => ( ( D != zero_zero_int )
% 5.02/5.38 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.02/5.38 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % diff_rat
% 5.02/5.38 thf(fact_9875_sgn__rat,axiom,
% 5.02/5.38 ! [A: int,B: int] :
% 5.02/5.38 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.02/5.38 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sgn_rat
% 5.02/5.38 thf(fact_9876_rat__number__collapse_I6_J,axiom,
% 5.02/5.38 ! [K: int] :
% 5.02/5.38 ( ( fract @ K @ zero_zero_int )
% 5.02/5.38 = zero_zero_rat ) ).
% 5.02/5.38
% 5.02/5.38 % rat_number_collapse(6)
% 5.02/5.38 thf(fact_9877_rat__number__collapse_I1_J,axiom,
% 5.02/5.38 ! [K: int] :
% 5.02/5.38 ( ( fract @ zero_zero_int @ K )
% 5.02/5.38 = zero_zero_rat ) ).
% 5.02/5.38
% 5.02/5.38 % rat_number_collapse(1)
% 5.02/5.38 thf(fact_9878_eq__rat_I1_J,axiom,
% 5.02/5.38 ! [B: int,D: int,A: int,C: int] :
% 5.02/5.38 ( ( B != zero_zero_int )
% 5.02/5.38 => ( ( D != zero_zero_int )
% 5.02/5.38 => ( ( ( fract @ A @ B )
% 5.02/5.38 = ( fract @ C @ D ) )
% 5.02/5.38 = ( ( times_times_int @ A @ D )
% 5.02/5.38 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % eq_rat(1)
% 5.02/5.38 thf(fact_9879_mult__rat__cancel,axiom,
% 5.02/5.38 ! [C: int,A: int,B: int] :
% 5.02/5.38 ( ( C != zero_zero_int )
% 5.02/5.38 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.02/5.38 = ( fract @ A @ B ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % mult_rat_cancel
% 5.02/5.38 thf(fact_9880_Fract__of__nat__eq,axiom,
% 5.02/5.38 ! [K: nat] :
% 5.02/5.38 ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 5.02/5.38 = ( semiri681578069525770553at_rat @ K ) ) ).
% 5.02/5.38
% 5.02/5.38 % Fract_of_nat_eq
% 5.02/5.38 thf(fact_9881_zero__notin__Suc__image,axiom,
% 5.02/5.38 ! [A3: set_nat] :
% 5.02/5.38 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A3 ) ) ).
% 5.02/5.38
% 5.02/5.38 % zero_notin_Suc_image
% 5.02/5.38 thf(fact_9882_eq__rat_I3_J,axiom,
% 5.02/5.38 ! [A: int,C: int] :
% 5.02/5.38 ( ( fract @ zero_zero_int @ A )
% 5.02/5.38 = ( fract @ zero_zero_int @ C ) ) ).
% 5.02/5.38
% 5.02/5.38 % eq_rat(3)
% 5.02/5.38 thf(fact_9883_Rat__induct__pos,axiom,
% 5.02/5.38 ! [P: rat > $o,Q2: rat] :
% 5.02/5.38 ( ! [A4: int,B3: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B3 )
% 5.02/5.38 => ( P @ ( fract @ A4 @ B3 ) ) )
% 5.02/5.38 => ( P @ Q2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % Rat_induct_pos
% 5.02/5.38 thf(fact_9884_eq__rat_I2_J,axiom,
% 5.02/5.38 ! [A: int] :
% 5.02/5.38 ( ( fract @ A @ zero_zero_int )
% 5.02/5.38 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % eq_rat(2)
% 5.02/5.38 thf(fact_9885_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.02/5.38 ! [L: nat,U: nat] :
% 5.02/5.38 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.02/5.38 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastSucAtMost_greaterThanAtMost
% 5.02/5.38 thf(fact_9886_Fract__coprime,axiom,
% 5.02/5.38 ! [A: int,B: int] :
% 5.02/5.38 ( ( fract @ ( divide_divide_int @ A @ ( gcd_gcd_int @ A @ B ) ) @ ( divide_divide_int @ B @ ( gcd_gcd_int @ A @ B ) ) )
% 5.02/5.38 = ( fract @ A @ B ) ) ).
% 5.02/5.38
% 5.02/5.38 % Fract_coprime
% 5.02/5.38 thf(fact_9887_One__rat__def,axiom,
% 5.02/5.38 ( one_one_rat
% 5.02/5.38 = ( fract @ one_one_int @ one_one_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % One_rat_def
% 5.02/5.38 thf(fact_9888_Fract__of__int__eq,axiom,
% 5.02/5.38 ! [K: int] :
% 5.02/5.38 ( ( fract @ K @ one_one_int )
% 5.02/5.38 = ( ring_1_of_int_rat @ K ) ) ).
% 5.02/5.38
% 5.02/5.38 % Fract_of_int_eq
% 5.02/5.38 thf(fact_9889_Zero__rat__def,axiom,
% 5.02/5.38 ( zero_zero_rat
% 5.02/5.38 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % Zero_rat_def
% 5.02/5.38 thf(fact_9890_rat__number__expand_I3_J,axiom,
% 5.02/5.38 ( numeral_numeral_rat
% 5.02/5.38 = ( ^ [K3: num] : ( fract @ ( numeral_numeral_int @ K3 ) @ one_one_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % rat_number_expand(3)
% 5.02/5.38 thf(fact_9891_rat__number__collapse_I3_J,axiom,
% 5.02/5.38 ! [W: num] :
% 5.02/5.38 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.02/5.38 = ( numeral_numeral_rat @ W ) ) ).
% 5.02/5.38
% 5.02/5.38 % rat_number_collapse(3)
% 5.02/5.38 thf(fact_9892_image__Suc__lessThan,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % image_Suc_lessThan
% 5.02/5.38 thf(fact_9893_image__Suc__atMost,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 5.02/5.38 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % image_Suc_atMost
% 5.02/5.38 thf(fact_9894_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.02/5.38 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeast0_atMost_Suc_eq_insert_0
% 5.02/5.38 thf(fact_9895_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.02/5.38 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeast0_lessThan_Suc_eq_insert_0
% 5.02/5.38 thf(fact_9896_lessThan__Suc__eq__insert__0,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 5.02/5.38 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % lessThan_Suc_eq_insert_0
% 5.02/5.38 thf(fact_9897_atMost__Suc__eq__insert__0,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 5.02/5.38 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atMost_Suc_eq_insert_0
% 5.02/5.38 thf(fact_9898_zero__less__Fract__iff,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.02/5.38 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % zero_less_Fract_iff
% 5.02/5.38 thf(fact_9899_Fract__less__zero__iff,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.02/5.38 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Fract_less_zero_iff
% 5.02/5.38 thf(fact_9900_one__less__Fract__iff,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.02/5.38 = ( ord_less_int @ B @ A ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % one_less_Fract_iff
% 5.02/5.38 thf(fact_9901_Fract__less__one__iff,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.02/5.38 = ( ord_less_int @ A @ B ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Fract_less_one_iff
% 5.02/5.38 thf(fact_9902_rat__number__collapse_I5_J,axiom,
% 5.02/5.38 ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.02/5.38 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.02/5.38
% 5.02/5.38 % rat_number_collapse(5)
% 5.02/5.38 thf(fact_9903_Fract__add__one,axiom,
% 5.02/5.38 ! [N2: int,M: int] :
% 5.02/5.38 ( ( N2 != zero_zero_int )
% 5.02/5.38 => ( ( fract @ ( plus_plus_int @ M @ N2 ) @ N2 )
% 5.02/5.38 = ( plus_plus_rat @ ( fract @ M @ N2 ) @ one_one_rat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Fract_add_one
% 5.02/5.38 thf(fact_9904_Fract__le__zero__iff,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.02/5.38 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Fract_le_zero_iff
% 5.02/5.38 thf(fact_9905_zero__le__Fract__iff,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.02/5.38 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % zero_le_Fract_iff
% 5.02/5.38 thf(fact_9906_Fract__le__one__iff,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.02/5.38 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Fract_le_one_iff
% 5.02/5.38 thf(fact_9907_one__le__Fract__iff,axiom,
% 5.02/5.38 ! [B: int,A: int] :
% 5.02/5.38 ( ( ord_less_int @ zero_zero_int @ B )
% 5.02/5.38 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.02/5.38 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % one_le_Fract_iff
% 5.02/5.38 thf(fact_9908_rat__number__expand_I5_J,axiom,
% 5.02/5.38 ! [K: num] :
% 5.02/5.38 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.02/5.38 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % rat_number_expand(5)
% 5.02/5.38 thf(fact_9909_rat__number__collapse_I4_J,axiom,
% 5.02/5.38 ! [W: num] :
% 5.02/5.38 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.02/5.38 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % rat_number_collapse(4)
% 5.02/5.38 thf(fact_9910_of__nat__eq__id,axiom,
% 5.02/5.38 semiri1316708129612266289at_nat = id_nat ).
% 5.02/5.38
% 5.02/5.38 % of_nat_eq_id
% 5.02/5.38 thf(fact_9911_Inf__real__def,axiom,
% 5.02/5.38 ( comple4887499456419720421f_real
% 5.02/5.38 = ( ^ [X4: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X4 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Inf_real_def
% 5.02/5.38 thf(fact_9912_less__int__def,axiom,
% 5.02/5.38 ( ord_less_int
% 5.02/5.38 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.02/5.38 @ ( produc8739625826339149834_nat_o
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_int_def
% 5.02/5.38 thf(fact_9913_less__eq__int__def,axiom,
% 5.02/5.38 ( ord_less_eq_int
% 5.02/5.38 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.02/5.38 @ ( produc8739625826339149834_nat_o
% 5.02/5.38 @ ^ [X: nat,Y6: nat] :
% 5.02/5.38 ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y6 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % less_eq_int_def
% 5.02/5.38 thf(fact_9914_nat__def,axiom,
% 5.02/5.38 ( nat2
% 5.02/5.38 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat_def
% 5.02/5.38 thf(fact_9915_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.02/5.38 ! [L: int,U: int] :
% 5.02/5.38 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.02/5.38 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.02/5.38 thf(fact_9916_image__add__int__atLeastLessThan,axiom,
% 5.02/5.38 ! [L: int,U: int] :
% 5.02/5.38 ( ( image_int_int
% 5.02/5.38 @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 5.02/5.38 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.02/5.38 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.02/5.38
% 5.02/5.38 % image_add_int_atLeastLessThan
% 5.02/5.38 thf(fact_9917_image__atLeastZeroLessThan__int,axiom,
% 5.02/5.38 ! [U: int] :
% 5.02/5.38 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.02/5.38 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.02/5.38 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % image_atLeastZeroLessThan_int
% 5.02/5.38 thf(fact_9918_range__mod,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( image_nat_nat
% 5.02/5.38 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N2 )
% 5.02/5.38 @ top_top_set_nat )
% 5.02/5.38 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % range_mod
% 5.02/5.38 thf(fact_9919_UNIV__nat__eq,axiom,
% 5.02/5.38 ( top_top_set_nat
% 5.02/5.38 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % UNIV_nat_eq
% 5.02/5.38 thf(fact_9920_card__UNIV__unit,axiom,
% 5.02/5.38 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.02/5.38 = one_one_nat ) ).
% 5.02/5.38
% 5.02/5.38 % card_UNIV_unit
% 5.02/5.38 thf(fact_9921_card__UNIV__bool,axiom,
% 5.02/5.38 ( ( finite_card_o @ top_top_set_o )
% 5.02/5.38 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_UNIV_bool
% 5.02/5.38 thf(fact_9922_range__mult,axiom,
% 5.02/5.38 ! [A: real] :
% 5.02/5.38 ( ( ( A = zero_zero_real )
% 5.02/5.38 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.02/5.38 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.02/5.38 & ( ( A != zero_zero_real )
% 5.02/5.38 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.02/5.38 = top_top_set_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % range_mult
% 5.02/5.38 thf(fact_9923_infinite__UNIV__int,axiom,
% 5.02/5.38 ~ ( finite_finite_int @ top_top_set_int ) ).
% 5.02/5.38
% 5.02/5.38 % infinite_UNIV_int
% 5.02/5.38 thf(fact_9924_int__in__range__abs,axiom,
% 5.02/5.38 ! [N2: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % int_in_range_abs
% 5.02/5.38 thf(fact_9925_root__def,axiom,
% 5.02/5.38 ( root
% 5.02/5.38 = ( ^ [N3: nat,X: real] :
% 5.02/5.38 ( if_real @ ( N3 = zero_zero_nat ) @ zero_zero_real
% 5.02/5.38 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.02/5.38 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N3 ) )
% 5.02/5.38 @ X ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % root_def
% 5.02/5.38 thf(fact_9926_card__UNIV__char,axiom,
% 5.02/5.38 ( ( finite_card_char @ top_top_set_char )
% 5.02/5.38 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_UNIV_char
% 5.02/5.38 thf(fact_9927_UNIV__char__of__nat,axiom,
% 5.02/5.38 ( top_top_set_char
% 5.02/5.38 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % UNIV_char_of_nat
% 5.02/5.38 thf(fact_9928_char_Osize_I2_J,axiom,
% 5.02/5.38 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.02/5.38 ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.02/5.38 = zero_zero_nat ) ).
% 5.02/5.38
% 5.02/5.38 % char.size(2)
% 5.02/5.38 thf(fact_9929_nat__of__char__less__256,axiom,
% 5.02/5.38 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nat_of_char_less_256
% 5.02/5.38 thf(fact_9930_range__nat__of__char,axiom,
% 5.02/5.38 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.02/5.38 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % range_nat_of_char
% 5.02/5.38 thf(fact_9931_integer__of__char__code,axiom,
% 5.02/5.38 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.02/5.38 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.02/5.38 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % integer_of_char_code
% 5.02/5.38 thf(fact_9932_char_Osize__gen,axiom,
% 5.02/5.38 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.02/5.38 ( ( size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.02/5.38 = zero_zero_nat ) ).
% 5.02/5.38
% 5.02/5.38 % char.size_gen
% 5.02/5.38 thf(fact_9933_String_Ochar__of__ascii__of,axiom,
% 5.02/5.38 ! [C: char] :
% 5.02/5.38 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.02/5.38 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % String.char_of_ascii_of
% 5.02/5.38 thf(fact_9934_sorted__list__of__set__lessThan__Suc,axiom,
% 5.02/5.38 ! [K: nat] :
% 5.02/5.38 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.02/5.38 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_list_of_set_lessThan_Suc
% 5.02/5.38 thf(fact_9935_sorted__list__of__set__atMost__Suc,axiom,
% 5.02/5.38 ! [K: nat] :
% 5.02/5.38 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.02/5.38 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_list_of_set_atMost_Suc
% 5.02/5.38 thf(fact_9936_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ ( suc @ I3 ) @ J )
% 5.02/5.38 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I3 @ J ) )
% 5.02/5.38 = ( cons_nat @ ( suc @ I3 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I3 ) @ J ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_list_of_set_greaterThanAtMost
% 5.02/5.38 thf(fact_9937_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( ord_less_nat @ ( suc @ I3 ) @ J )
% 5.02/5.38 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I3 @ J ) )
% 5.02/5.38 = ( cons_nat @ ( suc @ I3 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I3 ) @ J ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_list_of_set_greaterThanLessThan
% 5.02/5.38 thf(fact_9938_upto__aux__rec,axiom,
% 5.02/5.38 ( upto_aux
% 5.02/5.38 = ( ^ [I5: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I5 ) @ Js @ ( upto_aux @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_aux_rec
% 5.02/5.38 thf(fact_9939_list__encode_Oelims,axiom,
% 5.02/5.38 ! [X2: list_nat,Y: nat] :
% 5.02/5.38 ( ( ( nat_list_encode @ X2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ( X2 = nil_nat )
% 5.02/5.38 => ( Y != zero_zero_nat ) )
% 5.02/5.38 => ~ ! [X5: nat,Xs2: list_nat] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( cons_nat @ X5 @ Xs2 ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % list_encode.elims
% 5.02/5.38 thf(fact_9940_upto_Opsimps,axiom,
% 5.02/5.38 ! [I3: int,J: int] :
% 5.02/5.38 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J ) )
% 5.02/5.38 => ( ( ( ord_less_eq_int @ I3 @ J )
% 5.02/5.38 => ( ( upto @ I3 @ J )
% 5.02/5.38 = ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_int @ I3 @ J )
% 5.02/5.38 => ( ( upto @ I3 @ J )
% 5.02/5.38 = nil_int ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto.psimps
% 5.02/5.38 thf(fact_9941_upto__empty,axiom,
% 5.02/5.38 ! [J: int,I3: int] :
% 5.02/5.38 ( ( ord_less_int @ J @ I3 )
% 5.02/5.38 => ( ( upto @ I3 @ J )
% 5.02/5.38 = nil_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_empty
% 5.02/5.38 thf(fact_9942_upto__Nil2,axiom,
% 5.02/5.38 ! [I3: int,J: int] :
% 5.02/5.38 ( ( nil_int
% 5.02/5.38 = ( upto @ I3 @ J ) )
% 5.02/5.38 = ( ord_less_int @ J @ I3 ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_Nil2
% 5.02/5.38 thf(fact_9943_upto__Nil,axiom,
% 5.02/5.38 ! [I3: int,J: int] :
% 5.02/5.38 ( ( ( upto @ I3 @ J )
% 5.02/5.38 = nil_int )
% 5.02/5.38 = ( ord_less_int @ J @ I3 ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_Nil
% 5.02/5.38 thf(fact_9944_upto__single,axiom,
% 5.02/5.38 ! [I3: int] :
% 5.02/5.38 ( ( upto @ I3 @ I3 )
% 5.02/5.38 = ( cons_int @ I3 @ nil_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_single
% 5.02/5.38 thf(fact_9945_nth__upto,axiom,
% 5.02/5.38 ! [I3: int,K: nat,J: int] :
% 5.02/5.38 ( ( ord_less_eq_int @ ( plus_plus_int @ I3 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.02/5.38 => ( ( nth_int @ ( upto @ I3 @ J ) @ K )
% 5.02/5.38 = ( plus_plus_int @ I3 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nth_upto
% 5.02/5.38 thf(fact_9946_length__upto,axiom,
% 5.02/5.38 ! [I3: int,J: int] :
% 5.02/5.38 ( ( size_size_list_int @ ( upto @ I3 @ J ) )
% 5.02/5.38 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I3 ) @ one_one_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % length_upto
% 5.02/5.38 thf(fact_9947_upto__rec__numeral_I1_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 = nil_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_rec_numeral(1)
% 5.02/5.38 thf(fact_9948_upto__rec__numeral_I4_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = nil_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_rec_numeral(4)
% 5.02/5.38 thf(fact_9949_upto__rec__numeral_I3_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 = nil_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_rec_numeral(3)
% 5.02/5.38 thf(fact_9950_upto__rec__numeral_I2_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = nil_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_rec_numeral(2)
% 5.02/5.38 thf(fact_9951_upto__aux__def,axiom,
% 5.02/5.38 ( upto_aux
% 5.02/5.38 = ( ^ [I5: int,J3: int] : ( append_int @ ( upto @ I5 @ J3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_aux_def
% 5.02/5.38 thf(fact_9952_upto__code,axiom,
% 5.02/5.38 ( upto
% 5.02/5.38 = ( ^ [I5: int,J3: int] : ( upto_aux @ I5 @ J3 @ nil_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_code
% 5.02/5.38 thf(fact_9953_distinct__upto,axiom,
% 5.02/5.38 ! [I3: int,J: int] : ( distinct_int @ ( upto @ I3 @ J ) ) ).
% 5.02/5.38
% 5.02/5.38 % distinct_upto
% 5.02/5.38 thf(fact_9954_atLeastAtMost__upto,axiom,
% 5.02/5.38 ( set_or1266510415728281911st_int
% 5.02/5.38 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ J3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastAtMost_upto
% 5.02/5.38 thf(fact_9955_upto__split2,axiom,
% 5.02/5.38 ! [I3: int,J: int,K: int] :
% 5.02/5.38 ( ( ord_less_eq_int @ I3 @ J )
% 5.02/5.38 => ( ( ord_less_eq_int @ J @ K )
% 5.02/5.38 => ( ( upto @ I3 @ K )
% 5.02/5.38 = ( append_int @ ( upto @ I3 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_split2
% 5.02/5.38 thf(fact_9956_upto__split1,axiom,
% 5.02/5.38 ! [I3: int,J: int,K: int] :
% 5.02/5.38 ( ( ord_less_eq_int @ I3 @ J )
% 5.02/5.38 => ( ( ord_less_eq_int @ J @ K )
% 5.02/5.38 => ( ( upto @ I3 @ K )
% 5.02/5.38 = ( append_int @ ( upto @ I3 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_split1
% 5.02/5.38 thf(fact_9957_atLeastLessThan__upto,axiom,
% 5.02/5.38 ( set_or4662586982721622107an_int
% 5.02/5.38 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastLessThan_upto
% 5.02/5.38 thf(fact_9958_list__encode_Osimps_I1_J,axiom,
% 5.02/5.38 ( ( nat_list_encode @ nil_nat )
% 5.02/5.38 = zero_zero_nat ) ).
% 5.02/5.38
% 5.02/5.38 % list_encode.simps(1)
% 5.02/5.38 thf(fact_9959_greaterThanAtMost__upto,axiom,
% 5.02/5.38 ( set_or6656581121297822940st_int
% 5.02/5.38 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % greaterThanAtMost_upto
% 5.02/5.38 thf(fact_9960_upto_Oelims,axiom,
% 5.02/5.38 ! [X2: int,Xa2: int,Y: list_int] :
% 5.02/5.38 ( ( ( upto @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ( ord_less_eq_int @ X2 @ Xa2 )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa2 ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_int @ X2 @ Xa2 )
% 5.02/5.38 => ( Y = nil_int ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto.elims
% 5.02/5.38 thf(fact_9961_upto_Osimps,axiom,
% 5.02/5.38 ( upto
% 5.02/5.38 = ( ^ [I5: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I5 @ J3 ) @ ( cons_int @ I5 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto.simps
% 5.02/5.38 thf(fact_9962_upto__rec1,axiom,
% 5.02/5.38 ! [I3: int,J: int] :
% 5.02/5.38 ( ( ord_less_eq_int @ I3 @ J )
% 5.02/5.38 => ( ( upto @ I3 @ J )
% 5.02/5.38 = ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_rec1
% 5.02/5.38 thf(fact_9963_upto__rec2,axiom,
% 5.02/5.38 ! [I3: int,J: int] :
% 5.02/5.38 ( ( ord_less_eq_int @ I3 @ J )
% 5.02/5.38 => ( ( upto @ I3 @ J )
% 5.02/5.38 = ( append_int @ ( upto @ I3 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_rec2
% 5.02/5.38 thf(fact_9964_greaterThanLessThan__upto,axiom,
% 5.02/5.38 ( set_or5832277885323065728an_int
% 5.02/5.38 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % greaterThanLessThan_upto
% 5.02/5.38 thf(fact_9965_upto__split3,axiom,
% 5.02/5.38 ! [I3: int,J: int,K: int] :
% 5.02/5.38 ( ( ord_less_eq_int @ I3 @ J )
% 5.02/5.38 => ( ( ord_less_eq_int @ J @ K )
% 5.02/5.38 => ( ( upto @ I3 @ K )
% 5.02/5.38 = ( append_int @ ( upto @ I3 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto_split3
% 5.02/5.38 thf(fact_9966_list__encode_Osimps_I2_J,axiom,
% 5.02/5.38 ! [X2: nat,Xs: list_nat] :
% 5.02/5.38 ( ( nat_list_encode @ ( cons_nat @ X2 @ Xs ) )
% 5.02/5.38 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % list_encode.simps(2)
% 5.02/5.38 thf(fact_9967_upto_Opelims,axiom,
% 5.02/5.38 ! [X2: int,Xa2: int,Y: list_int] :
% 5.02/5.38 ( ( ( upto @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) )
% 5.02/5.38 => ~ ( ( ( ( ord_less_eq_int @ X2 @ Xa2 )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( cons_int @ X2 @ ( upto @ ( plus_plus_int @ X2 @ one_one_int ) @ Xa2 ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_int @ X2 @ Xa2 )
% 5.02/5.38 => ( Y = nil_int ) ) )
% 5.02/5.38 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X2 @ Xa2 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upto.pelims
% 5.02/5.38 thf(fact_9968_DERIV__even__real__root,axiom,
% 5.02/5.38 ! [N2: nat,X2: real] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X2 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_even_real_root
% 5.02/5.38 thf(fact_9969_DERIV__real__root__generic,axiom,
% 5.02/5.38 ! [N2: nat,X2: real,D4: real] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( X2 != zero_zero_real )
% 5.02/5.38 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.38 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( D4
% 5.02/5.38 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X2 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.02/5.38 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.02/5.38 => ( D4
% 5.02/5.38 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X2 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.02/5.38 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.38 => ( D4
% 5.02/5.38 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X2 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_real_root_generic
% 5.02/5.38 thf(fact_9970_has__real__derivative__pos__inc__right,axiom,
% 5.02/5.38 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.02/5.38 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.02/5.38 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.02/5.38 => ? [D3: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.02/5.38 & ! [H4: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.02/5.38 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S3 )
% 5.02/5.38 => ( ( ord_less_real @ H4 @ D3 )
% 5.02/5.38 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % has_real_derivative_pos_inc_right
% 5.02/5.38 thf(fact_9971_has__real__derivative__neg__dec__right,axiom,
% 5.02/5.38 ! [F: real > real,L: real,X2: real,S3: set_real] :
% 5.02/5.38 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ S3 ) )
% 5.02/5.38 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.02/5.38 => ? [D3: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.02/5.38 & ! [H4: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.02/5.38 => ( ( member_real @ ( plus_plus_real @ X2 @ H4 ) @ S3 )
% 5.02/5.38 => ( ( ord_less_real @ H4 @ D3 )
% 5.02/5.38 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % has_real_derivative_neg_dec_right
% 5.02/5.38 thf(fact_9972_DERIV__pos__inc__right,axiom,
% 5.02/5.38 ! [F: real > real,L: real,X2: real] :
% 5.02/5.38 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.02/5.38 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.02/5.38 => ? [D3: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.02/5.38 & ! [H4: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.02/5.38 => ( ( ord_less_real @ H4 @ D3 )
% 5.02/5.38 => ( ord_less_real @ ( F @ X2 ) @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_pos_inc_right
% 5.02/5.38 thf(fact_9973_DERIV__neg__dec__right,axiom,
% 5.02/5.38 ! [F: real > real,L: real,X2: real] :
% 5.02/5.38 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.02/5.38 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.02/5.38 => ? [D3: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.02/5.38 & ! [H4: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.02/5.38 => ( ( ord_less_real @ H4 @ D3 )
% 5.02/5.38 => ( ord_less_real @ ( F @ ( plus_plus_real @ X2 @ H4 ) ) @ ( F @ X2 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_neg_dec_right
% 5.02/5.38 thf(fact_9974_DERIV__const__ratio__const,axiom,
% 5.02/5.38 ! [A: real,B: real,F: real > real,K: real] :
% 5.02/5.38 ( ( A != B )
% 5.02/5.38 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.02/5.38 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.02/5.38 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_const_ratio_const
% 5.02/5.38 thf(fact_9975_MVT2,axiom,
% 5.02/5.38 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.02/5.38 ( ( ord_less_real @ A @ B )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ A @ X5 )
% 5.02/5.38 => ( ( ord_less_eq_real @ X5 @ B )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.02/5.38 => ? [Z3: real] :
% 5.02/5.38 ( ( ord_less_real @ A @ Z3 )
% 5.02/5.38 & ( ord_less_real @ Z3 @ B )
% 5.02/5.38 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.02/5.38 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z3 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % MVT2
% 5.02/5.38 thf(fact_9976_DERIV__const__average,axiom,
% 5.02/5.38 ! [A: real,B: real,V: real > real,K: real] :
% 5.02/5.38 ( ( A != B )
% 5.02/5.38 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.02/5.38 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.02/5.38 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_const_average
% 5.02/5.38 thf(fact_9977_DERIV__ln__divide,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X2 ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_ln_divide
% 5.02/5.38 thf(fact_9978_DERIV__pow,axiom,
% 5.02/5.38 ! [N2: nat,X2: real,S2: set_real] :
% 5.02/5.38 ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [X: real] : ( power_power_real @ X @ N2 )
% 5.02/5.38 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X2 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ X2 @ S2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_pow
% 5.02/5.38 thf(fact_9979_DERIV__fun__pow,axiom,
% 5.02/5.38 ! [G: real > real,M: real,X2: real,N2: nat] :
% 5.02/5.38 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N2 )
% 5.02/5.38 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( G @ X2 ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) @ M )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_fun_pow
% 5.02/5.38 thf(fact_9980_has__real__derivative__powr,axiom,
% 5.02/5.38 ! [Z: real,R2: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.02/5.38 => ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [Z6: real] : ( powr_real @ Z6 @ R2 )
% 5.02/5.38 @ ( times_times_real @ R2 @ ( powr_real @ Z @ ( minus_minus_real @ R2 @ one_one_real ) ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % has_real_derivative_powr
% 5.02/5.38 thf(fact_9981_DERIV__log,axiom,
% 5.02/5.38 ! [X2: real,B: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X2 ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_log
% 5.02/5.38 thf(fact_9982_DERIV__fun__powr,axiom,
% 5.02/5.38 ! [G: real > real,M: real,X2: real,R2: real] :
% 5.02/5.38 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.02/5.38 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R2 )
% 5.02/5.38 @ ( times_times_real @ ( times_times_real @ R2 @ ( powr_real @ ( G @ X2 ) @ ( minus_minus_real @ R2 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_fun_powr
% 5.02/5.38 thf(fact_9983_DERIV__powr,axiom,
% 5.02/5.38 ! [G: real > real,M: real,X2: real,F: real > real,R2: real] :
% 5.02/5.38 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.02/5.38 => ( ( ord_less_real @ zero_zero_real @ ( G @ X2 ) )
% 5.02/5.38 => ( ( has_fi5821293074295781190e_real @ F @ R2 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 5.02/5.38 @ ( times_times_real @ ( powr_real @ ( G @ X2 ) @ ( F @ X2 ) ) @ ( plus_plus_real @ ( times_times_real @ R2 @ ( ln_ln_real @ ( G @ X2 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X2 ) ) @ ( G @ X2 ) ) ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_powr
% 5.02/5.38 thf(fact_9984_DERIV__real__sqrt,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_real_sqrt
% 5.02/5.38 thf(fact_9985_DERIV__series_H,axiom,
% 5.02/5.38 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.02/5.38 ( ! [N: nat] :
% 5.02/5.38 ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [X: real] : ( F @ X @ N )
% 5.02/5.38 @ ( F4 @ X0 @ N )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.02/5.38 => ( summable_real @ ( F @ X5 ) ) )
% 5.02/5.38 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.02/5.38 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.02/5.38 => ( ( summable_real @ L5 )
% 5.02/5.38 => ( ! [N: nat,X5: real,Y3: real] :
% 5.02/5.38 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.02/5.38 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.02/5.38 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X5 @ N ) @ ( F @ Y3 @ N ) ) ) @ ( times_times_real @ ( L5 @ N ) @ ( abs_abs_real @ ( minus_minus_real @ X5 @ Y3 ) ) ) ) ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 5.02/5.38 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_series'
% 5.02/5.38 thf(fact_9986_DERIV__arctan,axiom,
% 5.02/5.38 ! [X2: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_arctan
% 5.02/5.38 thf(fact_9987_arsinh__real__has__field__derivative,axiom,
% 5.02/5.38 ! [X2: real,A3: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A3 ) ) ).
% 5.02/5.38
% 5.02/5.38 % arsinh_real_has_field_derivative
% 5.02/5.38 thf(fact_9988_DERIV__real__sqrt__generic,axiom,
% 5.02/5.38 ! [X2: real,D4: real] :
% 5.02/5.38 ( ( X2 != zero_zero_real )
% 5.02/5.38 => ( ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( D4
% 5.02/5.38 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 => ( ( ( ord_less_real @ X2 @ zero_zero_real )
% 5.02/5.38 => ( D4
% 5.02/5.38 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X2 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_real_sqrt_generic
% 5.02/5.38 thf(fact_9989_arcosh__real__has__field__derivative,axiom,
% 5.02/5.38 ! [X2: real,A3: set_real] :
% 5.02/5.38 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A3 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % arcosh_real_has_field_derivative
% 5.02/5.38 thf(fact_9990_artanh__real__has__field__derivative,axiom,
% 5.02/5.38 ! [X2: real,A3: set_real] :
% 5.02/5.38 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ A3 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % artanh_real_has_field_derivative
% 5.02/5.38 thf(fact_9991_DERIV__power__series_H,axiom,
% 5.02/5.38 ! [R: real,F: nat > real,X0: real] :
% 5.02/5.38 ( ! [X5: real] :
% 5.02/5.38 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.02/5.38 => ( summable_real
% 5.02/5.38 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X5 @ N3 ) ) ) )
% 5.02/5.38 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.02/5.38 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.02/5.38 => ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [X: real] :
% 5.02/5.38 ( suminf_real
% 5.02/5.38 @ ^ [N3: nat] : ( times_times_real @ ( F @ N3 ) @ ( power_power_real @ X @ ( suc @ N3 ) ) ) )
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [N3: nat] : ( times_times_real @ ( times_times_real @ ( F @ N3 ) @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ ( power_power_real @ X0 @ N3 ) ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_power_series'
% 5.02/5.38 thf(fact_9992_DERIV__real__root,axiom,
% 5.02/5.38 ! [N2: nat,X2: real] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( ord_less_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X2 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_real_root
% 5.02/5.38 thf(fact_9993_DERIV__arccos,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_arccos
% 5.02/5.38 thf(fact_9994_DERIV__arcsin,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_arcsin
% 5.02/5.38 thf(fact_9995_Maclaurin__all__le__objl,axiom,
% 5.02/5.38 ! [Diff: nat > real > real,F: real > real,X2: real,N2: nat] :
% 5.02/5.38 ( ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 & ! [M3: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.02/5.38 & ( ( F @ X2 )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Maclaurin_all_le_objl
% 5.02/5.38 thf(fact_9996_Maclaurin__all__le,axiom,
% 5.02/5.38 ! [Diff: nat > real > real,F: real > real,X2: real,N2: nat] :
% 5.02/5.38 ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ! [M3: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.02/5.38 & ( ( F @ X2 )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Maclaurin_all_le
% 5.02/5.38 thf(fact_9997_DERIV__odd__real__root,axiom,
% 5.02/5.38 ! [N2: nat,X2: real] :
% 5.02/5.38 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.38 => ( ( X2 != zero_zero_real )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X2 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_odd_real_root
% 5.02/5.38 thf(fact_9998_Maclaurin,axiom,
% 5.02/5.38 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.02/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ! [M3: nat,T3: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.02/5.38 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.02/5.38 & ( ord_less_real @ T3 @ H2 )
% 5.02/5.38 & ( ( F @ H2 )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Maclaurin
% 5.02/5.38 thf(fact_9999_Maclaurin2,axiom,
% 5.02/5.38 ! [H2: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.02/5.38 => ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ! [M3: nat,T3: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.02/5.38 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.02/5.38 & ( ord_less_eq_real @ T3 @ H2 )
% 5.02/5.38 & ( ( F @ H2 )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Maclaurin2
% 5.02/5.38 thf(fact_10000_Maclaurin__minus,axiom,
% 5.02/5.38 ! [H2: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.02/5.38 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.02/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ! [M3: nat,T3: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ H2 @ T3 )
% 5.02/5.38 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_real @ H2 @ T3 )
% 5.02/5.38 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.02/5.38 & ( ( F @ H2 )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H2 @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Maclaurin_minus
% 5.02/5.38 thf(fact_10001_Maclaurin__all__lt,axiom,
% 5.02/5.38 ! [Diff: nat > real > real,F: real > real,N2: nat,X2: real] :
% 5.02/5.38 ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( X2 != zero_zero_real )
% 5.02/5.38 => ( ! [M3: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.02/5.38 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.02/5.38 & ( ( F @ X2 )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Maclaurin_all_lt
% 5.02/5.38 thf(fact_10002_Maclaurin__bi__le,axiom,
% 5.02/5.38 ! [Diff: nat > real > real,F: real > real,N2: nat,X2: real] :
% 5.02/5.38 ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ! [M3: nat,T3: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X2 ) )
% 5.02/5.38 & ( ( F @ X2 )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X2 @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X2 @ N2 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Maclaurin_bi_le
% 5.02/5.38 thf(fact_10003_Taylor,axiom,
% 5.02/5.38 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X2: real] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ! [M3: nat,T3: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ A @ T3 )
% 5.02/5.38 & ( ord_less_eq_real @ T3 @ B ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.02/5.38 => ( ( ord_less_eq_real @ A @ C )
% 5.02/5.38 => ( ( ord_less_eq_real @ C @ B )
% 5.02/5.38 => ( ( ord_less_eq_real @ A @ X2 )
% 5.02/5.38 => ( ( ord_less_eq_real @ X2 @ B )
% 5.02/5.38 => ( ( X2 != C )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ( ord_less_real @ X2 @ C )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ T3 )
% 5.02/5.38 & ( ord_less_real @ T3 @ C ) ) )
% 5.02/5.38 & ( ~ ( ord_less_real @ X2 @ C )
% 5.02/5.38 => ( ( ord_less_real @ C @ T3 )
% 5.02/5.38 & ( ord_less_real @ T3 @ X2 ) ) )
% 5.02/5.38 & ( ( F @ X2 )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X2 @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Taylor
% 5.02/5.38 thf(fact_10004_Taylor__up,axiom,
% 5.02/5.38 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ! [M3: nat,T3: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ A @ T3 )
% 5.02/5.38 & ( ord_less_eq_real @ T3 @ B ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.02/5.38 => ( ( ord_less_eq_real @ A @ C )
% 5.02/5.38 => ( ( ord_less_real @ C @ B )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_real @ C @ T3 )
% 5.02/5.38 & ( ord_less_real @ T3 @ B )
% 5.02/5.38 & ( ( F @ B )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Taylor_up
% 5.02/5.38 thf(fact_10005_Taylor__down,axiom,
% 5.02/5.38 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( ( Diff @ zero_zero_nat )
% 5.02/5.38 = F )
% 5.02/5.38 => ( ! [M3: nat,T3: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ A @ T3 )
% 5.02/5.38 & ( ord_less_eq_real @ T3 @ B ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.02/5.38 => ( ( ord_less_real @ A @ C )
% 5.02/5.38 => ( ( ord_less_eq_real @ C @ B )
% 5.02/5.38 => ? [T3: real] :
% 5.02/5.38 ( ( ord_less_real @ A @ T3 )
% 5.02/5.38 & ( ord_less_real @ T3 @ C )
% 5.02/5.38 & ( ( F @ A )
% 5.02/5.38 = ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.02/5.38 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Taylor_down
% 5.02/5.38 thf(fact_10006_Maclaurin__lemma2,axiom,
% 5.02/5.38 ! [N2: nat,H2: real,Diff: nat > real > real,K: nat,B4: real] :
% 5.02/5.38 ( ! [M3: nat,T3: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M3 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.02/5.38 & ( ord_less_eq_real @ T3 @ H2 ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ ( Diff @ M3 ) @ ( Diff @ ( suc @ M3 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.02/5.38 => ( ( N2
% 5.02/5.38 = ( suc @ K ) )
% 5.02/5.38 => ! [M2: nat,T4: real] :
% 5.02/5.38 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.02/5.38 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.02/5.38 & ( ord_less_eq_real @ T4 @ H2 ) )
% 5.02/5.38 => ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [U2: real] :
% 5.02/5.38 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 5.02/5.38 @ ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ U2 @ P6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M2 ) ) )
% 5.02/5.38 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) )
% 5.02/5.38 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T4 )
% 5.02/5.38 @ ( plus_plus_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [P6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P6 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P6 ) ) @ ( power_power_real @ T4 @ P6 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) )
% 5.02/5.38 @ ( times_times_real @ B4 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) ) ) ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Maclaurin_lemma2
% 5.02/5.38 thf(fact_10007_DERIV__arctan__series,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.38 => ( has_fi5821293074295781190e_real
% 5.02/5.38 @ ^ [X9: real] :
% 5.02/5.38 ( suminf_real
% 5.02/5.38 @ ^ [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 ) ) ) ) )
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X2 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % DERIV_arctan_series
% 5.02/5.38 thf(fact_10008_take__bit__numeral__minus__numeral__int,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( case_option_int_num @ zero_zero_int
% 5.02/5.38 @ ^ [Q4: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q4 ) ) )
% 5.02/5.38 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_numeral_minus_numeral_int
% 5.02/5.38 thf(fact_10009_take__bit__num__simps_I1_J,axiom,
% 5.02/5.38 ! [M: num] :
% 5.02/5.38 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.02/5.38 = none_num ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_num_simps(1)
% 5.02/5.38 thf(fact_10010_take__bit__num__simps_I2_J,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 5.02/5.38 = ( some_num @ one ) ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_num_simps(2)
% 5.02/5.38 thf(fact_10011_take__bit__num__simps_I5_J,axiom,
% 5.02/5.38 ! [R2: num] :
% 5.02/5.38 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ one )
% 5.02/5.38 = ( some_num @ one ) ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_num_simps(5)
% 5.02/5.38 thf(fact_10012_take__bit__num__simps_I3_J,axiom,
% 5.02/5.38 ! [N2: nat,M: num] :
% 5.02/5.38 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 5.02/5.38 = ( case_o6005452278849405969um_num @ none_num
% 5.02/5.38 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.02/5.38 @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_num_simps(3)
% 5.02/5.38 thf(fact_10013_take__bit__num__simps_I4_J,axiom,
% 5.02/5.38 ! [N2: nat,M: num] :
% 5.02/5.38 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 5.02/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_num_simps(4)
% 5.02/5.38 thf(fact_10014_take__bit__num__simps_I6_J,axiom,
% 5.02/5.38 ! [R2: num,M: num] :
% 5.02/5.38 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit0 @ M ) )
% 5.02/5.38 = ( case_o6005452278849405969um_num @ none_num
% 5.02/5.38 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.02/5.38 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_num_simps(6)
% 5.02/5.38 thf(fact_10015_take__bit__num__simps_I7_J,axiom,
% 5.02/5.38 ! [R2: num,M: num] :
% 5.02/5.38 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R2 ) @ ( bit1 @ M ) )
% 5.02/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R2 ) @ M ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_num_simps(7)
% 5.02/5.38 thf(fact_10016_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.02/5.38 ! [N2: nat,M: num] :
% 5.02/5.38 ( ( bit_take_bit_num @ N2 @ ( bit0 @ M ) )
% 5.02/5.38 = ( case_nat_option_num @ none_num
% 5.02/5.38 @ ^ [N3: nat] :
% 5.02/5.38 ( case_o6005452278849405969um_num @ none_num
% 5.02/5.38 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.02/5.38 @ ( bit_take_bit_num @ N3 @ M ) )
% 5.02/5.38 @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.02/5.38 thf(fact_10017_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( bit_take_bit_num @ N2 @ one )
% 5.02/5.38 = ( case_nat_option_num @ none_num
% 5.02/5.38 @ ^ [N3: nat] : ( some_num @ one )
% 5.02/5.38 @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.02/5.38 thf(fact_10018_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.02/5.38 ! [N2: nat,M: num] :
% 5.02/5.38 ( ( bit_take_bit_num @ N2 @ ( bit1 @ M ) )
% 5.02/5.38 = ( case_nat_option_num @ none_num
% 5.02/5.38 @ ^ [N3: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N3 @ M ) ) )
% 5.02/5.38 @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.02/5.38 thf(fact_10019_take__bit__num__def,axiom,
% 5.02/5.38 ( bit_take_bit_num
% 5.02/5.38 = ( ^ [N3: nat,M6: num] :
% 5.02/5.38 ( if_option_num
% 5.02/5.38 @ ( ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M6 ) )
% 5.02/5.38 = zero_zero_nat )
% 5.02/5.38 @ none_num
% 5.02/5.38 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N3 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % take_bit_num_def
% 5.02/5.38 thf(fact_10020_and__minus__numerals_I7_J,axiom,
% 5.02/5.38 ! [N2: num,M: num] :
% 5.02/5.38 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.02/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_minus_numerals(7)
% 5.02/5.38 thf(fact_10021_and__minus__numerals_I3_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.02/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_minus_numerals(3)
% 5.02/5.38 thf(fact_10022_and__minus__numerals_I4_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.02/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_minus_numerals(4)
% 5.02/5.38 thf(fact_10023_and__minus__numerals_I8_J,axiom,
% 5.02/5.38 ! [N2: num,M: num] :
% 5.02/5.38 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.02/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_minus_numerals(8)
% 5.02/5.38 thf(fact_10024_and__not__num_Osimps_I1_J,axiom,
% 5.02/5.38 ( ( bit_and_not_num @ one @ one )
% 5.02/5.38 = none_num ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(1)
% 5.02/5.38 thf(fact_10025_and__not__num_Osimps_I4_J,axiom,
% 5.02/5.38 ! [M: num] :
% 5.02/5.38 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.02/5.38 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(4)
% 5.02/5.38 thf(fact_10026_and__not__num_Osimps_I2_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( bit_and_not_num @ one @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( some_num @ one ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(2)
% 5.02/5.38 thf(fact_10027_and__not__num_Osimps_I3_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( bit_and_not_num @ one @ ( bit1 @ N2 ) )
% 5.02/5.38 = none_num ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(3)
% 5.02/5.38 thf(fact_10028_and__not__num_Osimps_I7_J,axiom,
% 5.02/5.38 ! [M: num] :
% 5.02/5.38 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.02/5.38 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(7)
% 5.02/5.38 thf(fact_10029_and__not__num__eq__Some__iff,axiom,
% 5.02/5.38 ! [M: num,N2: num,Q2: num] :
% 5.02/5.38 ( ( ( bit_and_not_num @ M @ N2 )
% 5.02/5.38 = ( some_num @ Q2 ) )
% 5.02/5.38 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num_eq_Some_iff
% 5.02/5.38 thf(fact_10030_and__not__num_Osimps_I8_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.02/5.38 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.02/5.38 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(8)
% 5.02/5.38 thf(fact_10031_and__not__num__eq__None__iff,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( ( bit_and_not_num @ M @ N2 )
% 5.02/5.38 = none_num )
% 5.02/5.38 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = zero_zero_int ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num_eq_None_iff
% 5.02/5.38 thf(fact_10032_int__numeral__not__and__num,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.02/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % int_numeral_not_and_num
% 5.02/5.38 thf(fact_10033_int__numeral__and__not__num,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.02/5.38 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % int_numeral_and_not_num
% 5.02/5.38 thf(fact_10034_Bit__Operations_Otake__bit__num__code,axiom,
% 5.02/5.38 ( bit_take_bit_num
% 5.02/5.38 = ( ^ [N3: nat,M6: num] :
% 5.02/5.38 ( produc478579273971653890on_num
% 5.02/5.38 @ ^ [A5: nat,X: num] :
% 5.02/5.38 ( case_nat_option_num @ none_num
% 5.02/5.38 @ ^ [O: nat] :
% 5.02/5.38 ( case_num_option_num @ ( some_num @ one )
% 5.02/5.38 @ ^ [P6: num] :
% 5.02/5.38 ( case_o6005452278849405969um_num @ none_num
% 5.02/5.38 @ ^ [Q4: num] : ( some_num @ ( bit0 @ Q4 ) )
% 5.02/5.38 @ ( bit_take_bit_num @ O @ P6 ) )
% 5.02/5.38 @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 5.02/5.38 @ X )
% 5.02/5.38 @ A5 )
% 5.02/5.38 @ ( product_Pair_nat_num @ N3 @ M6 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Bit_Operations.take_bit_num_code
% 5.02/5.38 thf(fact_10035_isCont__arcosh,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.38 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % isCont_arcosh
% 5.02/5.38 thf(fact_10036_isCont__arccos,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.38 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % isCont_arccos
% 5.02/5.38 thf(fact_10037_isCont__arcsin,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.38 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % isCont_arcsin
% 5.02/5.38 thf(fact_10038_isCont__artanh,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X2 )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.38 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X2 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % isCont_artanh
% 5.02/5.38 thf(fact_10039_GMVT_H,axiom,
% 5.02/5.38 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.02/5.38 ( ( ord_less_real @ A @ B )
% 5.02/5.38 => ( ! [Z3: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ A @ Z3 )
% 5.02/5.38 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.02/5.38 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ F ) ) )
% 5.02/5.38 => ( ! [Z3: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ A @ Z3 )
% 5.02/5.38 => ( ( ord_less_eq_real @ Z3 @ B )
% 5.02/5.38 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) @ G ) ) )
% 5.02/5.38 => ( ! [Z3: real] :
% 5.02/5.38 ( ( ord_less_real @ A @ Z3 )
% 5.02/5.38 => ( ( ord_less_real @ Z3 @ B )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.02/5.38 => ( ! [Z3: real] :
% 5.02/5.38 ( ( ord_less_real @ A @ Z3 )
% 5.02/5.38 => ( ( ord_less_real @ Z3 @ B )
% 5.02/5.38 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z3 ) @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) )
% 5.02/5.38 => ? [C3: real] :
% 5.02/5.38 ( ( ord_less_real @ A @ C3 )
% 5.02/5.38 & ( ord_less_real @ C3 @ B )
% 5.02/5.38 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.02/5.38 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % GMVT'
% 5.02/5.38 thf(fact_10040_LIM__cos__div__sin,axiom,
% 5.02/5.38 ( filterlim_real_real
% 5.02/5.38 @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % LIM_cos_div_sin
% 5.02/5.38 thf(fact_10041_summable__Leibniz_I3_J,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ( topolo6980174941875973593q_real @ A )
% 5.02/5.38 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.02/5.38 => ! [N8: nat] :
% 5.02/5.38 ( member_real
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.02/5.38 @ ( set_or1222579329274155063t_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) )
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz(3)
% 5.02/5.38 thf(fact_10042_summable__Leibniz_I2_J,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ( topolo6980174941875973593q_real @ A )
% 5.02/5.38 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.02/5.38 => ! [N8: nat] :
% 5.02/5.38 ( member_real
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.02/5.38 @ ( set_or1222579329274155063t_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz(2)
% 5.02/5.38 thf(fact_10043_filterlim__Suc,axiom,
% 5.02/5.38 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.02/5.38
% 5.02/5.38 % filterlim_Suc
% 5.02/5.38 thf(fact_10044_mult__nat__left__at__top,axiom,
% 5.02/5.38 ! [C: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.02/5.38 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % mult_nat_left_at_top
% 5.02/5.38 thf(fact_10045_mult__nat__right__at__top,axiom,
% 5.02/5.38 ! [C: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.02/5.38 => ( filterlim_nat_nat
% 5.02/5.38 @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 5.02/5.38 @ at_top_nat
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % mult_nat_right_at_top
% 5.02/5.38 thf(fact_10046_LIMSEQ__root,axiom,
% 5.02/5.38 ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( root @ N3 @ ( semiri5074537144036343181t_real @ N3 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.02/5.38 @ at_top_nat ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_root
% 5.02/5.38 thf(fact_10047_nested__sequence__unique,axiom,
% 5.02/5.38 ! [F: nat > real,G: nat > real] :
% 5.02/5.38 ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N ) ) @ ( G @ N ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( G @ N ) )
% 5.02/5.38 => ( ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( minus_minus_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ at_top_nat )
% 5.02/5.38 => ? [L4: real] :
% 5.02/5.38 ( ! [N8: nat] : ( ord_less_eq_real @ ( F @ N8 ) @ L4 )
% 5.02/5.38 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.02/5.38 & ! [N8: nat] : ( ord_less_eq_real @ L4 @ ( G @ N8 ) )
% 5.02/5.38 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nested_sequence_unique
% 5.02/5.38 thf(fact_10048_LIMSEQ__inverse__zero,axiom,
% 5.02/5.38 ! [X8: nat > real] :
% 5.02/5.38 ( ! [R3: real] :
% 5.02/5.38 ? [N6: nat] :
% 5.02/5.38 ! [N: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ N6 @ N )
% 5.02/5.38 => ( ord_less_real @ R3 @ ( X8 @ N ) ) )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( inverse_inverse_real @ ( X8 @ N3 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_inverse_zero
% 5.02/5.38 thf(fact_10049_lim__inverse__n_H,axiom,
% 5.02/5.38 ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N3 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ at_top_nat ) ).
% 5.02/5.38
% 5.02/5.38 % lim_inverse_n'
% 5.02/5.38 thf(fact_10050_LIMSEQ__root__const,axiom,
% 5.02/5.38 ! [C: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ C )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( root @ N3 @ C )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_root_const
% 5.02/5.38 thf(fact_10051_LIMSEQ__inverse__real__of__nat,axiom,
% 5.02/5.38 ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ at_top_nat ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_inverse_real_of_nat
% 5.02/5.38 thf(fact_10052_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.02/5.38 ! [R2: real] :
% 5.02/5.38 ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ R2 )
% 5.02/5.38 @ at_top_nat ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_inverse_real_of_nat_add
% 5.02/5.38 thf(fact_10053_increasing__LIMSEQ,axiom,
% 5.02/5.38 ! [F: nat > real,L: real] :
% 5.02/5.38 ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ ( F @ N ) @ L )
% 5.02/5.38 => ( ! [E: real] :
% 5.02/5.38 ( ( ord_less_real @ zero_zero_real @ E )
% 5.02/5.38 => ? [N8: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N8 ) @ E ) ) )
% 5.02/5.38 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % increasing_LIMSEQ
% 5.02/5.38 thf(fact_10054_LIMSEQ__realpow__zero,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( ( ord_less_real @ X2 @ one_one_real )
% 5.02/5.38 => ( filterlim_nat_real @ ( power_power_real @ X2 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_realpow_zero
% 5.02/5.38 thf(fact_10055_LIMSEQ__divide__realpow__zero,axiom,
% 5.02/5.38 ! [X2: real,A: real] :
% 5.02/5.38 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( divide_divide_real @ A @ ( power_power_real @ X2 @ N3 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_divide_realpow_zero
% 5.02/5.38 thf(fact_10056_LIMSEQ__abs__realpow__zero2,axiom,
% 5.02/5.38 ! [C: real] :
% 5.02/5.38 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.02/5.38 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_abs_realpow_zero2
% 5.02/5.38 thf(fact_10057_LIMSEQ__abs__realpow__zero,axiom,
% 5.02/5.38 ! [C: real] :
% 5.02/5.38 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.02/5.38 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_abs_realpow_zero
% 5.02/5.38 thf(fact_10058_LIMSEQ__inverse__realpow__zero,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_real @ one_one_real @ X2 )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( inverse_inverse_real @ ( power_power_real @ X2 @ N3 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_inverse_realpow_zero
% 5.02/5.38 thf(fact_10059_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.02/5.38 ! [R2: real] :
% 5.02/5.38 ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( plus_plus_real @ R2 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ R2 )
% 5.02/5.38 @ at_top_nat ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.02/5.38 thf(fact_10060_tendsto__exp__limit__sequentially,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ ( semiri5074537144036343181t_real @ N3 ) ) ) @ N3 )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.02/5.38 @ at_top_nat ) ).
% 5.02/5.38
% 5.02/5.38 % tendsto_exp_limit_sequentially
% 5.02/5.38 thf(fact_10061_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.02/5.38 ! [R2: real] :
% 5.02/5.38 ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( times_times_real @ R2 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ R2 )
% 5.02/5.38 @ at_top_nat ) ).
% 5.02/5.38
% 5.02/5.38 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.02/5.38 thf(fact_10062_summable__Leibniz_I1_J,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ( topolo6980174941875973593q_real @ A )
% 5.02/5.38 => ( summable_real
% 5.02/5.38 @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz(1)
% 5.02/5.38 thf(fact_10063_summable,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.02/5.38 => ( summable_real
% 5.02/5.38 @ ^ [N3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N3 ) @ ( A @ N3 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable
% 5.02/5.38 thf(fact_10064_cos__diff__limit__1,axiom,
% 5.02/5.38 ! [Theta: nat > real,Theta2: real] :
% 5.02/5.38 ( ( filterlim_nat_real
% 5.02/5.38 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.02/5.38 @ at_top_nat )
% 5.02/5.38 => ~ ! [K2: nat > int] :
% 5.02/5.38 ~ ( filterlim_nat_real
% 5.02/5.38 @ ^ [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 ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % cos_diff_limit_1
% 5.02/5.38 thf(fact_10065_cos__limit__1,axiom,
% 5.02/5.38 ! [Theta: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real
% 5.02/5.38 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.02/5.38 @ at_top_nat )
% 5.02/5.38 => ? [K2: nat > int] :
% 5.02/5.38 ( filterlim_nat_real
% 5.02/5.38 @ ^ [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 ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % cos_limit_1
% 5.02/5.38 thf(fact_10066_summable__Leibniz_I4_J,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ( topolo6980174941875973593q_real @ A )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] :
% 5.02/5.38 ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.02/5.38 @ at_top_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz(4)
% 5.02/5.38 thf(fact_10067_zeroseq__arctan__series,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ ( abs_abs_real @ X2 ) @ one_one_real )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X2 @ ( plus_plus_nat @ ( times_times_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % zeroseq_arctan_series
% 5.02/5.38 thf(fact_10068_summable__Leibniz_H_I3_J,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] :
% 5.02/5.38 ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.02/5.38 @ at_top_nat ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz'(3)
% 5.02/5.38 thf(fact_10069_summable__Leibniz_H_I2_J,axiom,
% 5.02/5.38 ! [A: nat > real,N2: nat] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.02/5.38 => ( ord_less_eq_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz'(2)
% 5.02/5.38 thf(fact_10070_sums__alternating__upper__lower,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.02/5.38 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ? [L4: real] :
% 5.02/5.38 ( ! [N8: nat] :
% 5.02/5.38 ( ord_less_eq_real
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 5.02/5.38 @ L4 )
% 5.02/5.38 & ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] :
% 5.02/5.38 ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ L4 )
% 5.02/5.38 @ at_top_nat )
% 5.02/5.38 & ! [N8: nat] :
% 5.02/5.38 ( ord_less_eq_real @ L4
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) )
% 5.02/5.38 & ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] :
% 5.02/5.38 ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ L4 )
% 5.02/5.38 @ at_top_nat ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sums_alternating_upper_lower
% 5.02/5.38 thf(fact_10071_summable__Leibniz_I5_J,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ( topolo6980174941875973593q_real @ A )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] :
% 5.02/5.38 ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.02/5.38 @ at_top_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz(5)
% 5.02/5.38 thf(fact_10072_summable__Leibniz_H_I5_J,axiom,
% 5.02/5.38 ! [A: nat > real] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.02/5.38 => ( filterlim_nat_real
% 5.02/5.38 @ ^ [N3: nat] :
% 5.02/5.38 ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) @ one_one_nat ) ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.02/5.38 @ at_top_nat ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz'(5)
% 5.02/5.38 thf(fact_10073_summable__Leibniz_H_I4_J,axiom,
% 5.02/5.38 ! [A: nat > real,N2: nat] :
% 5.02/5.38 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N ) )
% 5.02/5.38 => ( ! [N: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N ) ) @ ( A @ N ) )
% 5.02/5.38 => ( ord_less_eq_real
% 5.02/5.38 @ ( suminf_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.02/5.38 @ ( groups6591440286371151544t_real
% 5.02/5.38 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.02/5.38 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % summable_Leibniz'(4)
% 5.02/5.38 thf(fact_10074_real__bounded__linear,axiom,
% 5.02/5.38 ( real_V5970128139526366754l_real
% 5.02/5.38 = ( ^ [F3: real > real] :
% 5.02/5.38 ? [C2: real] :
% 5.02/5.38 ( F3
% 5.02/5.38 = ( ^ [X: real] : ( times_times_real @ X @ C2 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % real_bounded_linear
% 5.02/5.38 thf(fact_10075_tendsto__exp__limit__at__right,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( filterlim_real_real
% 5.02/5.38 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X2 @ Y6 ) ) @ ( divide_divide_real @ one_one_real @ Y6 ) )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % tendsto_exp_limit_at_right
% 5.02/5.38 thf(fact_10076_tendsto__arctan__at__bot,axiom,
% 5.02/5.38 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.02/5.38
% 5.02/5.38 % tendsto_arctan_at_bot
% 5.02/5.38 thf(fact_10077_artanh__real__at__right__1,axiom,
% 5.02/5.38 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 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % artanh_real_at_right_1
% 5.02/5.38 thf(fact_10078_filterlim__tan__at__right,axiom,
% 5.02/5.38 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 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % filterlim_tan_at_right
% 5.02/5.38 thf(fact_10079_tanh__real__at__bot,axiom,
% 5.02/5.38 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.02/5.38
% 5.02/5.38 % tanh_real_at_bot
% 5.02/5.38 thf(fact_10080_tendsto__arcosh__at__left__1,axiom,
% 5.02/5.38 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % tendsto_arcosh_at_left_1
% 5.02/5.38 thf(fact_10081_filterlim__pow__at__bot__odd,axiom,
% 5.02/5.38 ! [N2: nat,F: real > real,F5: filter_real] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.02/5.38 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.38 => ( filterlim_real_real
% 5.02/5.38 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N2 )
% 5.02/5.38 @ at_bot_real
% 5.02/5.38 @ F5 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % filterlim_pow_at_bot_odd
% 5.02/5.38 thf(fact_10082_filterlim__pow__at__bot__even,axiom,
% 5.02/5.38 ! [N2: nat,F: real > real,F5: filter_real] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.02/5.38 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.02/5.38 => ( filterlim_real_real
% 5.02/5.38 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N2 )
% 5.02/5.38 @ at_top_real
% 5.02/5.38 @ F5 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % filterlim_pow_at_bot_even
% 5.02/5.38 thf(fact_10083_atLeast__0,axiom,
% 5.02/5.38 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.02/5.38 = top_top_set_nat ) ).
% 5.02/5.38
% 5.02/5.38 % atLeast_0
% 5.02/5.38 thf(fact_10084_atLeast__Suc__greaterThan,axiom,
% 5.02/5.38 ! [K: nat] :
% 5.02/5.38 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.02/5.38 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeast_Suc_greaterThan
% 5.02/5.38 thf(fact_10085_greaterThan__0,axiom,
% 5.02/5.38 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.02/5.38 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % greaterThan_0
% 5.02/5.38 thf(fact_10086_tanh__real__at__top,axiom,
% 5.02/5.38 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.02/5.38
% 5.02/5.38 % tanh_real_at_top
% 5.02/5.38 thf(fact_10087_artanh__real__at__left__1,axiom,
% 5.02/5.38 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % artanh_real_at_left_1
% 5.02/5.38 thf(fact_10088_greaterThan__Suc,axiom,
% 5.02/5.38 ! [K: nat] :
% 5.02/5.38 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.02/5.38 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % greaterThan_Suc
% 5.02/5.38 thf(fact_10089_atLeast__Suc,axiom,
% 5.02/5.38 ! [K: nat] :
% 5.02/5.38 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.02/5.38 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeast_Suc
% 5.02/5.38 thf(fact_10090_tendsto__exp__limit__at__top,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( filterlim_real_real
% 5.02/5.38 @ ^ [Y6: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X2 @ Y6 ) ) @ Y6 )
% 5.02/5.38 @ ( topolo2815343760600316023s_real @ ( exp_real @ X2 ) )
% 5.02/5.38 @ at_top_real ) ).
% 5.02/5.38
% 5.02/5.38 % tendsto_exp_limit_at_top
% 5.02/5.38 thf(fact_10091_filterlim__tan__at__left,axiom,
% 5.02/5.38 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 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % filterlim_tan_at_left
% 5.02/5.38 thf(fact_10092_tendsto__arctan__at__top,axiom,
% 5.02/5.38 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.02/5.38
% 5.02/5.38 % tendsto_arctan_at_top
% 5.02/5.38 thf(fact_10093_GMVT,axiom,
% 5.02/5.38 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.02/5.38 ( ( ord_less_real @ A @ B )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.02/5.38 & ( ord_less_eq_real @ X5 @ B ) )
% 5.02/5.38 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( ( ord_less_real @ A @ X5 )
% 5.02/5.38 & ( ord_less_real @ X5 @ B ) )
% 5.02/5.38 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.02/5.38 & ( ord_less_eq_real @ X5 @ B ) )
% 5.02/5.38 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ G ) )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( ( ord_less_real @ A @ X5 )
% 5.02/5.38 & ( ord_less_real @ X5 @ B ) )
% 5.02/5.38 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.02/5.38 => ? [G_c: real,F_c: real,C3: real] :
% 5.02/5.38 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.02/5.38 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.02/5.38 & ( ord_less_real @ A @ C3 )
% 5.02/5.38 & ( ord_less_real @ C3 @ B )
% 5.02/5.38 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.02/5.38 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % GMVT
% 5.02/5.38 thf(fact_10094_eventually__sequentially__Suc,axiom,
% 5.02/5.38 ! [P: nat > $o] :
% 5.02/5.38 ( ( eventually_nat
% 5.02/5.38 @ ^ [I5: nat] : ( P @ ( suc @ I5 ) )
% 5.02/5.38 @ at_top_nat )
% 5.02/5.38 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % eventually_sequentially_Suc
% 5.02/5.38 thf(fact_10095_eventually__sequentially__seg,axiom,
% 5.02/5.38 ! [P: nat > $o,K: nat] :
% 5.02/5.38 ( ( eventually_nat
% 5.02/5.38 @ ^ [N3: nat] : ( P @ ( plus_plus_nat @ N3 @ K ) )
% 5.02/5.38 @ at_top_nat )
% 5.02/5.38 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % eventually_sequentially_seg
% 5.02/5.38 thf(fact_10096_sequentially__offset,axiom,
% 5.02/5.38 ! [P: nat > $o,K: nat] :
% 5.02/5.38 ( ( eventually_nat @ P @ at_top_nat )
% 5.02/5.38 => ( eventually_nat
% 5.02/5.38 @ ^ [I5: nat] : ( P @ ( plus_plus_nat @ I5 @ K ) )
% 5.02/5.38 @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % sequentially_offset
% 5.02/5.38 thf(fact_10097_eventually__sequentiallyI,axiom,
% 5.02/5.38 ! [C: nat,P: nat > $o] :
% 5.02/5.38 ( ! [X5: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ C @ X5 )
% 5.02/5.38 => ( P @ X5 ) )
% 5.02/5.38 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % eventually_sequentiallyI
% 5.02/5.38 thf(fact_10098_eventually__sequentially,axiom,
% 5.02/5.38 ! [P: nat > $o] :
% 5.02/5.38 ( ( eventually_nat @ P @ at_top_nat )
% 5.02/5.38 = ( ? [N9: nat] :
% 5.02/5.38 ! [N3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ N9 @ N3 )
% 5.02/5.38 => ( P @ N3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % eventually_sequentially
% 5.02/5.38 thf(fact_10099_le__sequentially,axiom,
% 5.02/5.38 ! [F5: filter_nat] :
% 5.02/5.38 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.02/5.38 = ( ! [N9: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N9 ) @ F5 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % le_sequentially
% 5.02/5.38 thf(fact_10100_eventually__at__right__to__0,axiom,
% 5.02/5.38 ! [P: real > $o,A: real] :
% 5.02/5.38 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.02/5.38 = ( eventually_real
% 5.02/5.38 @ ^ [X: real] : ( P @ ( plus_plus_real @ X @ A ) )
% 5.02/5.38 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % eventually_at_right_to_0
% 5.02/5.38 thf(fact_10101_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.02/5.38 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.38 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.02/5.38 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.02/5.38 ( X2
% 5.02/5.38 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.38 => ( Xa2 = one_one_nat ) )
% 5.02/5.38 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.02/5.38 => ( ( Deg2 = Xa2 )
% 5.02/5.38 & ! [X5: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.02/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 & ( case_o184042715313410164at_nat
% 5.02/5.38 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 @ ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [Mi3: nat,Ma3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.02/5.38 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 & ! [I5: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.02/5.38 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.02/5.38 & ( ( Mi3 = Ma3 )
% 5.02/5.38 => ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 & ( ( Mi3 != Ma3 )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.02/5.38 & ! [X: nat] :
% 5.02/5.38 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.02/5.38 => ( ( ord_less_nat @ Mi3 @ X )
% 5.02/5.38 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.02/5.38 @ Mima ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT_internal.valid'.elims(3)
% 5.02/5.38 thf(fact_10102_GreatestI__ex__nat,axiom,
% 5.02/5.38 ! [P: nat > $o,B: nat] :
% 5.02/5.38 ( ? [X_1: nat] : ( P @ X_1 )
% 5.02/5.38 => ( ! [Y3: nat] :
% 5.02/5.38 ( ( P @ Y3 )
% 5.02/5.38 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.02/5.38 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % GreatestI_ex_nat
% 5.02/5.38 thf(fact_10103_Greatest__le__nat,axiom,
% 5.02/5.38 ! [P: nat > $o,K: nat,B: nat] :
% 5.02/5.38 ( ( P @ K )
% 5.02/5.38 => ( ! [Y3: nat] :
% 5.02/5.38 ( ( P @ Y3 )
% 5.02/5.38 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.02/5.38 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Greatest_le_nat
% 5.02/5.38 thf(fact_10104_GreatestI__nat,axiom,
% 5.02/5.38 ! [P: nat > $o,K: nat,B: nat] :
% 5.02/5.38 ( ( P @ K )
% 5.02/5.38 => ( ! [Y3: nat] :
% 5.02/5.38 ( ( P @ Y3 )
% 5.02/5.38 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.02/5.38 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % GreatestI_nat
% 5.02/5.38 thf(fact_10105_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.02/5.38 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.02/5.38 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList @ Summary ) @ Deg4 )
% 5.02/5.38 = ( ( Deg = Deg4 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.02/5.38 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.02/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 & ( case_o184042715313410164at_nat
% 5.02/5.38 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X4 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 @ ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [Mi3: nat,Ma3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.02/5.38 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.02/5.38 & ! [I5: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X4 ) )
% 5.02/5.38 = ( vEBT_V8194947554948674370ptions @ Summary @ I5 ) ) )
% 5.02/5.38 & ( ( Mi3 = Ma3 )
% 5.02/5.38 => ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 & ( ( Mi3 != Ma3 )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 5.02/5.38 & ! [X: nat] :
% 5.02/5.38 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X )
% 5.02/5.38 => ( ( ord_less_nat @ Mi3 @ X )
% 5.02/5.38 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.02/5.38 @ Mima2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT_internal.valid'.simps(2)
% 5.02/5.38 thf(fact_10106_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.02/5.38 ! [X2: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.02/5.38 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.02/5.38 ( X2
% 5.02/5.38 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( Xa2 != one_one_nat ) ) )
% 5.02/5.38 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 = ( ~ ( ( Deg2 = Xa2 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.02/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 & ( case_o184042715313410164at_nat
% 5.02/5.38 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 @ ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [Mi3: nat,Ma3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.02/5.38 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 & ! [I5: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.02/5.38 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.02/5.38 & ( ( Mi3 = Ma3 )
% 5.02/5.38 => ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 & ( ( Mi3 != Ma3 )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.02/5.38 & ! [X: nat] :
% 5.02/5.38 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.02/5.38 => ( ( ord_less_nat @ Mi3 @ X )
% 5.02/5.38 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.02/5.38 @ Mima ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT_internal.valid'.elims(1)
% 5.02/5.38 thf(fact_10107_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.02/5.38 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.38 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.02/5.38 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.02/5.38 ( X2
% 5.02/5.38 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.38 => ( Xa2 != one_one_nat ) )
% 5.02/5.38 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.02/5.38 => ~ ( ( Deg2 = Xa2 )
% 5.02/5.38 & ! [X3: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.02/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 & ( case_o184042715313410164at_nat
% 5.02/5.38 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 @ ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [Mi3: nat,Ma3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.02/5.38 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 & ! [I5: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.02/5.38 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.02/5.38 & ( ( Mi3 = Ma3 )
% 5.02/5.38 => ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 & ( ( Mi3 != Ma3 )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.02/5.38 & ! [X: nat] :
% 5.02/5.38 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.02/5.38 => ( ( ord_less_nat @ Mi3 @ X )
% 5.02/5.38 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.02/5.38 @ Mima ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT_internal.valid'.elims(2)
% 5.02/5.38 thf(fact_10108_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.02/5.38 ! [X2: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.02/5.38 ( ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.38 => ( ! [Uu2: $o,Uv2: $o] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.38 => ( ( Y
% 5.02/5.38 = ( Xa2 = one_one_nat ) )
% 5.02/5.38 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.02/5.38 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.02/5.38 => ( ( Y
% 5.02/5.38 = ( ( Deg2 = Xa2 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.02/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 & ( case_o184042715313410164at_nat
% 5.02/5.38 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 @ ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [Mi3: nat,Ma3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.02/5.38 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 & ! [I5: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.02/5.38 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.02/5.38 & ( ( Mi3 = Ma3 )
% 5.02/5.38 => ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 & ( ( Mi3 != Ma3 )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.02/5.38 & ! [X: nat] :
% 5.02/5.38 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.02/5.38 => ( ( ord_less_nat @ Mi3 @ X )
% 5.02/5.38 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.02/5.38 @ Mima ) ) )
% 5.02/5.38 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT_internal.valid'.pelims(1)
% 5.02/5.38 thf(fact_10109_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.02/5.38 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.38 ( ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.02/5.38 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.38 => ( ! [Uu2: $o,Uv2: $o] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.38 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.02/5.38 => ( Xa2 != one_one_nat ) ) )
% 5.02/5.38 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.02/5.38 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.02/5.38 => ~ ( ( Deg2 = Xa2 )
% 5.02/5.38 & ! [X3: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.02/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 & ( case_o184042715313410164at_nat
% 5.02/5.38 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 @ ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [Mi3: nat,Ma3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.02/5.38 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 & ! [I5: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.02/5.38 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.02/5.38 & ( ( Mi3 = Ma3 )
% 5.02/5.38 => ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 & ( ( Mi3 != Ma3 )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.02/5.38 & ! [X: nat] :
% 5.02/5.38 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.02/5.38 => ( ( ord_less_nat @ Mi3 @ X )
% 5.02/5.38 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.02/5.38 @ Mima ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT_internal.valid'.pelims(2)
% 5.02/5.38 thf(fact_10110_Sup__int__def,axiom,
% 5.02/5.38 ( complete_Sup_Sup_int
% 5.02/5.38 = ( ^ [X4: set_int] :
% 5.02/5.38 ( the_int
% 5.02/5.38 @ ^ [X: int] :
% 5.02/5.38 ( ( member_int @ X @ X4 )
% 5.02/5.38 & ! [Y6: int] :
% 5.02/5.38 ( ( member_int @ Y6 @ X4 )
% 5.02/5.38 => ( ord_less_eq_int @ Y6 @ X ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Sup_int_def
% 5.02/5.38 thf(fact_10111_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.02/5.38 ! [X2: vEBT_VEBT,Xa2: nat] :
% 5.02/5.38 ( ~ ( vEBT_VEBT_valid @ X2 @ Xa2 )
% 5.02/5.38 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X2 @ Xa2 ) )
% 5.02/5.38 => ( ! [Uu2: $o,Uv2: $o] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.02/5.38 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.02/5.38 => ( Xa2 = one_one_nat ) ) )
% 5.02/5.38 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList2: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) )
% 5.02/5.38 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList2 @ Summary2 ) @ Xa2 ) )
% 5.02/5.38 => ( ( Deg2 = Xa2 )
% 5.02/5.38 & ! [X5: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.02/5.38 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.02/5.38 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 & ( case_o184042715313410164at_nat
% 5.02/5.38 @ ( ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X4 )
% 5.02/5.38 & ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 @ ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [Mi3: nat,Ma3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.02/5.38 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 & ! [I5: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.02/5.38 => ( ( ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X4 ) )
% 5.02/5.38 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.02/5.38 & ( ( Mi3 = Ma3 )
% 5.02/5.38 => ! [X: vEBT_VEBT] :
% 5.02/5.38 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.02/5.38 => ~ ? [X4: nat] : ( vEBT_V8194947554948674370ptions @ X @ X4 ) ) )
% 5.02/5.38 & ( ( Mi3 != Ma3 )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.02/5.38 & ! [X: nat] :
% 5.02/5.38 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.02/5.38 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.02/5.38 => ( ( ord_less_nat @ Mi3 @ X )
% 5.02/5.38 & ( ord_less_eq_nat @ X @ Ma3 ) ) ) ) ) ) ) )
% 5.02/5.38 @ Mima ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % VEBT_internal.valid'.pelims(3)
% 5.02/5.38 thf(fact_10112_Bseq__realpow,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( ( ord_less_eq_real @ X2 @ one_one_real )
% 5.02/5.38 => ( bfun_nat_real @ ( power_power_real @ X2 ) @ at_top_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Bseq_realpow
% 5.02/5.38 thf(fact_10113_MVT,axiom,
% 5.02/5.38 ! [A: real,B: real,F: real > real] :
% 5.02/5.38 ( ( ord_less_real @ A @ B )
% 5.02/5.38 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( ord_less_real @ A @ X5 )
% 5.02/5.38 => ( ( ord_less_real @ X5 @ B )
% 5.02/5.38 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.02/5.38 => ? [L4: real,Z3: real] :
% 5.02/5.38 ( ( ord_less_real @ A @ Z3 )
% 5.02/5.38 & ( ord_less_real @ Z3 @ B )
% 5.02/5.38 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) )
% 5.02/5.38 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.02/5.38 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % MVT
% 5.02/5.38 thf(fact_10114_continuous__on__arcosh,axiom,
% 5.02/5.38 ! [A3: set_real] :
% 5.02/5.38 ( ( ord_less_eq_set_real @ A3 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.02/5.38 => ( topolo5044208981011980120l_real @ A3 @ arcosh_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % continuous_on_arcosh
% 5.02/5.38 thf(fact_10115_continuous__on__arcosh_H,axiom,
% 5.02/5.38 ! [A3: set_real,F: real > real] :
% 5.02/5.38 ( ( topolo5044208981011980120l_real @ A3 @ F )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( member_real @ X5 @ A3 )
% 5.02/5.38 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.02/5.38 => ( topolo5044208981011980120l_real @ A3
% 5.02/5.38 @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % continuous_on_arcosh'
% 5.02/5.38 thf(fact_10116_continuous__on__arccos_H,axiom,
% 5.02/5.38 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.02/5.38
% 5.02/5.38 % continuous_on_arccos'
% 5.02/5.38 thf(fact_10117_continuous__on__arcsin_H,axiom,
% 5.02/5.38 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.02/5.38
% 5.02/5.38 % continuous_on_arcsin'
% 5.02/5.38 thf(fact_10118_continuous__on__artanh,axiom,
% 5.02/5.38 ! [A3: set_real] :
% 5.02/5.38 ( ( ord_less_eq_set_real @ A3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.02/5.38 => ( topolo5044208981011980120l_real @ A3 @ artanh_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % continuous_on_artanh
% 5.02/5.38 thf(fact_10119_continuous__on__artanh_H,axiom,
% 5.02/5.38 ! [A3: set_real,F: real > real] :
% 5.02/5.38 ( ( topolo5044208981011980120l_real @ A3 @ F )
% 5.02/5.38 => ( ! [X5: real] :
% 5.02/5.38 ( ( member_real @ X5 @ A3 )
% 5.02/5.38 => ( member_real @ ( F @ X5 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.02/5.38 => ( topolo5044208981011980120l_real @ A3
% 5.02/5.38 @ ^ [X: real] : ( artanh_real @ ( F @ X ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % continuous_on_artanh'
% 5.02/5.38 thf(fact_10120_mono__Suc,axiom,
% 5.02/5.38 order_mono_nat_nat @ suc ).
% 5.02/5.38
% 5.02/5.38 % mono_Suc
% 5.02/5.38 thf(fact_10121_mono__times__nat,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % mono_times_nat
% 5.02/5.38 thf(fact_10122_mono__ge2__power__minus__self,axiom,
% 5.02/5.38 ! [K: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.02/5.38 => ( order_mono_nat_nat
% 5.02/5.38 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % mono_ge2_power_minus_self
% 5.02/5.38 thf(fact_10123_and__not__num_Oelims,axiom,
% 5.02/5.38 ! [X2: num,Xa2: num,Y: option_num] :
% 5.02/5.38 ( ( ( bit_and_not_num @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y != none_num ) ) )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ( ? [N: num] :
% 5.02/5.38 ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ one ) ) ) )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ( ? [N: num] :
% 5.02/5.38 ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y != none_num ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.02/5.38 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.02/5.38 @ ( bit_and_not_num @ M3 @ N ) ) ) ) )
% 5.02/5.38 => ~ ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.elims
% 5.02/5.38 thf(fact_10124_and__not__num_Osimps_I5_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(5)
% 5.02/5.38 thf(fact_10125_and__not__num_Osimps_I6_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(6)
% 5.02/5.38 thf(fact_10126_and__not__num_Osimps_I9_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_not_num.simps(9)
% 5.02/5.38 thf(fact_10127_and__num_Oelims,axiom,
% 5.02/5.38 ! [X2: num,Xa2: num,Y: option_num] :
% 5.02/5.38 ( ( ( bit_un7362597486090784418nd_num @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ one ) ) ) )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ( ? [N: num] :
% 5.02/5.38 ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y != none_num ) ) )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ( ? [N: num] :
% 5.02/5.38 ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ one ) ) ) )
% 5.02/5.38 => ( ( ? [M3: num] :
% 5.02/5.38 ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y != none_num ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N ) ) ) ) )
% 5.02/5.38 => ( ( ? [M3: num] :
% 5.02/5.38 ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ one ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N ) ) ) ) )
% 5.02/5.38 => ~ ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.02/5.38 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.02/5.38 @ ( bit_un7362597486090784418nd_num @ M3 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.elims
% 5.02/5.38 thf(fact_10128_and__num_Osimps_I1_J,axiom,
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.02/5.38 = ( some_num @ one ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(1)
% 5.02/5.38 thf(fact_10129_and__num_Osimps_I5_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(5)
% 5.02/5.38 thf(fact_10130_and__num_Osimps_I3_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( some_num @ one ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(3)
% 5.02/5.38 thf(fact_10131_and__num_Osimps_I7_J,axiom,
% 5.02/5.38 ! [M: num] :
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.02/5.38 = ( some_num @ one ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(7)
% 5.02/5.38 thf(fact_10132_and__num_Osimps_I2_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N2 ) )
% 5.02/5.38 = none_num ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(2)
% 5.02/5.38 thf(fact_10133_and__num_Osimps_I4_J,axiom,
% 5.02/5.38 ! [M: num] :
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.02/5.38 = none_num ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(4)
% 5.02/5.38 thf(fact_10134_and__num_Osimps_I8_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(8)
% 5.02/5.38 thf(fact_10135_and__num_Osimps_I6_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(6)
% 5.02/5.38 thf(fact_10136_and__num_Osimps_I9_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.02/5.38 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.02/5.38 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % and_num.simps(9)
% 5.02/5.38 thf(fact_10137_xor__num_Oelims,axiom,
% 5.02/5.38 ! [X2: num,Xa2: num,Y: option_num] :
% 5.02/5.38 ( ( ( bit_un2480387367778600638or_num @ X2 @ Xa2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y != none_num ) ) )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ ( bit1 @ N ) ) ) ) )
% 5.02/5.38 => ( ( ( X2 = one )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ ( bit0 @ N ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ ( bit1 @ M3 ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit0 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N ) ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ( ( Xa2 = one )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 5.02/5.38 => ( ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit0 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N ) ) ) ) ) )
% 5.02/5.38 => ~ ! [M3: num] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( bit1 @ M3 ) )
% 5.02/5.38 => ! [N: num] :
% 5.02/5.38 ( ( Xa2
% 5.02/5.38 = ( bit1 @ N ) )
% 5.02/5.38 => ( Y
% 5.02/5.38 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.elims
% 5.02/5.38 thf(fact_10138_and__num__dict,axiom,
% 5.02/5.38 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.02/5.38
% 5.02/5.38 % and_num_dict
% 5.02/5.38 thf(fact_10139_xor__num_Osimps_I1_J,axiom,
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.02/5.38 = none_num ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(1)
% 5.02/5.38 thf(fact_10140_xor__num_Osimps_I5_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(5)
% 5.02/5.38 thf(fact_10141_xor__num_Osimps_I9_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(9)
% 5.02/5.38 thf(fact_10142_xor__num_Osimps_I7_J,axiom,
% 5.02/5.38 ! [M: num] :
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.02/5.38 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(7)
% 5.02/5.38 thf(fact_10143_xor__num_Osimps_I4_J,axiom,
% 5.02/5.38 ! [M: num] :
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.02/5.38 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(4)
% 5.02/5.38 thf(fact_10144_xor__num_Osimps_I3_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( some_num @ ( bit0 @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(3)
% 5.02/5.38 thf(fact_10145_xor__num_Osimps_I2_J,axiom,
% 5.02/5.38 ! [N2: num] :
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( some_num @ ( bit1 @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(2)
% 5.02/5.38 thf(fact_10146_xor__num_Osimps_I8_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.02/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(8)
% 5.02/5.38 thf(fact_10147_xor__num_Osimps_I6_J,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.02/5.38 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % xor_num.simps(6)
% 5.02/5.38 thf(fact_10148_xor__num__dict,axiom,
% 5.02/5.38 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.02/5.38
% 5.02/5.38 % xor_num_dict
% 5.02/5.38 thf(fact_10149_range__abs__Nats,axiom,
% 5.02/5.38 ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 5.02/5.38 = semiring_1_Nats_int ) ).
% 5.02/5.38
% 5.02/5.38 % range_abs_Nats
% 5.02/5.38 thf(fact_10150_inj__sgn__power,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 => ( inj_on_real_real
% 5.02/5.38 @ ^ [Y6: real] : ( times_times_real @ ( sgn_sgn_real @ Y6 ) @ ( power_power_real @ ( abs_abs_real @ Y6 ) @ N2 ) )
% 5.02/5.38 @ top_top_set_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % inj_sgn_power
% 5.02/5.38 thf(fact_10151_log__inj,axiom,
% 5.02/5.38 ! [B: real] :
% 5.02/5.38 ( ( ord_less_real @ one_one_real @ B )
% 5.02/5.38 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % log_inj
% 5.02/5.38 thf(fact_10152_inj__on__diff__nat,axiom,
% 5.02/5.38 ! [N4: set_nat,K: nat] :
% 5.02/5.38 ( ! [N: nat] :
% 5.02/5.38 ( ( member_nat @ N @ N4 )
% 5.02/5.38 => ( ord_less_eq_nat @ K @ N ) )
% 5.02/5.38 => ( inj_on_nat_nat
% 5.02/5.38 @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ K )
% 5.02/5.38 @ N4 ) ) ).
% 5.02/5.38
% 5.02/5.38 % inj_on_diff_nat
% 5.02/5.38 thf(fact_10153_inj__Suc,axiom,
% 5.02/5.38 ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 5.02/5.38
% 5.02/5.38 % inj_Suc
% 5.02/5.38 thf(fact_10154_inj__on__char__of__nat,axiom,
% 5.02/5.38 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % inj_on_char_of_nat
% 5.02/5.38 thf(fact_10155_Rats__eq__int__div__nat,axiom,
% 5.02/5.38 ( field_5140801741446780682s_real
% 5.02/5.38 = ( collect_real
% 5.02/5.38 @ ^ [Uu3: real] :
% 5.02/5.38 ? [I5: int,N3: nat] :
% 5.02/5.38 ( ( Uu3
% 5.02/5.38 = ( divide_divide_real @ ( ring_1_of_int_real @ I5 ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 5.02/5.38 & ( N3 != zero_zero_nat ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Rats_eq_int_div_nat
% 5.02/5.38 thf(fact_10156_Rats__abs__iff,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ( ( member_real @ ( abs_abs_real @ X2 ) @ field_5140801741446780682s_real )
% 5.02/5.38 = ( member_real @ X2 @ field_5140801741446780682s_real ) ) ).
% 5.02/5.38
% 5.02/5.38 % Rats_abs_iff
% 5.02/5.38 thf(fact_10157_Rats__no__top__le,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ? [X5: real] :
% 5.02/5.38 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.02/5.38 & ( ord_less_eq_real @ X2 @ X5 ) ) ).
% 5.02/5.38
% 5.02/5.38 % Rats_no_top_le
% 5.02/5.38 thf(fact_10158_Rats__no__bot__less,axiom,
% 5.02/5.38 ! [X2: real] :
% 5.02/5.38 ? [X5: real] :
% 5.02/5.38 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.02/5.38 & ( ord_less_real @ X5 @ X2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % Rats_no_bot_less
% 5.02/5.38 thf(fact_10159_Rats__dense__in__real,axiom,
% 5.02/5.38 ! [X2: real,Y: real] :
% 5.02/5.38 ( ( ord_less_real @ X2 @ Y )
% 5.02/5.38 => ? [X5: real] :
% 5.02/5.38 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.02/5.38 & ( ord_less_real @ X2 @ X5 )
% 5.02/5.38 & ( ord_less_real @ X5 @ Y ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Rats_dense_in_real
% 5.02/5.38 thf(fact_10160_Rats__eq__int__div__int,axiom,
% 5.02/5.38 ( field_5140801741446780682s_real
% 5.02/5.38 = ( collect_real
% 5.02/5.38 @ ^ [Uu3: real] :
% 5.02/5.38 ? [I5: int,J3: int] :
% 5.02/5.38 ( ( Uu3
% 5.02/5.38 = ( divide_divide_real @ ( ring_1_of_int_real @ I5 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.02/5.38 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % Rats_eq_int_div_int
% 5.02/5.38 thf(fact_10161_sup__int__def,axiom,
% 5.02/5.38 sup_sup_int = ord_max_int ).
% 5.02/5.38
% 5.02/5.38 % sup_int_def
% 5.02/5.38 thf(fact_10162_sup__nat__def,axiom,
% 5.02/5.38 sup_sup_nat = ord_max_nat ).
% 5.02/5.38
% 5.02/5.38 % sup_nat_def
% 5.02/5.38 thf(fact_10163_atLeastLessThan__add__Un,axiom,
% 5.02/5.38 ! [I3: nat,J: nat,K: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.38 => ( ( set_or4665077453230672383an_nat @ I3 @ ( plus_plus_nat @ J @ K ) )
% 5.02/5.38 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I3 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastLessThan_add_Un
% 5.02/5.38 thf(fact_10164_powr__real__of__int_H,axiom,
% 5.02/5.38 ! [X2: real,N2: int] :
% 5.02/5.38 ( ( ord_less_eq_real @ zero_zero_real @ X2 )
% 5.02/5.38 => ( ( ( X2 != zero_zero_real )
% 5.02/5.38 | ( ord_less_int @ zero_zero_int @ N2 ) )
% 5.02/5.38 => ( ( powr_real @ X2 @ ( ring_1_of_int_real @ N2 ) )
% 5.02/5.38 = ( power_int_real @ X2 @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % powr_real_of_int'
% 5.02/5.38 thf(fact_10165_pairs__le__eq__Sigma,axiom,
% 5.02/5.38 ! [M: nat] :
% 5.02/5.38 ( ( collec3392354462482085612at_nat
% 5.02/5.38 @ ( produc6081775807080527818_nat_o
% 5.02/5.38 @ ^ [I5: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I5 @ J3 ) @ M ) ) )
% 5.02/5.38 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.02/5.38 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % pairs_le_eq_Sigma
% 5.02/5.38 thf(fact_10166_remdups__upt,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( remdups_nat @ ( upt @ M @ N2 ) )
% 5.02/5.38 = ( upt @ M @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % remdups_upt
% 5.02/5.38 thf(fact_10167_length__upt,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( size_size_list_nat @ ( upt @ I3 @ J ) )
% 5.02/5.38 = ( minus_minus_nat @ J @ I3 ) ) ).
% 5.02/5.38
% 5.02/5.38 % length_upt
% 5.02/5.38 thf(fact_10168_upt__conv__Nil,axiom,
% 5.02/5.38 ! [J: nat,I3: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ J @ I3 )
% 5.02/5.38 => ( ( upt @ I3 @ J )
% 5.02/5.38 = nil_nat ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_conv_Nil
% 5.02/5.38 thf(fact_10169_sorted__list__of__set__range,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.02/5.38 = ( upt @ M @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_list_of_set_range
% 5.02/5.38 thf(fact_10170_upt__eq__Nil__conv,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( ( upt @ I3 @ J )
% 5.02/5.38 = nil_nat )
% 5.02/5.38 = ( ( J = zero_zero_nat )
% 5.02/5.38 | ( ord_less_eq_nat @ J @ I3 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_eq_Nil_conv
% 5.02/5.38 thf(fact_10171_nth__upt,axiom,
% 5.02/5.38 ! [I3: nat,K: nat,J: nat] :
% 5.02/5.38 ( ( ord_less_nat @ ( plus_plus_nat @ I3 @ K ) @ J )
% 5.02/5.38 => ( ( nth_nat @ ( upt @ I3 @ J ) @ K )
% 5.02/5.38 = ( plus_plus_nat @ I3 @ K ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % nth_upt
% 5.02/5.38 thf(fact_10172_upt__rec__numeral,axiom,
% 5.02/5.38 ! [M: num,N2: num] :
% 5.02/5.38 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.38 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.38 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.38 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.02/5.38 = nil_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_rec_numeral
% 5.02/5.38 thf(fact_10173_map__Suc__upt,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( map_nat_nat @ suc @ ( upt @ M @ N2 ) )
% 5.02/5.38 = ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % map_Suc_upt
% 5.02/5.38 thf(fact_10174_map__add__upt,axiom,
% 5.02/5.38 ! [N2: nat,M: nat] :
% 5.02/5.38 ( ( map_nat_nat
% 5.02/5.38 @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ N2 )
% 5.02/5.38 @ ( upt @ zero_zero_nat @ M ) )
% 5.02/5.38 = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % map_add_upt
% 5.02/5.38 thf(fact_10175_distinct__upt,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] : ( distinct_nat @ ( upt @ I3 @ J ) ) ).
% 5.02/5.38
% 5.02/5.38 % distinct_upt
% 5.02/5.38 thf(fact_10176_upt__conv__Cons__Cons,axiom,
% 5.02/5.38 ! [M: nat,N2: nat,Ns: list_nat,Q2: nat] :
% 5.02/5.38 ( ( ( cons_nat @ M @ ( cons_nat @ N2 @ Ns ) )
% 5.02/5.38 = ( upt @ M @ Q2 ) )
% 5.02/5.38 = ( ( cons_nat @ N2 @ Ns )
% 5.02/5.38 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_conv_Cons_Cons
% 5.02/5.38 thf(fact_10177_upt__0,axiom,
% 5.02/5.38 ! [I3: nat] :
% 5.02/5.38 ( ( upt @ I3 @ zero_zero_nat )
% 5.02/5.38 = nil_nat ) ).
% 5.02/5.38
% 5.02/5.38 % upt_0
% 5.02/5.38 thf(fact_10178_atLeast__upt,axiom,
% 5.02/5.38 ( set_ord_lessThan_nat
% 5.02/5.38 = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeast_upt
% 5.02/5.38 thf(fact_10179_atLeastLessThan__upt,axiom,
% 5.02/5.38 ( set_or4665077453230672383an_nat
% 5.02/5.38 = ( ^ [I5: nat,J3: nat] : ( set_nat2 @ ( upt @ I5 @ J3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastLessThan_upt
% 5.02/5.38 thf(fact_10180_greaterThanAtMost__upt,axiom,
% 5.02/5.38 ( set_or6659071591806873216st_nat
% 5.02/5.38 = ( ^ [N3: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N3 ) @ ( suc @ M6 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % greaterThanAtMost_upt
% 5.02/5.38 thf(fact_10181_greaterThanLessThan__upt,axiom,
% 5.02/5.38 ( set_or5834768355832116004an_nat
% 5.02/5.38 = ( ^ [N3: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N3 ) @ M6 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % greaterThanLessThan_upt
% 5.02/5.38 thf(fact_10182_atLeastAtMost__upt,axiom,
% 5.02/5.38 ( set_or1269000886237332187st_nat
% 5.02/5.38 = ( ^ [N3: nat,M6: nat] : ( set_nat2 @ ( upt @ N3 @ ( suc @ M6 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atLeastAtMost_upt
% 5.02/5.38 thf(fact_10183_atMost__upto,axiom,
% 5.02/5.38 ( set_ord_atMost_nat
% 5.02/5.38 = ( ^ [N3: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N3 ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % atMost_upto
% 5.02/5.38 thf(fact_10184_upt__conv__Cons,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I3 @ J )
% 5.02/5.38 => ( ( upt @ I3 @ J )
% 5.02/5.38 = ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_conv_Cons
% 5.02/5.38 thf(fact_10185_map__decr__upt,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( map_nat_nat
% 5.02/5.38 @ ^ [N3: nat] : ( minus_minus_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 5.02/5.38 @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.02/5.38 = ( upt @ M @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % map_decr_upt
% 5.02/5.38 thf(fact_10186_upt__add__eq__append,axiom,
% 5.02/5.38 ! [I3: nat,J: nat,K: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.38 => ( ( upt @ I3 @ ( plus_plus_nat @ J @ K ) )
% 5.02/5.38 = ( append_nat @ ( upt @ I3 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_add_eq_append
% 5.02/5.38 thf(fact_10187_upt__eq__Cons__conv,axiom,
% 5.02/5.38 ! [I3: nat,J: nat,X2: nat,Xs: list_nat] :
% 5.02/5.38 ( ( ( upt @ I3 @ J )
% 5.02/5.38 = ( cons_nat @ X2 @ Xs ) )
% 5.02/5.38 = ( ( ord_less_nat @ I3 @ J )
% 5.02/5.38 & ( I3 = X2 )
% 5.02/5.38 & ( ( upt @ ( plus_plus_nat @ I3 @ one_one_nat ) @ J )
% 5.02/5.38 = Xs ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_eq_Cons_conv
% 5.02/5.38 thf(fact_10188_upt__rec,axiom,
% 5.02/5.38 ( upt
% 5.02/5.38 = ( ^ [I5: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I5 @ J3 ) @ ( cons_nat @ I5 @ ( upt @ ( suc @ I5 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_rec
% 5.02/5.38 thf(fact_10189_upt__Suc,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.38 => ( ( upt @ I3 @ ( suc @ J ) )
% 5.02/5.38 = ( append_nat @ ( upt @ I3 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.02/5.38 & ( ~ ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.38 => ( ( upt @ I3 @ ( suc @ J ) )
% 5.02/5.38 = nil_nat ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_Suc
% 5.02/5.38 thf(fact_10190_upt__Suc__append,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ I3 @ J )
% 5.02/5.38 => ( ( upt @ I3 @ ( suc @ J ) )
% 5.02/5.38 = ( append_nat @ ( upt @ I3 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % upt_Suc_append
% 5.02/5.38 thf(fact_10191_list__encode_Opelims,axiom,
% 5.02/5.38 ! [X2: list_nat,Y: nat] :
% 5.02/5.38 ( ( ( nat_list_encode @ X2 )
% 5.02/5.38 = Y )
% 5.02/5.38 => ( ( accp_list_nat @ nat_list_encode_rel @ X2 )
% 5.02/5.38 => ( ( ( X2 = nil_nat )
% 5.02/5.38 => ( ( Y = zero_zero_nat )
% 5.02/5.38 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.02/5.38 => ~ ! [X5: nat,Xs2: list_nat] :
% 5.02/5.38 ( ( X2
% 5.02/5.38 = ( cons_nat @ X5 @ Xs2 ) )
% 5.02/5.38 => ( ( Y
% 5.02/5.38 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 5.02/5.38 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs2 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % list_encode.pelims
% 5.02/5.38 thf(fact_10192_sum__list__upt,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ M @ N2 )
% 5.02/5.38 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 5.02/5.38 = ( groups3542108847815614940at_nat
% 5.02/5.38 @ ^ [X: nat] : X
% 5.02/5.38 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sum_list_upt
% 5.02/5.38 thf(fact_10193_card__length__sum__list__rec,axiom,
% 5.02/5.38 ! [M: nat,N4: nat] :
% 5.02/5.38 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.02/5.38 => ( ( finite_card_list_nat
% 5.02/5.38 @ ( collect_list_nat
% 5.02/5.38 @ ^ [L2: list_nat] :
% 5.02/5.38 ( ( ( size_size_list_nat @ L2 )
% 5.02/5.38 = M )
% 5.02/5.38 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.02/5.38 = N4 ) ) ) )
% 5.02/5.38 = ( plus_plus_nat
% 5.02/5.38 @ ( finite_card_list_nat
% 5.02/5.38 @ ( collect_list_nat
% 5.02/5.38 @ ^ [L2: list_nat] :
% 5.02/5.38 ( ( ( size_size_list_nat @ L2 )
% 5.02/5.38 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.02/5.38 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.02/5.38 = N4 ) ) ) )
% 5.02/5.38 @ ( finite_card_list_nat
% 5.02/5.38 @ ( collect_list_nat
% 5.02/5.38 @ ^ [L2: list_nat] :
% 5.02/5.38 ( ( ( size_size_list_nat @ L2 )
% 5.02/5.38 = M )
% 5.02/5.38 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.02/5.38 = N4 ) ) ) ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_length_sum_list_rec
% 5.02/5.38 thf(fact_10194_card__length__sum__list,axiom,
% 5.02/5.38 ! [M: nat,N4: nat] :
% 5.02/5.38 ( ( finite_card_list_nat
% 5.02/5.38 @ ( collect_list_nat
% 5.02/5.38 @ ^ [L2: list_nat] :
% 5.02/5.38 ( ( ( size_size_list_nat @ L2 )
% 5.02/5.38 = M )
% 5.02/5.38 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.02/5.38 = N4 ) ) ) )
% 5.02/5.38 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 5.02/5.38
% 5.02/5.38 % card_length_sum_list
% 5.02/5.38 thf(fact_10195_sorted__upt,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_upt
% 5.02/5.38 thf(fact_10196_sorted__wrt__upt,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_wrt_upt
% 5.02/5.38 thf(fact_10197_sorted__wrt__less__idx,axiom,
% 5.02/5.38 ! [Ns: list_nat,I3: nat] :
% 5.02/5.38 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.02/5.38 => ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Ns ) )
% 5.02/5.38 => ( ord_less_eq_nat @ I3 @ ( nth_nat @ Ns @ I3 ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_wrt_less_idx
% 5.02/5.38 thf(fact_10198_sorted__wrt__upto,axiom,
% 5.02/5.38 ! [I3: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I3 @ J ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_wrt_upto
% 5.02/5.38 thf(fact_10199_sorted__upto,axiom,
% 5.02/5.38 ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % sorted_upto
% 5.02/5.38 thf(fact_10200_tl__upt,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( tl_nat @ ( upt @ M @ N2 ) )
% 5.02/5.38 = ( upt @ ( suc @ M ) @ N2 ) ) ).
% 5.02/5.38
% 5.02/5.38 % tl_upt
% 5.02/5.38 thf(fact_10201_hd__upt,axiom,
% 5.02/5.38 ! [I3: nat,J: nat] :
% 5.02/5.38 ( ( ord_less_nat @ I3 @ J )
% 5.02/5.38 => ( ( hd_nat @ ( upt @ I3 @ J ) )
% 5.02/5.38 = I3 ) ) ).
% 5.02/5.38
% 5.02/5.38 % hd_upt
% 5.02/5.38 thf(fact_10202_min__Suc__Suc,axiom,
% 5.02/5.38 ! [M: nat,N2: nat] :
% 5.02/5.38 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.02/5.38 = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % min_Suc_Suc
% 5.02/5.38 thf(fact_10203_min__0R,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 5.02/5.38 = zero_zero_nat ) ).
% 5.02/5.38
% 5.02/5.38 % min_0R
% 5.02/5.38 thf(fact_10204_min__0L,axiom,
% 5.02/5.38 ! [N2: nat] :
% 5.02/5.38 ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 5.02/5.38 = zero_zero_nat ) ).
% 5.02/5.38
% 5.02/5.38 % min_0L
% 5.02/5.38 thf(fact_10205_min__Suc__numeral,axiom,
% 5.02/5.38 ! [N2: nat,K: num] :
% 5.02/5.38 ( ( ord_min_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.02/5.38 = ( suc @ ( ord_min_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % min_Suc_numeral
% 5.02/5.38 thf(fact_10206_min__numeral__Suc,axiom,
% 5.02/5.38 ! [K: num,N2: nat] :
% 5.02/5.38 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.02/5.38 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % min_numeral_Suc
% 5.02/5.38 thf(fact_10207_concat__bit__assoc__sym,axiom,
% 5.02/5.38 ! [M: nat,N2: nat,K: int,L: int,R2: int] :
% 5.02/5.38 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N2 @ K @ L ) @ R2 )
% 5.02/5.38 = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N2 ) @ L @ R2 ) ) ) ).
% 5.02/5.38
% 5.02/5.38 % concat_bit_assoc_sym
% 5.02/5.38 thf(fact_10208_min__diff,axiom,
% 5.02/5.38 ! [M: nat,I3: nat,N2: nat] :
% 5.02/5.38 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I3 ) @ ( minus_minus_nat @ N2 @ I3 ) )
% 5.02/5.38 = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I3 ) ) ).
% 5.02/5.38
% 5.02/5.38 % min_diff
% 5.02/5.38
% 5.02/5.38 % Helper facts (41)
% 5.02/5.38 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.02/5.38 ! [X2: int,Y: int] :
% 5.02/5.38 ( ( if_int @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.02/5.38 ! [X2: int,Y: int] :
% 5.02/5.38 ( ( if_int @ $true @ X2 @ Y )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.02/5.38 ! [X2: nat,Y: nat] :
% 5.02/5.38 ( ( if_nat @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.02/5.38 ! [X2: nat,Y: nat] :
% 5.02/5.38 ( ( if_nat @ $true @ X2 @ Y )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.02/5.38 ! [X2: num,Y: num] :
% 5.02/5.38 ( ( if_num @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.02/5.38 ! [X2: num,Y: num] :
% 5.02/5.38 ( ( if_num @ $true @ X2 @ Y )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.02/5.38 ! [X2: rat,Y: rat] :
% 5.02/5.38 ( ( if_rat @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.02/5.38 ! [X2: rat,Y: rat] :
% 5.02/5.38 ( ( if_rat @ $true @ X2 @ Y )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.02/5.38 ! [X2: real,Y: real] :
% 5.02/5.38 ( ( if_real @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.02/5.38 ! [X2: real,Y: real] :
% 5.02/5.38 ( ( if_real @ $true @ X2 @ Y )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( if_complex @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.02/5.38 ! [X2: complex,Y: complex] :
% 5.02/5.38 ( ( if_complex @ $true @ X2 @ Y )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.02/5.38 ! [X2: code_integer,Y: code_integer] :
% 5.02/5.38 ( ( if_Code_integer @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.02/5.38 ! [X2: code_integer,Y: code_integer] :
% 5.02/5.38 ( ( if_Code_integer @ $true @ X2 @ Y )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.02/5.38 ! [X2: set_int,Y: set_int] :
% 5.02/5.38 ( ( if_set_int @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.02/5.38 ! [X2: set_int,Y: set_int] :
% 5.02/5.38 ( ( if_set_int @ $true @ X2 @ Y )
% 5.02/5.38 = X2 ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.02/5.38 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.38 ( ( if_set_nat @ $false @ X2 @ Y )
% 5.02/5.38 = Y ) ).
% 5.02/5.38
% 5.02/5.38 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.02/5.38 ! [X2: set_nat,Y: set_nat] :
% 5.02/5.39 ( ( if_set_nat @ $true @ X2 @ Y )
% 5.02/5.39 = X2 ) ).
% 5.02/5.39
% 5.02/5.39 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.02/5.39 ! [X2: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.02/5.39 ( ( if_VEBT_VEBT @ $false @ X2 @ Y )
% 5.02/5.39 = Y ) ).
% 5.02/5.39
% 5.02/5.39 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.02/5.39 ! [X2: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.02/5.39 ( ( if_VEBT_VEBT @ $true @ X2 @ Y )
% 5.02/5.39 = X2 ) ).
% 5.02/5.39
% 5.02/5.39 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.02/5.39 ! [X2: list_int,Y: list_int] :
% 5.02/5.39 ( ( if_list_int @ $false @ X2 @ Y )
% 5.02/5.39 = Y ) ).
% 5.02/5.39
% 5.02/5.39 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.02/5.39 ! [X2: list_int,Y: list_int] :
% 5.02/5.39 ( ( if_list_int @ $true @ X2 @ Y )
% 5.02/5.39 = X2 ) ).
% 5.02/5.39
% 5.02/5.39 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.02/5.39 ! [X2: list_nat,Y: list_nat] :
% 5.02/5.39 ( ( if_list_nat @ $false @ X2 @ Y )
% 5.02/5.39 = Y ) ).
% 5.02/5.39
% 5.02/5.39 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.02/5.39 ! [X2: list_nat,Y: list_nat] :
% 5.02/5.39 ( ( if_list_nat @ $true @ X2 @ Y )
% 5.02/5.39 = X2 ) ).
% 5.02/5.39
% 5.02/5.39 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.31/6.59 ! [X2: int > int,Y: int > int] :
% 6.31/6.59 ( ( if_int_int @ $false @ X2 @ Y )
% 6.31/6.59 = Y ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.31/6.59 ! [X2: int > int,Y: int > int] :
% 6.31/6.59 ( ( if_int_int @ $true @ X2 @ Y )
% 6.31/6.59 = X2 ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 6.31/6.59 ! [X2: option_num,Y: option_num] :
% 6.31/6.59 ( ( if_option_num @ $false @ X2 @ Y )
% 6.31/6.59 = Y ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 6.31/6.59 ! [X2: option_num,Y: option_num] :
% 6.31/6.59 ( ( if_option_num @ $true @ X2 @ Y )
% 6.31/6.59 = X2 ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.31/6.59 ! [X2: product_prod_int_int,Y: product_prod_int_int] :
% 6.31/6.59 ( ( if_Pro3027730157355071871nt_int @ $false @ X2 @ Y )
% 6.31/6.59 = Y ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.31/6.59 ! [X2: product_prod_int_int,Y: product_prod_int_int] :
% 6.31/6.59 ( ( if_Pro3027730157355071871nt_int @ $true @ X2 @ Y )
% 6.31/6.59 = X2 ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.31/6.59 ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 6.31/6.59 ( ( if_Pro6206227464963214023at_nat @ $false @ X2 @ Y )
% 6.31/6.59 = Y ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.31/6.59 ! [X2: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 6.31/6.59 ( ( if_Pro6206227464963214023at_nat @ $true @ X2 @ Y )
% 6.31/6.59 = X2 ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 6.31/6.59 ! [X2: nat > int > int,Y: nat > int > int] :
% 6.31/6.59 ( ( if_nat_int_int @ $false @ X2 @ Y )
% 6.31/6.59 = Y ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 6.31/6.59 ! [X2: nat > int > int,Y: nat > int > int] :
% 6.31/6.59 ( ( if_nat_int_int @ $true @ X2 @ Y )
% 6.31/6.59 = X2 ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.31/6.59 ! [X2: nat > nat > nat,Y: nat > nat > nat] :
% 6.31/6.59 ( ( if_nat_nat_nat @ $false @ X2 @ Y )
% 6.31/6.59 = Y ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.31/6.59 ! [X2: nat > nat > nat,Y: nat > nat > nat] :
% 6.31/6.59 ( ( if_nat_nat_nat @ $true @ X2 @ Y )
% 6.31/6.59 = X2 ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.31/6.59 ! [X2: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.31/6.59 ( ( if_Pro5737122678794959658eger_o @ $false @ X2 @ Y )
% 6.31/6.59 = Y ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.31/6.59 ! [X2: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.31/6.59 ( ( if_Pro5737122678794959658eger_o @ $true @ X2 @ Y )
% 6.31/6.59 = X2 ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.31/6.59 ! [P: $o] :
% 6.31/6.59 ( ( P = $true )
% 6.31/6.59 | ( P = $false ) ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.31/6.59 ! [X2: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.31/6.59 ( ( if_Pro6119634080678213985nteger @ $false @ X2 @ Y )
% 6.31/6.59 = Y ) ).
% 6.31/6.59
% 6.31/6.59 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.31/6.59 ! [X2: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.31/6.59 ( ( if_Pro6119634080678213985nteger @ $true @ X2 @ Y )
% 6.31/6.59 = X2 ) ).
% 6.31/6.59
% 6.31/6.59 % Conjectures (1)
% 6.31/6.59 thf(conj_0,conjecture,
% 6.31/6.59 vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ ya ).
% 6.31/6.59
% 6.31/6.59 %------------------------------------------------------------------------------
% 6.31/6.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.WsRwshhXsD/cvc5---1.0.5_13355.p...
% 6.31/6.59 (declare-sort $$unsorted 0)
% 6.31/6.59 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.31/6.59 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.31/6.59 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.31/6.59 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.31/6.59 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.31/6.59 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.31/6.59 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.31/6.59 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.31/6.59 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.31/6.59 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.31/6.59 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.31/6.59 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.31/6.59 (declare-sort tptp.list_P8526636022914148096eger_o 0)
% 6.31/6.59 (declare-sort tptp.set_Pr448751882837621926eger_o 0)
% 6.31/6.59 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.31/6.59 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.31/6.59 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.31/6.59 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.31/6.59 (declare-sort tptp.set_Pr8218934625190621173um_num 0)
% 6.31/6.59 (declare-sort tptp.set_Pr6200539531224447659at_num 0)
% 6.31/6.59 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.31/6.59 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.31/6.59 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.31/6.59 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.31/6.59 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.31/6.59 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.31/6.59 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.31/6.59 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.31/6.59 (declare-sort tptp.product_prod_num_num 0)
% 6.31/6.59 (declare-sort tptp.product_prod_nat_num 0)
% 6.31/6.59 (declare-sort tptp.product_prod_nat_nat 0)
% 6.31/6.59 (declare-sort tptp.product_prod_int_int 0)
% 6.31/6.59 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.31/6.59 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.31/6.59 (declare-sort tptp.set_list_nat 0)
% 6.31/6.59 (declare-sort tptp.product_prod_o_nat 0)
% 6.31/6.59 (declare-sort tptp.product_prod_o_int 0)
% 6.31/6.59 (declare-sort tptp.list_set_nat 0)
% 6.31/6.59 (declare-sort tptp.list_Code_integer 0)
% 6.31/6.59 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.31/6.59 (declare-sort tptp.set_set_nat 0)
% 6.31/6.59 (declare-sort tptp.set_Code_integer 0)
% 6.31/6.59 (declare-sort tptp.set_Product_unit 0)
% 6.31/6.59 (declare-sort tptp.list_complex 0)
% 6.31/6.59 (declare-sort tptp.product_prod_o_o 0)
% 6.31/6.59 (declare-sort tptp.set_complex 0)
% 6.31/6.59 (declare-sort tptp.filter_real 0)
% 6.31/6.59 (declare-sort tptp.option_num 0)
% 6.31/6.59 (declare-sort tptp.filter_nat 0)
% 6.31/6.59 (declare-sort tptp.set_char 0)
% 6.31/6.59 (declare-sort tptp.list_real 0)
% 6.31/6.59 (declare-sort tptp.set_real 0)
% 6.31/6.59 (declare-sort tptp.list_num 0)
% 6.31/6.59 (declare-sort tptp.list_nat 0)
% 6.31/6.59 (declare-sort tptp.list_int 0)
% 6.31/6.59 (declare-sort tptp.vEBT_VEBT 0)
% 6.31/6.59 (declare-sort tptp.set_rat 0)
% 6.31/6.59 (declare-sort tptp.set_num 0)
% 6.31/6.59 (declare-sort tptp.set_nat 0)
% 6.31/6.59 (declare-sort tptp.set_int 0)
% 6.31/6.59 (declare-sort tptp.code_integer 0)
% 6.31/6.59 (declare-sort tptp.extended_enat 0)
% 6.31/6.59 (declare-sort tptp.list_o 0)
% 6.31/6.59 (declare-sort tptp.complex 0)
% 6.31/6.59 (declare-sort tptp.set_o 0)
% 6.31/6.59 (declare-sort tptp.char 0)
% 6.31/6.59 (declare-sort tptp.real 0)
% 6.31/6.59 (declare-sort tptp.rat 0)
% 6.31/6.59 (declare-sort tptp.num 0)
% 6.31/6.59 (declare-sort tptp.nat 0)
% 6.31/6.59 (declare-sort tptp.int 0)
% 6.31/6.59 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.31/6.59 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.31/6.59 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.31/6.59 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.31/6.59 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.31/6.59 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.31/6.59 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se1080825931792720795nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.31/6.59 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.31/6.59 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.31/6.59 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.31/6.59 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.31/6.59 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.31/6.59 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.31/6.59 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.31/6.59 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.31/6.59 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.31/6.59 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.31/6.59 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.31/6.59 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.31/6.59 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.31/6.59 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.31/6.59 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.31/6.59 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.31/6.59 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.31/6.59 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.31/6.59 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.31/6.59 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.31/6.59 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.31/6.59 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.31/6.59 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.31/6.59 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.31/6.59 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.31/6.59 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.31/6.59 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.31/6.59 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.31/6.59 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.31/6.59 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.31/6.59 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.31/6.59 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.31/6.59 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.31/6.59 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.31/6.59 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.31/6.59 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.31/6.59 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.31/6.59 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.31/6.59 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.31/6.59 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.31/6.59 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.31/6.59 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.31/6.59 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.31/6.59 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.31/6.59 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.31/6.59 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.31/6.59 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.31/6.59 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.31/6.59 (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)
% 6.31/6.59 (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)
% 6.31/6.59 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.31/6.59 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.id_o (Bool) Bool)
% 6.31/6.59 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.31/6.59 (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)
% 6.31/6.59 (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)
% 6.31/6.59 (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)
% 6.31/6.59 (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)
% 6.31/6.59 (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)
% 6.31/6.59 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.31/6.59 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.31/6.59 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.31/6.59 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.31/6.59 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.59 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.31/6.59 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.31/6.59 (declare-fun tptp.one_one_int () tptp.int)
% 6.31/6.59 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.31/6.59 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.31/6.59 (declare-fun tptp.one_one_real () tptp.real)
% 6.31/6.59 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.59 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.31/6.59 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.31/6.59 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.31/6.59 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.31/6.59 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.31/6.59 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.31/6.59 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.31/6.59 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.31/6.59 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.31/6.59 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.31/6.59 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.31/6.59 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.31/6.59 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.31/6.59 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups5107569545109728110t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups861055069439313189ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups225925009352817453ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.31/6.59 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.31/6.59 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.31/6.59 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups4075276357253098568at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups4696554848551431203al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.31/6.59 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.31/6.59 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups1092910753850256091omplex ((-> tptp.set_nat tptp.complex) tptp.set_set_nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.groups3619160379726066777t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.31/6.59 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.31/6.59 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.31/6.59 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.if_nat_int_int (Bool (-> tptp.nat tptp.int tptp.int) (-> tptp.nat tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.if_nat_nat_nat (Bool (-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.31/6.59 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.31/6.59 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.31/6.59 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.31/6.59 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.31/6.59 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.31/6.59 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.31/6.59 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.31/6.59 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.31/6.59 (declare-fun tptp.power_int_real (tptp.real tptp.int) tptp.real)
% 6.31/6.59 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.31/6.59 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.31/6.59 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.31/6.59 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.31/6.59 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.31/6.59 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.31/6.59 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 6.31/6.59 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 6.31/6.59 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.31/6.59 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.nil_int () tptp.list_int)
% 6.31/6.59 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.31/6.59 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.31/6.59 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.31/6.59 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.31/6.59 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.31/6.59 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.31/6.59 (declare-fun tptp.list_update_set_nat (tptp.list_set_nat tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.31/6.59 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.31/6.59 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.31/6.59 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.31/6.59 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.31/6.59 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.31/6.59 (declare-fun tptp.nth_Pr8522763379788166057eger_o (tptp.list_P8526636022914148096eger_o tptp.nat) tptp.produc6271795597528267376eger_o)
% 6.31/6.59 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.31/6.59 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.31/6.59 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.31/6.59 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.31/6.59 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.31/6.59 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.31/6.59 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.31/6.59 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.31/6.59 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.31/6.59 (declare-fun tptp.produc3607205314601156340eger_o (tptp.list_Code_integer tptp.list_o) tptp.list_P8526636022914148096eger_o)
% 6.31/6.59 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.31/6.59 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.31/6.59 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.31/6.59 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.31/6.59 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.31/6.59 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.31/6.59 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.31/6.59 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.31/6.59 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.31/6.59 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.31/6.59 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.31/6.59 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.31/6.59 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.31/6.59 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.31/6.59 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.31/6.59 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.31/6.59 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.31/6.59 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.31/6.59 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.semiring_1_Nats_int () tptp.set_int)
% 6.31/6.59 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.31/6.59 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.31/6.59 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.31/6.59 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.31/6.59 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.31/6.59 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.one () tptp.num)
% 6.31/6.59 (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)
% 6.31/6.59 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.31/6.59 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.31/6.59 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.31/6.59 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.31/6.59 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.31/6.59 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.31/6.59 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.31/6.59 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.31/6.59 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.31/6.59 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.none_num () tptp.option_num)
% 6.31/6.59 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.31/6.59 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.31/6.59 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.31/6.59 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.31/6.59 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.31/6.59 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.31/6.59 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.bot_bo4731626569425807221er_o_o (tptp.code_integer Bool) Bool)
% 6.31/6.59 (declare-fun tptp.bot_bot_int_int_o (tptp.int tptp.int) Bool)
% 6.31/6.59 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.bot_bot_nat_num_o (tptp.nat tptp.num) Bool)
% 6.31/6.59 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.bot_bot_num_num_o (tptp.num tptp.num) Bool)
% 6.31/6.59 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.31/6.59 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.31/6.59 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.31/6.59 (declare-fun tptp.bot_bo5379713665208646970eger_o () tptp.set_Pr448751882837621926eger_o)
% 6.31/6.59 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 6.31/6.59 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.31/6.59 (declare-fun tptp.bot_bo7038385379056416535at_num () tptp.set_Pr6200539531224447659at_num)
% 6.31/6.59 (declare-fun tptp.bot_bo9056780473022590049um_num () tptp.set_Pr8218934625190621173um_num)
% 6.31/6.59 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.31/6.59 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.31/6.59 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le2162486998276636481er_o_o ((-> tptp.code_integer Bool Bool) (-> tptp.code_integer Bool Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le4573692005234683329plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le2646555220125990790_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le3404735783095501756_num_o ((-> tptp.nat tptp.num Bool) (-> tptp.nat tptp.num Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le6124364862034508274_num_o ((-> tptp.num tptp.num Bool) (-> tptp.num tptp.num Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le8980329558974975238eger_o (tptp.set_Pr448751882837621926eger_o tptp.set_Pr448751882837621926eger_o) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le8085105155179020875at_num (tptp.set_Pr6200539531224447659at_num tptp.set_Pr6200539531224447659at_num) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le880128212290418581um_num (tptp.set_Pr8218934625190621173um_num tptp.set_Pr8218934625190621173um_num) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.31/6.59 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.31/6.59 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.ord_max_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.ord_max_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.31/6.59 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.31/6.59 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.31/6.59 (declare-fun tptp.top_top_set_int () tptp.set_int)
% 6.31/6.59 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.31/6.59 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.31/6.59 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.31/6.59 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.31/6.59 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.31/6.59 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.31/6.59 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.31/6.59 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.31/6.59 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.31/6.59 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.31/6.59 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.31/6.59 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.31/6.59 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.31/6.59 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.31/6.59 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.31/6.59 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.31/6.59 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.31/6.59 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.31/6.59 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.31/6.59 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.31/6.59 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.31/6.59 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.31/6.59 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.31/6.59 (declare-fun tptp.produc7828578312038201481er_o_o ((-> tptp.code_integer Bool Bool) tptp.produc6271795597528267376eger_o) Bool)
% 6.31/6.59 (declare-fun tptp.produc1043322548047392435omplex ((-> tptp.code_integer Bool tptp.set_complex) tptp.produc6271795597528267376eger_o) tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.produc1253318751659547953et_int ((-> tptp.code_integer Bool tptp.set_int) tptp.produc6271795597528267376eger_o) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.produc5431169771168744661et_nat ((-> tptp.code_integer Bool tptp.set_nat) tptp.produc6271795597528267376eger_o) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.produc242741666403216561t_real ((-> tptp.code_integer Bool tptp.set_real) tptp.produc6271795597528267376eger_o) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.31/6.59 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.31/6.59 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.31/6.59 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.31/6.59 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.31/6.59 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.31/6.59 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.31/6.59 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.31/6.59 (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)
% 6.31/6.59 (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)
% 6.31/6.59 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.31/6.59 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.31/6.59 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.produc4927758841916487424_num_o ((-> tptp.nat tptp.num Bool) tptp.product_prod_nat_num) Bool)
% 6.31/6.59 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.31/6.59 (declare-fun tptp.produc6231982587499038204omplex ((-> tptp.nat tptp.num tptp.set_complex) tptp.product_prod_nat_num) tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.produc1435849484188172666t_real ((-> tptp.nat tptp.num tptp.set_real) tptp.product_prod_nat_num) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.produc5703948589228662326_num_o ((-> tptp.num tptp.num Bool) tptp.product_prod_num_num) Bool)
% 6.31/6.59 (declare-fun tptp.produc2866383454006189126omplex ((-> tptp.num tptp.num tptp.set_complex) tptp.product_prod_num_num) tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.produc6406642877701697732et_int ((-> tptp.num tptp.num tptp.set_int) tptp.product_prod_num_num) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.produc1361121860356118632et_nat ((-> tptp.num tptp.num tptp.set_nat) tptp.product_prod_num_num) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.produc8296048397933160132t_real ((-> tptp.num tptp.num tptp.set_real) tptp.product_prod_num_num) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.31/6.59 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.31/6.59 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.31/6.59 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.31/6.59 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.31/6.59 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.31/6.59 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 6.31/6.59 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.31/6.59 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.31/6.59 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.31/6.59 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.31/6.59 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.31/6.59 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.31/6.59 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.31/6.59 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.31/6.59 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.31/6.59 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.31/6.59 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.31/6.59 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.31/6.59 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.31/6.59 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.31/6.59 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.31/6.59 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.31/6.59 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.31/6.59 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.31/6.59 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.31/6.59 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.31/6.59 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.31/6.59 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.31/6.59 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.31/6.59 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.31/6.59 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.31/6.59 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.31/6.59 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.31/6.59 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.31/6.59 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.31/6.59 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.31/6.59 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.31/6.59 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.31/6.59 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.31/6.59 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.31/6.59 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.31/6.59 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.31/6.59 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.31/6.59 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.31/6.59 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.31/6.59 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.31/6.59 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.31/6.59 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.31/6.59 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.31/6.59 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.31/6.59 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.31/6.59 (declare-fun tptp.size_char (tptp.char) tptp.nat)
% 6.31/6.59 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.31/6.59 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.31/6.59 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.31/6.59 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.31/6.59 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.31/6.59 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.31/6.59 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.31/6.59 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.31/6.59 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.31/6.59 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.31/6.59 (declare-fun tptp.topolo7278393974255667507et_nat ((-> tptp.nat tptp.set_nat)) Bool)
% 6.31/6.59 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.31/6.59 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.31/6.59 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.31/6.59 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.cot_complex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.31/6.59 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.31/6.59 (declare-fun tptp.diffs_rat ((-> tptp.nat tptp.rat) tptp.nat) tptp.rat)
% 6.31/6.59 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.pi () tptp.real)
% 6.31/6.59 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.31/6.59 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.31/6.59 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.31/6.59 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.31/6.59 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.31/6.59 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.31/6.59 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.59 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.31/6.59 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.31/6.59 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.31/6.59 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.31/6.59 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.31/6.59 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.31/6.59 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.31/6.59 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.31/6.59 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.31/6.59 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.31/6.59 (declare-fun tptp.member1379723562493234055eger_o (tptp.produc6271795597528267376eger_o tptp.set_Pr448751882837621926eger_o) Bool)
% 6.31/6.59 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.31/6.59 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.31/6.59 (declare-fun tptp.member9148766508732265716at_num (tptp.product_prod_nat_num tptp.set_Pr6200539531224447659at_num) Bool)
% 6.31/6.59 (declare-fun tptp.member7279096912039735102um_num (tptp.product_prod_num_num tptp.set_Pr8218934625190621173um_num) Bool)
% 6.31/6.59 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.31/6.59 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.31/6.59 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.31/6.59 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.31/6.59 (declare-fun tptp.deg () tptp.nat)
% 6.31/6.59 (declare-fun tptp.m () tptp.nat)
% 6.31/6.59 (declare-fun tptp.ma () tptp.nat)
% 6.31/6.59 (declare-fun tptp.mi () tptp.nat)
% 6.31/6.59 (declare-fun tptp.na () tptp.nat)
% 6.31/6.59 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.31/6.59 (declare-fun tptp.xa () tptp.nat)
% 6.31/6.59 (declare-fun tptp.ya () tptp.nat)
% 6.31/6.59 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 6.31/6.59 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T) X) (@ (@ tptp.vEBT_VEBT_membermima T) X)))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T2) tptp.zero_zero_nat))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T2) tptp.zero_zero_nat))))
% 6.31/6.59 (assert (forall ((X2 tptp.nat)) (=> (forall ((N tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N) N)))) (not (forall ((N tptp.nat)) (not (= X2 (@ (@ tptp.plus_plus_nat N) (@ tptp.suc N)))))))))
% 6.31/6.59 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.31/6.59 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary)) N2) (= Deg N2))))
% 6.31/6.59 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.31/6.59 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.31/6.59 (assert (not (= (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na) (@ (@ tptp.vEBT_VEBT_high tptp.ya) tptp.na))))
% 6.31/6.59 (assert (=> (= tptp.mi tptp.ma) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T2) X2) (@ (@ tptp.vEBT_vebt_member T2) X2)))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T2) X2) (@ (@ tptp.vEBT_vebt_member T2) X2)))))
% 6.31/6.59 (assert (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.ya) tptp.na))) (@ (@ tptp.vEBT_VEBT_low tptp.ya) tptp.na)))
% 6.31/6.59 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N2))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N2))) TreeList2) S))))))
% 6.31/6.59 (assert (@ (@ tptp.ord_less_nat tptp.xa) tptp.mi))
% 6.31/6.59 (assert (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.ya) tptp.na)))) (and (@ (@ tptp.vEBT_invar_vebt _let_1) tptp.na) (@ (@ tptp.member_VEBT_VEBT _let_1) (@ tptp.set_VEBT_VEBT2 tptp.treeList)))))
% 6.31/6.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg) (=> (= Mi Ma) (and (forall ((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))))) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))))))))
% 6.31/6.59 (assert (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa)) tptp.ya))
% 6.31/6.59 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.31/6.59 (assert (@ (@ tptp.ord_less_nat tptp.ya) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.31/6.59 (assert (=> (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.ya) tptp.na))) (@ (@ tptp.vEBT_VEBT_low tptp.ya) tptp.na)) (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.ya)))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T2)) (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T2) X_12)))))
% 6.31/6.59 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))))
% 6.31/6.59 (assert (@ (@ tptp.ord_less_nat tptp.xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.31/6.59 (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)))))
% 6.31/6.59 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y2 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y2)) (= X22 Y2))))
% 6.31/6.59 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y2)) (= X22 Y2))))
% 6.31/6.59 (assert (forall ((X1 tptp.code_integer) (X22 Bool) (Y1 tptp.code_integer) (Y2 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o X1) X22) (@ (@ tptp.produc6677183202524767010eger_o Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.31/6.59 (assert (forall ((X1 tptp.num) (X22 tptp.num) (Y1 tptp.num) (Y2 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num X1) X22) (@ (@ tptp.product_Pair_num_num Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.31/6.59 (assert (forall ((X1 tptp.nat) (X22 tptp.num) (Y1 tptp.nat) (Y2 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num X1) X22) (@ (@ tptp.product_Pair_nat_num Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.31/6.59 (assert (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat X1) X22) (@ (@ tptp.product_Pair_nat_nat Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.31/6.59 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y2)) (and (= X1 Y1) (= X22 Y2)))))
% 6.31/6.59 (assert (forall ((A tptp.code_integer) (B Bool) (A2 tptp.code_integer) (B2 Bool)) (= (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A2) B2)) (and (= A A2) (= B B2)))))
% 6.31/6.59 (assert (forall ((A tptp.num) (B tptp.num) (A2 tptp.num) (B2 tptp.num)) (= (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A2) B2)) (and (= A A2) (= B B2)))))
% 6.31/6.59 (assert (forall ((A tptp.nat) (B tptp.num) (A2 tptp.nat) (B2 tptp.num)) (= (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A2) B2)) (and (= A A2) (= B B2)))))
% 6.31/6.59 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (= (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (and (= A A2) (= B B2)))))
% 6.31/6.59 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A2) B2)) (and (= A A2) (= B B2)))))
% 6.31/6.59 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.31/6.59 (assert (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X2) (@ (@ tptp.vEBT_VEBT_membermima Tree) X2))))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT) (X2 tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T2) (not (@ (@ tptp.vEBT_vebt_member T2) X2)))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.59 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ tptp.set_complex2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N2))))))
% 6.31/6.59 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N2))))))
% 6.31/6.59 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) (@ tptp.set_set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) N2))))))
% 6.31/6.59 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N2))))))
% 6.31/6.59 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N2 tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N2))))))
% 6.31/6.59 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N2))))))
% 6.31/6.59 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N2))))))
% 6.31/6.59 (assert (forall ((X2 tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X2) D)) (@ (@ tptp.vEBT_VEBT_low X2) D)) D) X2)))
% 6.31/6.59 (assert (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m))) (and (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na)) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.ya) tptp.na)) _let_1))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (= (@ (@ tptp.vEBT_vebt_member T2) X2) (@ (@ tptp.member_nat X2) (@ tptp.vEBT_set_vebt T2))))))
% 6.31/6.59 (assert (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X3) tptp.na) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.ord_less_nat Xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (forall ((Xb tptp.nat)) (=> (@ (@ tptp.ord_less_nat Xb) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na)) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert X3) Xa)) Xb) (or (@ (@ tptp.vEBT_vebt_member X3) Xb) (= Xa Xb)))))))))))
% 6.31/6.59 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.na) (= (@ tptp.suc tptp.na) tptp.m) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.deg) (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat _let_1) tptp.m)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.na))))
% 6.31/6.59 (assert (forall ((Ma tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N2)) (@ _let_1 M))))))
% 6.31/6.59 (assert (forall ((Tree tptp.vEBT_VEBT) (X2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X2) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N2) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.59 (assert (forall ((X2 tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary))) (=> (or (= X2 Mi) (= X2 Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T2) X2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T2) Y)) X2))))))))
% 6.31/6.59 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T2) X2)) X2)))))
% 6.31/6.59 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low X3) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X3) (@ (@ tptp.ord_less_eq_nat X3) tptp.ma)))))))))
% 6.31/6.59 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.31/6.59 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.31/6.59 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.31/6.59 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 6.31/6.59 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.31/6.59 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.31/6.59 (assert (forall ((A3 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A3))) A3)))
% 6.31/6.59 (assert (forall ((A3 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A3))) A3)))
% 6.31/6.59 (assert (forall ((A3 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A3))) A3)))
% 6.31/6.59 (assert (forall ((A3 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A3))) A3)))
% 6.31/6.59 (assert (forall ((A3 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A3))) A3)))
% 6.31/6.59 (assert (forall ((A3 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A3))) A3)))
% 6.31/6.59 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_real P) (@ tptp.collect_real Q)))))
% 6.31/6.59 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 6.31/6.59 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X5 tptp.set_nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 6.31/6.59 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.31/6.59 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (= (@ P X5) (@ Q X5))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.31/6.59 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) N2) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 6.31/6.59 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert tptp.summary) X2)) Y) (or (@ (@ tptp.vEBT_vebt_member tptp.summary) Y) (= X2 Y))))))))
% 6.31/6.59 (assert (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))) (and (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)) _let_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.ya) tptp.na)) _let_1))))
% 6.31/6.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2)))))
% 6.31/6.59 (assert (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 tptp.m))) (let ((_let_3 (@ _let_1 tptp.na))) (and (not (or (= tptp.xa tptp.mi) (= tptp.xa tptp.ma))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na)) _let_2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na)) _let_2) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)) _let_3) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na)) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) _let_2))))))
% 6.31/6.59 (assert (forall ((X2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X2) N2)) (@ _let_1 N2)))))))))
% 6.31/6.59 (assert (forall ((X2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X2) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (=> (@ _let_2 N2) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X2) N2)) (@ _let_1 M)))))))))
% 6.31/6.59 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (=> (not (= X2 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va tptp.nat)) (not (= X2 (@ tptp.suc (@ tptp.suc Va))))))))))
% 6.31/6.59 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) (@ tptp.suc tptp.zero_zero_nat)) Ts) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 6.31/6.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.31/6.59 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I2)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I2)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) Deg)))))))))))))))
% 6.31/6.59 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) tptp.zero_zero_nat) Ts) S2))) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X2) _let_1))))
% 6.31/6.59 (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))))
% 6.31/6.59 (assert (forall ((A tptp.code_integer) (B Bool) (A2 tptp.code_integer) (B2 Bool)) (=> (= (@ (@ tptp.produc6677183202524767010eger_o A) B) (@ (@ tptp.produc6677183202524767010eger_o A2) B2)) (not (=> (= A A2) (= B (not B2)))))))
% 6.31/6.59 (assert (forall ((A tptp.num) (B tptp.num) (A2 tptp.num) (B2 tptp.num)) (=> (= (@ (@ tptp.product_Pair_num_num A) B) (@ (@ tptp.product_Pair_num_num A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.31/6.59 (assert (forall ((A tptp.nat) (B tptp.num) (A2 tptp.nat) (B2 tptp.num)) (=> (= (@ (@ tptp.product_Pair_nat_num A) B) (@ (@ tptp.product_Pair_nat_num A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.31/6.59 (assert (forall ((A tptp.nat) (B tptp.nat) (A2 tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A) B) (@ (@ tptp.product_Pair_nat_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.31/6.59 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.31/6.59 (assert (forall ((P (-> tptp.produc6271795597528267376eger_o Bool)) (P2 tptp.produc6271795597528267376eger_o)) (=> (forall ((A4 tptp.code_integer) (B3 Bool)) (@ P (@ (@ tptp.produc6677183202524767010eger_o A4) B3))) (@ P P2))))
% 6.31/6.59 (assert (forall ((P (-> tptp.product_prod_num_num Bool)) (P2 tptp.product_prod_num_num)) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (@ P (@ (@ tptp.product_Pair_num_num A4) B3))) (@ P P2))))
% 6.31/6.59 (assert (forall ((P (-> tptp.product_prod_nat_num Bool)) (P2 tptp.product_prod_nat_num)) (=> (forall ((A4 tptp.nat) (B3 tptp.num)) (@ P (@ (@ tptp.product_Pair_nat_num A4) B3))) (@ P P2))))
% 6.31/6.60 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (@ P (@ (@ tptp.product_Pair_nat_nat A4) B3))) (@ P P2))))
% 6.31/6.60 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P2 tptp.product_prod_int_int)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A4) B3))) (@ P P2))))
% 6.31/6.60 (assert (forall ((P2 tptp.produc6271795597528267376eger_o)) (exists ((X5 tptp.code_integer) (Y3 Bool)) (= P2 (@ (@ tptp.produc6677183202524767010eger_o X5) Y3)))))
% 6.31/6.60 (assert (forall ((P2 tptp.product_prod_num_num)) (exists ((X5 tptp.num) (Y3 tptp.num)) (= P2 (@ (@ tptp.product_Pair_num_num X5) Y3)))))
% 6.31/6.60 (assert (forall ((P2 tptp.product_prod_nat_num)) (exists ((X5 tptp.nat) (Y3 tptp.num)) (= P2 (@ (@ tptp.product_Pair_nat_num X5) Y3)))))
% 6.31/6.60 (assert (forall ((P2 tptp.product_prod_nat_nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (= P2 (@ (@ tptp.product_Pair_nat_nat X5) Y3)))))
% 6.31/6.60 (assert (forall ((P2 tptp.product_prod_int_int)) (exists ((X5 tptp.int) (Y3 tptp.int)) (= P2 (@ (@ tptp.product_Pair_int_int X5) Y3)))))
% 6.31/6.60 (assert (forall ((Y tptp.produc6271795597528267376eger_o)) (not (forall ((A4 tptp.code_integer) (B3 Bool)) (not (= Y (@ (@ tptp.produc6677183202524767010eger_o A4) B3)))))))
% 6.31/6.60 (assert (forall ((Y tptp.product_prod_num_num)) (not (forall ((A4 tptp.num) (B3 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_num_num A4) B3)))))))
% 6.31/6.60 (assert (forall ((Y tptp.product_prod_nat_num)) (not (forall ((A4 tptp.nat) (B3 tptp.num)) (not (= Y (@ (@ tptp.product_Pair_nat_num A4) B3)))))))
% 6.31/6.60 (assert (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A4 tptp.nat) (B3 tptp.nat)) (not (= Y (@ (@ tptp.product_Pair_nat_nat A4) B3)))))))
% 6.31/6.60 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A4 tptp.int) (B3 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A4) B3)))))))
% 6.31/6.60 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X2 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va2) Vb)) X2) (or (= X2 Mi) (= X2 Ma)))))
% 6.31/6.60 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N3 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) (@ (@ tptp.vEBT_VEBT_high X) N3))) (@ (@ tptp.vEBT_VEBT_low X) N3)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (assert (forall ((X2 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 X2) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X2 Y))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X2 Y))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X2) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X2 Y))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X2 Y))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.31/6.60 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X2 Mi) (= X2 Ma) (and (@ (@ tptp.ord_less_nat X2) Ma) (@ (@ tptp.ord_less_nat Mi) X2) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))))))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.60 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_insert (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na)))) (@ (@ tptp.vEBT_VEBT_high tptp.ya) tptp.na))) (@ (@ tptp.vEBT_VEBT_low tptp.ya) tptp.na))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N2)) (= M N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N2)) (= M N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N2)) (= M N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N2)) (= M N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N2)) (= M N2))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (= tptp.vEBT_VEBT_high (lambda ((X tptp.nat) (N3 tptp.nat)) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N2) tptp.one_one_rat)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N2) tptp.one_one_real)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N2) tptp.one_one_complex)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.31/6.60 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (= (@ tptp.vEBT_set_vebt T2) (@ tptp.vEBT_VEBT_set_vebt T2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N2)) (= tptp.one N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N2)) (= tptp.one N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N2)) (= tptp.one N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N2)) (= tptp.one N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N2)) (= tptp.one N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N2) tptp.one_one_complex) (= N2 tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real N2) tptp.one_one_real) (= N2 tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_rat N2) tptp.one_one_rat) (= N2 tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat N2) tptp.one_one_nat) (= N2 tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int N2) tptp.one_one_int) (= N2 tptp.one))))
% 6.31/6.60 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N2)) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X2) M) _let_1) (or (= M tptp.zero_zero_nat) (= X2 _let_1))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X2) N2)) (or (@ _let_1 X2) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.60 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N2) (=> (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_3))) (@ (@ tptp.vEBT_VEBT_low X2) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X2)))))))))
% 6.31/6.60 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (= X2 Mi) (= X2 Ma)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.60 (assert (forall ((B tptp.real) (X2 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (X2 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (X2 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (X2 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X2) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low X2) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2))))))))
% 6.31/6.60 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (forall ((B tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.31/6.60 (assert (forall ((B tptp.real) (X2 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (X2 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (X2 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (X2 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 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 6.31/6.60 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (forall ((B tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_complex A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N2) (@ (@ tptp.plus_plus_num N2) tptp.one))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N2) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X2) tptp.one) (= X2 tptp.one))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.60 (assert (forall ((V tptp.num) (N2 tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N2))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X2))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.31/6.60 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.31/6.60 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.31/6.60 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.31/6.60 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.31/6.60 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.31/6.60 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.one_one_real)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) tptp.one_one_rat)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N2)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N2))) A)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N2))) A)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) A)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) A)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N2))) tptp.one_one_real)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N2))) tptp.one_one_rat)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) tptp.one_one_nat)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) tptp.one_one_int)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N2))))))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_nat A) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_int A) N2)))))))
% 6.31/6.60 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I3) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.31/6.60 (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 ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (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)))))))))))
% 6.31/6.60 (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 ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (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))))))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2) tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N2) tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N2) tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2) tptp.zero_zero_complex))))
% 6.31/6.60 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N2) K)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I3) (@ _let_1 (@ (@ tptp.power_power_nat I3) N2))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (= A B))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (= A B))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (= A B))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (= A B))))))))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.31/6.60 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.31/6.60 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat K) M)))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= X2 Y))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= X2 Y))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= X2 Y))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= X2 Y))))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 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 X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 6.31/6.60 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.mi) tptp.na))) (let ((_let_2 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.xa) (@ (@ tptp.ord_max_nat tptp.mi) tptp.ma)))) tptp.deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_insert _let_2) (@ (@ tptp.vEBT_VEBT_low tptp.mi) tptp.na)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ tptp.vEBT_vebt_insert tptp.summary) _let_1)) tptp.summary))))))
% 6.31/6.60 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.31/6.60 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.31/6.60 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.31/6.60 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Xs))) (let ((_let_2 (@ tptp.size_s6755466524823107622T_VEBT Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) (@ _let_1 J))) J) (@ _let_1 I3))) (@ tptp.set_VEBT_VEBT2 Xs))))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (let ((_let_2 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs) I3) (@ _let_1 J))) J) (@ _let_1 I3))) (@ tptp.set_o2 Xs))))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (let ((_let_2 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat (@ (@ (@ tptp.list_update_nat Xs) I3) (@ _let_1 J))) J) (@ _let_1 I3))) (@ tptp.set_nat2 Xs))))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (let ((_let_2 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat I3) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int (@ (@ (@ tptp.list_update_int Xs) I3) (@ _let_1 J))) J) (@ _let_1 I3))) (@ tptp.set_int2 Xs))))))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M) _let_1))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X2 tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat X2) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (=> (@ (@ tptp.ord_less_nat Mi) X2) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X2 Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X2) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X2) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I3 tptp.nat) (X2 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3))) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ _let_1 X2)) I3) Y) (@ _let_1 Y)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I3 tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) X2)) (@ tptp.size_s6755466524823107622T_VEBT Xs))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_o) (I3 tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs) I3) X2)) (@ tptp.size_size_list_o Xs))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) (@ tptp.size_size_list_nat Xs))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (I3 tptp.nat) (X2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ (@ tptp.list_update_int Xs) I3) X2)) (@ tptp.size_size_list_int Xs))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I3) (@ (@ tptp.nth_nat Xs) I3)) Xs)))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs) I3) (@ (@ tptp.nth_int Xs) I3)) Xs)))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I3 tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) (@ (@ tptp.nth_VEBT_VEBT Xs) I3)) Xs)))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (not (= I3 J)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) J) (@ (@ tptp.nth_nat Xs) J)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (Xs tptp.list_int) (X2 tptp.int)) (=> (not (= I3 J)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I3) X2)) J) (@ (@ tptp.nth_int Xs) J)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (not (= I3 J)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) X2)) J) (@ (@ tptp.nth_VEBT_VEBT Xs) J)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.60 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.60 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.60 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.31/6.60 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.60 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.60 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.60 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.60 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.31/6.60 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.31/6.60 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.31/6.60 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X2))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X2))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X2))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.31/6.60 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X2))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I3 tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) I3) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) X2) Xs))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_o) (I3 tptp.nat) (X2 Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) I3) (= (@ (@ (@ tptp.list_update_o Xs) I3) X2) Xs))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) I3) (= (@ (@ (@ tptp.list_update_nat Xs) I3) X2) Xs))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (I3 tptp.nat) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) I3) (= (@ (@ (@ tptp.list_update_int Xs) I3) X2) Xs))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) X2)) I3) X2))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I3) X2)) I3) X2))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) I3) X2))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I3) X2)) I3) X2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((X3 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X3))))
% 6.31/6.60 (assert (forall ((X3 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X3))))
% 6.31/6.60 (assert (forall ((X3 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X3) X_12))))
% 6.31/6.60 (assert (forall ((X3 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X3) X_12))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_complex) (B4 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) B4) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 (@ tptp.set_complex2 Xs)) (@ _let_1 B4)))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_real) (B4 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B4) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B4)))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_set_nat) (B4 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) B4) (forall ((X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs)) (@ _let_1 B4)))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B4 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B4) (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B4)))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B4) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B4)))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B4) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B4)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o Xs2) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N2))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys))) (not (= Xs Ys)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (I4 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (X6 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs))) (=> (not (= I3 I4)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I3) X2)) I4) X6) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I4) X6)) I3) X2))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 6.31/6.60 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs2 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 6.31/6.60 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 6.31/6.60 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N2) K)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))
% 6.31/6.60 (assert (forall ((Xs tptp.list_complex) (A3 tptp.set_complex) (X2 tptp.complex) (I3 tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A3) (=> (@ (@ tptp.member_complex X2) A3) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs) I3) X2))) A3)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_real) (A3 tptp.set_real) (X2 tptp.real) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) A3) (=> (@ (@ tptp.member_real X2) A3) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I3) X2))) A3)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_set_nat) (A3 tptp.set_set_nat) (X2 tptp.set_nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) A3) (=> (@ (@ tptp.member_set_nat X2) A3) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) I3) X2))) A3)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (A3 tptp.set_int) (X2 tptp.int) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) A3) (=> (@ (@ tptp.member_int X2) A3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I3) X2))) A3)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (A3 tptp.set_VEBT_VEBT) (X2 tptp.vEBT_VEBT) (I3 tptp.nat)) (=> (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) A3) (=> (@ (@ tptp.member_VEBT_VEBT X2) A3) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) X2))) A3)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (A3 tptp.set_nat) (X2 tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) A3) (=> (@ (@ tptp.member_nat X2) A3) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I3) X2))) A3)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) 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 X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) 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 X2) Y))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) 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 X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) 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 X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N2))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I2) (@ (@ tptp.nth_VEBT_VEBT Ys) I2)))) (= Xs Ys)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I2) (@ (@ tptp.nth_o Ys) I2)))) (= Xs Ys)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I2) (@ (@ tptp.nth_nat Ys) I2)))) (= Xs Ys)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I2) (@ (@ tptp.nth_int Ys) I2)))) (= Xs Ys)))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.vEBT_VEBT)) (@ (@ P I5) X4)))) (exists ((Xs3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_VEBT_VEBT Xs3) I5)))))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 Bool)) (@ (@ P I5) X4)))) (exists ((Xs3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_o Xs3) I5)))))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.nat)) (@ (@ P I5) X4)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_nat Xs3) I5)))))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X4 tptp.int)) (@ (@ P I5) X4)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_int Xs3) I5)))))))))
% 6.31/6.60 (assert (= (lambda ((Y4 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (= (@ (@ tptp.nth_VEBT_VEBT Xs3) I5) (@ (@ tptp.nth_VEBT_VEBT Ys3) I5))))))))
% 6.31/6.60 (assert (= (lambda ((Y4 tptp.list_o) (Z2 tptp.list_o)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) (@ tptp.size_size_list_o Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs3)) (= (@ (@ tptp.nth_o Xs3) I5) (@ (@ tptp.nth_o Ys3) I5))))))))
% 6.31/6.60 (assert (= (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I5) (@ (@ tptp.nth_nat Ys3) I5))))))))
% 6.31/6.60 (assert (= (lambda ((Y4 tptp.list_int) (Z2 tptp.list_int)) (= Y4 Z2)) (lambda ((Xs3 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I5) (@ (@ tptp.nth_int Ys3) I5))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real Y) E)))) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat Y) E)))) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (X2 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (X2 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat X2) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X2) Y)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) 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 X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) 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 X2) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) tptp.zero_zero_rat)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))))
% 6.31/6.60 (assert (forall ((X2 tptp.set_nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3254054031482475050et_nat Xs)))))
% 6.31/6.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 6.31/6.60 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs) N2)) (@ tptp.set_complex2 Xs)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N2)) (@ tptp.set_real2 Xs)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs) N2)) (@ tptp.set_set_nat2 Xs)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N2)) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N2)) (@ tptp.set_o2 Xs)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N2)) (@ tptp.set_nat2 Xs)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N2)) (@ tptp.set_int2 Xs)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_o Xs) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_nat Xs) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_int Xs) N2))))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex) (Xs tptp.list_complex)) (= (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s3451745648224563538omplex Xs)) (= (@ (@ tptp.nth_complex Xs) I5) X2))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I5) X2))))))
% 6.31/6.60 (assert (forall ((X2 tptp.set_nat) (Xs tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs) I5) X2))))))
% 6.31/6.60 (assert (forall ((X2 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I5) X2))))))
% 6.31/6.60 (assert (forall ((X2 Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I5) X2))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I5) X2))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I5) X2))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (X2 tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) I2)))) (=> (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 Xs)) (@ P X2)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X2 tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) I2)))) (=> (@ (@ tptp.member_real X2) (@ tptp.set_real2 Xs)) (@ P X2)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (X2 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) I2)))) (=> (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 Xs)) (@ P X2)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I2)))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X2)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X2 Bool)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I2)))) (=> (@ (@ tptp.member_o X2) (@ tptp.set_o2 Xs)) (@ P X2)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I2)))) (=> (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 Xs)) (@ P X2)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X2 tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I2)))) (=> (@ (@ tptp.member_int X2) (@ tptp.set_int2 Xs)) (@ P X2)))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I5)))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X Bool)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ P X))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I5)))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I5)))))))
% 6.31/6.60 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I5)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_complex) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs) N2) X2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) N2) X2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) N2) X2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N2) X2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o X2) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) N2) X2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N2) X2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N2) X2))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) X2)) J))) (let ((_let_2 (= I3 J))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_VEBT_VEBT Xs) J)))))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_o) (X2 Bool) (J tptp.nat)) (let ((_let_1 (= I3 J))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I3) X2)) J) (and (=> _let_1 X2) (=> (not _let_1) (@ (@ tptp.nth_o Xs) J))))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (J tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.nth_nat (@ (@ (@ tptp.list_update_nat Xs) I3) X2)) J))) (let ((_let_2 (= I3 J))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_nat Xs) J)))))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_int) (J tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ (@ tptp.nth_int (@ (@ (@ tptp.list_update_int Xs) I3) X2)) J))) (let ((_let_2 (= I3 J))) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (and (=> _let_2 (= _let_1 X2)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_int Xs) J)))))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) X2) Xs) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I3) X2)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_o) (X2 Bool)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (= (@ (@ (@ tptp.list_update_o Xs) I3) X2) Xs) (= (@ (@ tptp.nth_o Xs) I3) X2)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (= (@ (@ (@ tptp.list_update_nat Xs) I3) X2) Xs) (= (@ (@ tptp.nth_nat Xs) I3) X2)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (Xs tptp.list_int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (= (@ (@ (@ tptp.list_update_int Xs) I3) X2) Xs) (= (@ (@ tptp.nth_int Xs) I3) X2)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.60 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))))
% 6.31/6.60 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (@ _let_1 M) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.31/6.60 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N2)) (= M N2))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.31/6.60 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X2) Y)) (and (= X2 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X2) Y) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.31/6.60 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit0 N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex)) (= (= tptp.zero_zero_complex X2) (= X2 tptp.zero_zero_complex))))
% 6.31/6.60 (assert (forall ((X2 tptp.real)) (= (= tptp.zero_zero_real X2) (= X2 tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat)) (= (= tptp.zero_zero_rat X2) (= X2 tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat)) (= (= tptp.zero_zero_nat X2) (= X2 tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((X2 tptp.int)) (= (= tptp.zero_zero_int X2) (= X2 tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (@ (@ tptp.ord_less_rat Y) X2)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (@ (@ tptp.ord_less_int Y) X2)))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex)) (= (= tptp.one_one_complex X2) (= X2 tptp.one_one_complex))))
% 6.31/6.60 (assert (forall ((X2 tptp.real)) (= (= tptp.one_one_real X2) (= X2 tptp.one_one_real))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat)) (= (= tptp.one_one_rat X2) (= X2 tptp.one_one_rat))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat)) (= (= tptp.one_one_nat X2) (= X2 tptp.one_one_nat))))
% 6.31/6.60 (assert (forall ((X2 tptp.int)) (= (= tptp.one_one_int X2) (= X2 tptp.one_one_int))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (= tptp.plus_plus_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.plus_plus_real B5) A5))))
% 6.31/6.60 (assert (= tptp.plus_plus_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.plus_plus_rat B5) A5))))
% 6.31/6.60 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.plus_plus_nat B5) A5))))
% 6.31/6.60 (assert (= tptp.plus_plus_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.plus_plus_int B5) A5))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.60 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.60 (assert (forall ((B4 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.60 (assert (forall ((B4 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B4 (@ _let_2 B)) (= (@ _let_1 B4) (@ _let_2 (@ _let_1 B))))))))
% 6.31/6.60 (assert (forall ((A3 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A3) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.31/6.60 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A3) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.31/6.60 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A3) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.31/6.60 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A3) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I3 J) (= K L)) (= (@ (@ tptp.plus_plus_real I3) K) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I3 J) (= K L)) (= (@ (@ tptp.plus_plus_rat I3) K) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I3 J) (= K L)) (= (@ (@ tptp.plus_plus_nat I3) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I3 J) (= K L)) (= (@ (@ tptp.plus_plus_int I3) K) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X2) (@ tptp.suc Y)) (= X2 Y))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (not (@ P N)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (not (@ P M2)))))) (@ P N2))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (@ P N))) (@ P N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.31/6.60 (assert (forall ((S2 tptp.nat) (T2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T2) (not (= S2 T2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X5 tptp.nat)) (and (@ P X5) (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) X5)))))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I3))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)))
% 6.31/6.60 (assert (forall ((X2 tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X2) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X2 Y)))))
% 6.31/6.60 (assert (forall ((X2 tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X2) (@ tptp.size_size_list_o Y))) (not (= X2 Y)))))
% 6.31/6.60 (assert (forall ((X2 tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X2) (@ tptp.size_size_list_nat Y))) (not (= X2 Y)))))
% 6.31/6.60 (assert (forall ((X2 tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X2) (@ tptp.size_size_list_int Y))) (not (= X2 Y)))))
% 6.31/6.60 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X2) (@ tptp.size_size_num Y))) (not (= X2 Y)))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (exists ((C2 tptp.nat)) (= B5 (@ (@ tptp.plus_plus_nat A5) C2))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C3))))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I3) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I3) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I3) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I3) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I3) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I3) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I3 J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I3) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I3 J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I3) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I3 J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I3 J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I3) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I3) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I3) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I3) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I3) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I3) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I3) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I3) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.31/6.60 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.31/6.60 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.31/6.60 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.31/6.60 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I3) J) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I3) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I3) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I3) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I3) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I3) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I3) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I3 J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I3) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I3 J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I3) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I3 J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I3 J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I3) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I3) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I3) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I3) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I3) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I3) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I3) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I3) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (@ (@ P X5) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X5) Y3) (@ (@ P (@ tptp.suc X5)) (@ tptp.suc Y3)))) (@ (@ P M) N2))))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ P N) (@ P (@ tptp.suc N)))) (@ P N2)))))
% 6.31/6.60 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.31/6.60 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.31/6.60 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N2 M))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (forall ((I2 tptp.nat)) (=> (= J (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I3))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I3) J))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I3)) K)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M) (exists ((M4 tptp.nat)) (and (= M (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N2) M4))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (and (@ P N2) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N2) (@ P I5)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (or (@ P N2) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N2) (@ P I5)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M N2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I3)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (=> (not (= K (@ tptp.suc I3))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ P N)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (not (@ P M2))))))) (@ P N2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (forall ((X5 tptp.nat)) (@ (@ R X5) X5)) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ R X5))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z3) (@ _let_1 Z3))))) (=> (forall ((N tptp.nat)) (@ (@ R N) (@ tptp.suc N))) (@ (@ R M) N2)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P M) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P N) (@ P (@ tptp.suc N))))) (@ P N2))))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N) (@ P M2))) (@ P N))) (@ P N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M _let_1)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M5) (exists ((M3 tptp.nat)) (= M5 (@ tptp.suc M3))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M _let_1)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.31/6.60 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ tptp.suc A3) (@ _let_1 (@ tptp.suc A)))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (I3 tptp.nat) (J tptp.nat)) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (@ (@ tptp.ord_less_nat (@ F I2)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ F J))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N3) (= M6 N3)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.60 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N3) (not (= M6 N3))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)))
% 6.31/6.60 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I3))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I3))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.31/6.60 (assert (forall ((J tptp.nat) (I3 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I3)) I3))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J)) I3))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) J)) K) (@ (@ tptp.ord_less_nat I3) K))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (exists ((K3 tptp.nat)) (= N3 (@ (@ tptp.plus_plus_nat M6) K3))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I3))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I3))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X2))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X2))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X2) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X2) Z)) (@ (@ tptp.plus_plus_real Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X2) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X2) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X2) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X2) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X2) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X2) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N2)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N2) Q2)))))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X2) Y) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X2) Y) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X2) Y) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X2) Y) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X2) Y) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X2) Y) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X2) Y) tptp.zero_zero_nat) (and (= X2 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X2) Y) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I3) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I3) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I3) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I3) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I3) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I3) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I3) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I3) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I3) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I3) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I3) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I3) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I3) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X2) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X2) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.31/6.60 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ F N)) (@ F (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_real (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N)) (@ F (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_rat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_num (@ F N)) (@ F (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_num (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N)) (@ F (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ F N)) (@ F (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_num (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_num (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N5)) (@ F N2))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N2))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N2))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N2))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N))) (@ F N))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N2))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_nat (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N5))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N2)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (and (@ P tptp.zero_zero_nat) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N2) (@ P (@ tptp.suc I5))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M6 tptp.nat)) (= N2 (@ tptp.suc M6))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N2)) (@ P I5))) (or (@ P tptp.zero_zero_nat) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N2) (@ P (@ tptp.suc I5))))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))))
% 6.31/6.60 (assert (= tptp.ord_less_nat (lambda ((N3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N3)) __flatten_var_0))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)) (= N2 M)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (=> (@ P J) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (=> (@ (@ tptp.ord_less_nat N) J) (=> (@ P (@ tptp.suc N)) (@ P N))))) (@ P I3))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (=> (@ P I3) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N) (=> (@ (@ tptp.ord_less_nat N) J) (=> (@ P N) (@ P (@ tptp.suc N)))))) (@ P J))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 6.31/6.60 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (exists ((K3 tptp.nat)) (= N3 (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I3) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I3)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I3) (@ tptp.suc (@ (@ tptp.plus_plus_nat I3) M)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (forall ((Q3 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I3) K2) J))))))
% 6.31/6.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.ord_less_nat (@ F M3)) (@ F N)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.31/6.60 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.60 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.31/6.60 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.31/6.60 (assert (= tptp.suc (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P tptp.one_one_nat) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P N) (@ P (@ tptp.suc N))))) (@ P N2))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N tptp.nat)) (=> (@ P N) (@ P (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N2))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.60 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L2 tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L2))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X2)) N2) X2)))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat X2) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X2)) N2) Y)))))
% 6.31/6.60 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X2))))
% 6.31/6.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X2) Y)) Z) (and (@ (@ tptp.ord_less_real X2) Z) (@ (@ tptp.ord_less_real Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X2) Y)) Z) (and (@ (@ tptp.ord_less_rat X2) Z) (@ (@ tptp.ord_less_rat Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X2) Y)) Z) (and (@ (@ tptp.ord_less_num X2) Z) (@ (@ tptp.ord_less_num Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X2) Y)) Z) (and (@ (@ tptp.ord_less_nat X2) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X2) Y)) Z) (and (@ (@ tptp.ord_less_int X2) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.31/6.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.31/6.60 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.31/6.60 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_max_int A) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_max_nat A) B))) (= (@ (@ tptp.ord_max_nat _let_1) B) _let_1))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.ord_max_int A) B))) (= (@ (@ tptp.ord_max_int _let_1) B) _let_1))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.31/6.60 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.31/6.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 6.31/6.60 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C) A)))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 6.31/6.60 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (= M _let_1) (= N2 _let_1))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N2)))))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N2)) N2) M))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M)) N2) M))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (M tptp.num) (N2 tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (M tptp.num) (N2 tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.num) (N2 tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (= tptp.times_times_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.times_times_real B5) A5))))
% 6.31/6.60 (assert (= tptp.times_times_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.times_times_rat B5) A5))))
% 6.31/6.60 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.times_times_nat B5) A5))))
% 6.31/6.60 (assert (= tptp.times_times_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.times_times_int B5) A5))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (= A B)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (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))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex Y) W)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y) W)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y) W)))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X2) W)) (@ (@ tptp.times_times_complex Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X2) W)) (@ (@ tptp.times_times_real Y) Z)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X2) W)) (@ (@ tptp.times_times_rat Y) Z)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (= (@ (@ tptp.times_times_rat _let_1) A) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) N2))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) N2))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) N2))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X2) N2))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X2) N2))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X2) Y) (@ _let_2 X2)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_int (@ _let_1 M)) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_real (@ _let_1 M)) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N2)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (= M N2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I3) K)) (@ (@ tptp.times_times_nat J) L))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I3) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I3)) (@ _let_1 J))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I3) J)) U)) K))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N2) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N2)) Q2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N2)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N2) Q2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q2))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.31/6.60 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (forall ((M tptp.real) (N2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_real M) N2)))))))
% 6.31/6.60 (assert (forall ((M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_rat M) N2)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.31/6.60 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M) N2)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X2) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X2) Z) (@ (@ tptp.times_times_complex W) Y)))))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X2) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X2) Z) (@ (@ tptp.times_times_real W) Y)))))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X2) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X2) Z) (@ (@ tptp.times_times_rat W) Y)))))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.31/6.60 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X2) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) N2)) (@ (@ tptp.power_power_complex Y) N2)) tptp.one_one_complex))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X2) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) N2)) (@ (@ tptp.power_power_real Y) N2)) tptp.one_one_real))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X2) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) N2)) (@ (@ tptp.power_power_rat Y) N2)) tptp.one_one_rat))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X2) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X2) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X2) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) A)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) A)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) A)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) A)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) A)))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I3) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.31/6.60 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I3)) (@ _let_1 J)))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M) N2)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (I3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I3) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) I3))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2))) M)))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2)) M)))
% 6.31/6.60 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1)))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1)))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_rat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat (@ _let_2 N2)) _let_1)))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1)))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1)))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N2)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X2)) X2)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X2)) X2)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X2)) X2)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Y)) X2)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Y)) X2)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Y)) X2)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X2 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X2 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X2 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y)))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y)))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X2 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X2 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X2 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 6.31/6.60 (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))))))))))))
% 6.31/6.60 (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))))))))))))
% 6.31/6.60 (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))))))))))))
% 6.31/6.60 (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))))))))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y)) Z)))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y)) Z)))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X2) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X2) Y))))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X2) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X2) Y))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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)))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.31/6.60 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.31/6.60 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.31/6.60 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.31/6.60 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.31/6.60 (assert (forall ((Y tptp.complex) (X2 tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.31/6.60 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X2 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.31/6.60 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X2) Z)) Y)) Z)))))
% 6.31/6.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) Z)) Y)) Z)))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X2) Z)) Y)) Z)))))
% 6.31/6.60 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X2) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.31/6.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X2) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.60 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N2) Q2))))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.divide_divide_nat M) N2))))))
% 6.31/6.60 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.31/6.60 (assert (forall ((L tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L) L)))
% 6.31/6.60 (assert (forall ((K tptp.int) (I3 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P K) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (@ P I3))))))
% 6.31/6.60 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 6.31/6.60 (assert (forall ((K tptp.int) (I3 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (@ P I3))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat A))) (= (@ (@ tptp.ord_max_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_nat B) C))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int A))) (= (@ (@ tptp.ord_max_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.ord_max_int B) C))))))
% 6.31/6.60 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_max_nat B5) A5))))
% 6.31/6.60 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.ord_max_int B5) A5))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_max_nat B))) (let ((_let_2 (@ tptp.ord_max_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_max_int B))) (let ((_let_2 (@ tptp.ord_max_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z3) (=> (@ (@ tptp.ord_less_real Z3) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z3) X2)) Y)))) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (forall ((Z3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z3) (=> (@ (@ tptp.ord_less_rat Z3) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z3) X2)) Y)))) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))))))))
% 6.31/6.60 (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)))))))))))
% 6.31/6.60 (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))))))))))))
% 6.31/6.60 (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))))))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (X2 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) Z)))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) Z)))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X2) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X2) Y))))))
% 6.31/6.60 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X2) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X2) Y))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (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))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) 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) X2)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) 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) X2)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) 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) X2)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.31/6.60 (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)))))))))))))
% 6.31/6.60 (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)))))))))))))
% 6.31/6.60 (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)))))))))))))
% 6.31/6.60 (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)))))))))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 6.31/6.60 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X2) X2)) X2)) X2))))
% 6.31/6.60 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X2) X2)) X2)) X2))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X2) X2)) X2)) X2))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.power_power_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X2) X2)) X2)) X2))))
% 6.31/6.60 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X2) X2)) X2)) X2))))
% 6.31/6.60 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.31/6.60 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.31/6.60 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1))))))
% 6.31/6.60 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N2) Q2))))))
% 6.31/6.60 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N2) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N2)))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I5)) J3)) (@ P I5))))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2)))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) 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) X2)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) 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) X2)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.31/6.60 (assert (forall ((X2 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 X2) 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) X2)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.31/6.60 (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))))))))))))
% 6.31/6.60 (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))))))))))))
% 6.31/6.60 (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)))))))))))))
% 6.31/6.60 (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)))))))))))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q4)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q4))) (@ P Q4))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X2) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X2) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X2) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X2) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X2)) Y))))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X2) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y)))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.31/6.60 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (=> (forall ((N tptp.nat)) (=> (@ P N) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))) (@ P N2))))))
% 6.31/6.60 (assert (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((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 D22)))))))))
% 6.31/6.60 (assert (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((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 D22)))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.60 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D)) (@ (@ tptp.ord_max_num A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B))))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.31/6.60 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.31/6.60 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 6.31/6.60 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C) A)))))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 6.31/6.60 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A)))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.ord_max_rat A5) B5)))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_num (lambda ((B5 tptp.num) (A5 tptp.num)) (= A5 (@ (@ tptp.ord_max_num A5) B5)))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.ord_max_nat A5) B5)))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_int (lambda ((B5 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.ord_max_int A5) B5)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.31/6.60 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.31/6.60 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B5) A5))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_num (lambda ((B5 tptp.num) (A5 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B5) A5))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B5) A5))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_int (lambda ((B5 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B5) A5))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (= (@ (@ tptp.ord_max_rat A5) B5) B5))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B5 tptp.num)) (= (@ (@ tptp.ord_max_num A5) B5) B5))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ tptp.ord_max_nat A5) B5) B5))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B5 tptp.int)) (= (@ (@ tptp.ord_max_int A5) B5) B5))))
% 6.31/6.60 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.31/6.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.num) (X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X2) Y)) (or (@ _let_1 X2) (@ _let_1 Y))))))
% 6.31/6.60 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 6.31/6.60 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 6.31/6.60 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C) A)))))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 6.31/6.60 (assert (= tptp.ord_less_real (lambda ((B5 tptp.real) (A5 tptp.real)) (and (= A5 (@ (@ tptp.ord_max_real A5) B5)) (not (= A5 B5))))))
% 6.31/6.60 (assert (= tptp.ord_less_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (and (= A5 (@ (@ tptp.ord_max_rat A5) B5)) (not (= A5 B5))))))
% 6.31/6.60 (assert (= tptp.ord_less_num (lambda ((B5 tptp.num) (A5 tptp.num)) (and (= A5 (@ (@ tptp.ord_max_num A5) B5)) (not (= A5 B5))))))
% 6.31/6.60 (assert (= tptp.ord_less_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (and (= A5 (@ (@ tptp.ord_max_nat A5) B5)) (not (= A5 B5))))))
% 6.31/6.60 (assert (= tptp.ord_less_int (lambda ((B5 tptp.int) (A5 tptp.int)) (and (= A5 (@ (@ tptp.ord_max_int A5) B5)) (not (= A5 B5))))))
% 6.31/6.60 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.31/6.60 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_rat))))
% 6.31/6.60 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.31/6.60 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 6.31/6.60 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 6.31/6.60 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.31/6.60 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((X2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X2) K)) X2)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) __flatten_var_0))))
% 6.31/6.60 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A5) tptp.one_one_int)) __flatten_var_0))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((K tptp.int) (I3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I3) K)) (@ (@ tptp.ord_less_eq_int K) I3))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.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)))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B2)) (@ _let_1 B))))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A2) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I3) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I3) (@ (@ tptp.ord_less_int I3) K)) (and (@ (@ tptp.ord_less_eq_int I3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I3))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B2 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) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B2))))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (A2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A2) B))))))
% 6.31/6.60 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X2))))
% 6.31/6.60 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X2))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X2))))
% 6.31/6.60 (assert (forall ((U tptp.real) (X2 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 X2) Y)) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.31/6.60 (assert (forall ((U tptp.rat) (X2 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 X2) Y)) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X2) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 6.31/6.60 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))))
% 6.31/6.60 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X2) Y)))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X2) Y)))))
% 6.31/6.60 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X2) Y)))))
% 6.31/6.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X2) Y))))))
% 6.31/6.60 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X2) Y))))))
% 6.31/6.60 (assert (forall ((Q2 tptp.nat) (R2 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R2)) (= R2 tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R2)) (= R2 tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) (@ _let_1 K)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) (@ _let_1 K)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.31/6.60 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.60 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N2) N2)))
% 6.31/6.60 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N2) (@ tptp.bit0 N2))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.31/6.60 (assert (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.31/6.60 (assert (forall ((S3 tptp.set_real)) (=> (exists ((X3 tptp.real)) (@ (@ tptp.member_real X3) S3)) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Z4)))) (exists ((Y3 tptp.real)) (and (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) S3) (@ (@ tptp.ord_less_eq_real X3) Y3))) (forall ((Z4 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S3) (@ (@ tptp.ord_less_eq_real X5) Z4))) (@ (@ tptp.ord_less_eq_real Y3) Z4)))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X2) N))))))
% 6.31/6.60 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y6) (= X Y6)))))
% 6.31/6.60 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) N)) Y))))))
% 6.31/6.60 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.31/6.60 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((L tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L) tptp.zero_zero_int)))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) K)))
% 6.31/6.60 (assert (forall ((K tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N2) K))))
% 6.31/6.60 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 6.31/6.60 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) _let_2))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (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)))))))
% 6.31/6.60 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I3) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I3)) (@ _let_1 J)))))))
% 6.31/6.60 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (and (= M tptp.one_one_int) (= N2 tptp.one_one_int))))))
% 6.31/6.60 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) (@ tptp.suc N2)) A))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((B2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q5)) R4)) (=> (@ (@ tptp.ord_less_int R4) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ _let_1 Q5)))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B2) (=> (@ _let_1 R2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q5)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R2) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R2) B) (@ (@ tptp.ord_less_eq_int Q5) Q2))))))))
% 6.31/6.60 (assert (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q5)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ _let_1 R2) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q2) Q5)))))))))
% 6.31/6.60 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N2) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P I5)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P I5))))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N2) A) (forall ((Y5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y5) (= (@ (@ tptp.power_power_real Y5) N2) A)) (= Y5 X5)))))))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (= (@ (@ tptp.power_power_real R3) N2) A)))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (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))))))
% 6.31/6.60 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X2) Y)))))
% 6.31/6.60 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X2) Y)))))
% 6.31/6.60 (assert (forall ((Z tptp.int) (X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X2) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X2) Y)))))
% 6.31/6.60 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) (@ (@ tptp.times_times_int K) D))))))))))
% 6.31/6.60 (assert (= tptp.vEBT_VEBT_low (lambda ((X tptp.nat) (N3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.60 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.31/6.60 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.31/6.60 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.31/6.60 (assert (forall ((T2 tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T2) tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T2 (@ (@ tptp.vEBT_Leaf A5) B5))))))
% 6.31/6.60 (assert (forall ((T2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T2) tptp.one_one_nat) (exists ((A4 Bool) (B3 Bool)) (= T2 (@ (@ tptp.vEBT_Leaf A4) B3))))))
% 6.31/6.60 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (=> (= N2 tptp.one_one_nat) (exists ((A4 Bool) (B3 Bool)) (= T2 (@ (@ tptp.vEBT_Leaf A4) B3)))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B) _let_1))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (= (@ (@ tptp.modulo_modulo_int _let_1) B) _let_1))))
% 6.31/6.60 (assert (forall ((R2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R2)) (@ (@ tptp.divide_divide_real A) R2)))))
% 6.31/6.60 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))))
% 6.31/6.60 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (forall ((Y6 tptp.product_prod_nat_nat)) (not (= X2 (@ tptp.some_P7363390416028606310at_nat Y6)))) (= X2 tptp.none_P5556105721700978146at_nat))))
% 6.31/6.60 (assert (forall ((X2 tptp.option_num)) (= (forall ((Y6 tptp.num)) (not (= X2 (@ tptp.some_num Y6)))) (= X2 tptp.none_num))))
% 6.31/6.60 (assert (forall ((X2 tptp.option4927543243414619207at_nat)) (= (not (= X2 tptp.none_P5556105721700978146at_nat)) (exists ((Y6 tptp.product_prod_nat_nat)) (= X2 (@ tptp.some_P7363390416028606310at_nat Y6))))))
% 6.31/6.60 (assert (forall ((X2 tptp.option_num)) (= (not (= X2 tptp.none_num)) (exists ((Y6 tptp.num)) (= X2 (@ tptp.some_num Y6))))))
% 6.31/6.60 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.60 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.60 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.31/6.60 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.31/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.31/6.60 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.31/6.60 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.31/6.60 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.31/6.60 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.31/6.60 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.31/6.60 (assert (forall ((X2 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X2) X2))) (= X2 tptp.zero_zero_real))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.31/6.60 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.31/6.60 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N2) K)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.31/6.60 (assert (forall ((K tptp.nat) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N2)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.31/6.60 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.31/6.60 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.31/6.60 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.31/6.60 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ (@ tptp.modulo_modulo_nat M) _let_1)))))
% 6.31/6.60 (assert (forall ((K tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) _let_1) tptp.one_one_nat)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (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)))))
% 6.31/6.60 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 6.31/6.60 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.31/6.60 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.31/6.60 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.31/6.60 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))))
% 6.31/6.60 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.31/6.60 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.60 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A2) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B2) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) C))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B2) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) C))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A2) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B2) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A2) B2)) C))))))
% 6.31/6.60 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B2) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A2) B2)) C))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.31/6.60 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.31/6.60 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X2) (=> (not (= X2 (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 6.31/6.60 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N2)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N2)) B))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N2)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N2)) B))))
% 6.31/6.61 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) Deg3))))))))
% 6.31/6.61 (assert (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.31/6.61 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N2))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)))
% 6.31/6.61 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y))) (=> (=> (= X2 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)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A4)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X2) Y)))) _let_1))))))
% 6.31/6.61 (assert (forall ((X2 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y))) (=> (=> (= X2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.product_prod_nat_nat) (B3 tptp.num)) (=> (= X2 (@ tptp.some_P7363390416028606310at_nat A4)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X2) Y)))) _let_1))))))
% 6.31/6.61 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X2) Y))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A4 tptp.num) (B3 tptp.product_prod_nat_nat)) (=> (= X2 (@ tptp.some_num A4)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B3)) (@ (@ P X2) Y)))) _let_1))))))
% 6.31/6.61 (assert (forall ((X2 tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X2) Y))) (=> (=> (= X2 tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (= X2 (@ tptp.some_num A4)) (=> (= Y (@ tptp.some_num B3)) (@ (@ P X2) Y)))) _let_1))))))
% 6.31/6.61 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X7 tptp.option4927543243414619207at_nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 6.31/6.61 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X7 tptp.option_num)) (@ P3 X7))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))))
% 6.31/6.61 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X7 tptp.option4927543243414619207at_nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 6.31/6.61 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X7 tptp.option_num)) (@ P3 X7))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))))
% 6.31/6.61 (assert (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 6.31/6.61 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))))
% 6.31/6.61 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.31/6.61 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 6.31/6.61 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 6.31/6.61 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 6.31/6.61 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 6.31/6.61 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.31/6.61 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.31/6.61 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X2) Y) (=> (=> (= X2 (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))))
% 6.31/6.61 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))))
% 6.31/6.61 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))
% 6.31/6.61 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D3 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (let ((_let_3 (= _let_1 N2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) P2) (=> (@ (@ tptp.ord_less_nat M) P2) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) P2) (=> (@ P N) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N)) P2))))) (@ P M)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)))
% 6.31/6.61 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q3))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X2) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X2) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 6.31/6.61 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.31/6.61 (assert (= tptp.neg_numeral_dbl_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) X))))
% 6.31/6.61 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat X) X))))
% 6.31/6.61 (assert (= tptp.neg_numeral_dbl_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) X))))
% 6.31/6.61 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X2 tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B3)) X5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X5)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X5)))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2)) X5)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2)) X5)))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd)) X5)))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B3)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S)) X5)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S)) X5)))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList2) Summary2)) X5)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2)) X5)))))))))))
% 6.31/6.61 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.31/6.61 (assert (forall ((X2 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A4 Bool) (B3 Bool) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A4) B3)) X5)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X2 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S)) X5)))))))))
% 6.31/6.61 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))))
% 6.31/6.61 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))))
% 6.31/6.61 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))))
% 6.31/6.61 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))
% 6.31/6.61 (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)))
% 6.31/6.61 (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)))
% 6.31/6.61 (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)))
% 6.31/6.61 (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)))
% 6.31/6.61 (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)))
% 6.31/6.61 (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)))
% 6.31/6.61 (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)))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.31/6.61 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (forall ((S tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q2) S))))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (forall ((S tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X2) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (exists ((Q3 tptp.nat)) (= X2 (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q3))))))))
% 6.31/6.61 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X2))) (let ((_let_4 (= X2 tptp.one_one_nat))) (let ((_let_5 (= X2 tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N2)) Q2))) (@ _let_1 N2)))))))
% 6.31/6.61 (assert (forall ((A Bool) (B Bool) (X2 tptp.nat)) (let ((_let_1 (= X2 tptp.one_one_nat))) (let ((_let_2 (= X2 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X2) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (not (@ (@ tptp.ord_less_real T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (not (@ (@ tptp.ord_less_rat T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (not (@ (@ tptp.ord_less_num T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (not (@ (@ tptp.ord_less_nat T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (not (@ (@ tptp.ord_less_int T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X3))) (=> (@ _let_1 Z3) (@ _let_1 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X3))) (=> (@ _let_1 Z3) (@ _let_1 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X3))) (=> (@ _let_1 Z3) (@ _let_1 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X3))) (=> (@ _let_1 Z3) (@ _let_1 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X3))) (=> (@ _let_1 Z3) (@ _let_1 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (@ (@ tptp.ord_less_real T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (@ (@ tptp.ord_less_rat T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (@ (@ tptp.ord_less_num T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (@ (@ tptp.ord_less_nat T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (@ (@ tptp.ord_less_int T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (not (@ (@ tptp.ord_less_real X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (not (@ (@ tptp.ord_less_rat X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (not (@ (@ tptp.ord_less_num X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (not (@ (@ tptp.ord_less_nat X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (not (@ (@ tptp.ord_less_int X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (not (= X3 T2)))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (or (@ P X3) (@ Q X3)) (or (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (P5 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.rat Bool)) (P5 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.num Bool)) (P5 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (P5 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (= (and (@ P X3) (@ Q X3)) (and (@ P5 X3) (@ Q6 X3))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X2)) (=> (forall ((Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (X2 tptp.nat) (M7 tptp.nat)) (=> (@ P X2) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M3 tptp.nat)) (=> (@ P M3) (not (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M3)))))))))))
% 6.31/6.61 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))))
% 6.31/6.61 (assert (forall ((X2 tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A4 tptp.nat) (B3 tptp.nat) (Acc tptp.num)) (not (= X2 (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A4) (@ (@ tptp.product_Pair_nat_num B3) Acc)))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A4 tptp.nat) (B3 tptp.nat) (Acc tptp.nat)) (not (= X2 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A4) (@ (@ tptp.product_Pair_nat_nat B3) Acc)))))))))
% 6.31/6.61 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.61 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N2)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I5)) J3)) (@ P J3))))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N2))) M) tptp.one_one_nat))))
% 6.31/6.61 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Summary)) X2) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X2) X2))) _let_1) TreeList) Summary)))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (not (@ (@ tptp.ord_less_eq_real T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (not (@ (@ tptp.ord_less_eq_rat T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (not (@ (@ tptp.ord_less_eq_num T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (not (@ (@ tptp.ord_less_eq_nat T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (not (@ (@ tptp.ord_less_eq_int T2) X3)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real X3) Z3) (@ (@ tptp.ord_less_eq_real X3) T2))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z3) (@ (@ tptp.ord_less_eq_rat X3) T2))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z3) (@ (@ tptp.ord_less_eq_num X3) T2))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z3) (@ (@ tptp.ord_less_eq_nat X3) T2))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z3) (@ (@ tptp.ord_less_eq_int X3) T2))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (@ (@ tptp.ord_less_eq_real T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (@ (@ tptp.ord_less_eq_rat T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (@ (@ tptp.ord_less_eq_num T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (@ (@ tptp.ord_less_eq_nat T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (@ (@ tptp.ord_less_eq_int T2) X3))))))
% 6.31/6.61 (assert (forall ((T2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X3) (not (@ (@ tptp.ord_less_eq_real X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X3) (not (@ (@ tptp.ord_less_eq_rat X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.num)) (exists ((Z3 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X3) (not (@ (@ tptp.ord_less_eq_num X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X3) (not (@ (@ tptp.ord_less_eq_nat X3) T2)))))))
% 6.31/6.61 (assert (forall ((T2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X3) (not (@ (@ tptp.ord_less_eq_int X3) T2)))))))
% 6.31/6.61 (assert (forall ((X2 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))) (=> (= X2 X6) (=> (=> _let_2 (= P P5)) (= (and (@ _let_1 X2) P) (and _let_2 P5))))))))
% 6.31/6.61 (assert (forall ((X2 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))) (=> (= X2 X6) (=> (=> _let_2 (= P P5)) (= (=> (@ _let_1 X2) P) (=> _let_2 P5))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.31/6.61 (assert (forall ((M tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X2))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.31/6.61 (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))))))))))
% 6.31/6.61 (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))))))))))
% 6.31/6.61 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A5 Bool) (B5 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A5) B5))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) N3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (= A22 (@ (@ tptp.plus_plus_nat N3) N3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N3))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N3) _let_1)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) N3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 N3)) (= A22 (@ (@ tptp.plus_plus_nat N3) N3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N3))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList3) Summary3)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X) N3))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N3) _let_3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N3))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N3))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N3) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) (@ (@ tptp.vEBT_VEBT_low X) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))))))
% 6.31/6.61 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A4 Bool) (B3 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A4) B3))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ 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 N) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N) M3)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ 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 N)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N) M3)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_1))) (not (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M3)) (=> (= M3 N) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N) M3)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M3 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList2) Summary2)) (=> (= A23 Deg2) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X3) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M3) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M3)) (=> (= M3 (@ tptp.suc N)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N) M3)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I)))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M3)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I)) (@ (@ tptp.vEBT_VEBT_low Ma2) N))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I)) (@ (@ tptp.vEBT_VEBT_low X3) N))) (and (@ (@ tptp.ord_less_nat Mi2) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma2)))))))))))))))))))))))))))))))
% 6.31/6.61 (assert (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList) Summary)) Deg))))))))))
% 6.31/6.61 (assert (forall ((A3 tptp.nat) (B4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A3) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B4) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B4) N2))))))
% 6.31/6.61 (assert (forall ((A3 tptp.nat) (N2 tptp.nat)) (= A3 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A3) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A3) N2)))))
% 6.31/6.61 (assert (forall ((A3 tptp.nat) (B4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A3) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B4) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A3) N2)) (@ (@ tptp.divide_divide_nat B4) N2))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs) Ys)) N2) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs) Ys)) N2) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) N2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) N2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) N2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) N2) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) N2) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R2)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R2)))))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M3 tptp.nat)) (@ (@ P M3) tptp.zero_zero_nat)) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ P N) (@ (@ tptp.modulo_modulo_nat M3) N)) (@ (@ P M3) N)))) (@ (@ P M) N2)))))
% 6.31/6.61 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X2 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((X2 (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X2) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X2 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y2)) (= X22 Y2))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) (@ _let_1 K)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_int Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_nat Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_int Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.31/6.61 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.modulo_modulo_int K) L) R2))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= Q2 Q5))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q5) R4)) (= R2 R4))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.31/6.61 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R2)) (= (@ (@ tptp.divide_divide_int K) L) Q2))))
% 6.31/6.61 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q4))))))
% 6.31/6.61 (assert (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q3))))))
% 6.31/6.61 (assert (forall ((A3 tptp.int) (B4 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (=> (= (@ (@ tptp.modulo_modulo_int A3) N2) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B4) N2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A3) N2)) (@ (@ tptp.divide_divide_int B4) N2))))))))
% 6.31/6.61 (assert (forall ((A3 tptp.int) (N2 tptp.int)) (= A3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A3) N2)) N2)) (@ (@ tptp.modulo_modulo_int A3) N2)))))
% 6.31/6.61 (assert (forall ((L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q2) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((I3 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I3) K) I3) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I3) (@ (@ tptp.ord_less_int I3) K)) (and (@ (@ tptp.ord_less_eq_int I3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I3))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.31/6.61 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.31/6.61 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.31/6.61 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.31/6.61 (assert (forall ((A tptp.int) (X2 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X2) (= A X2) (@ (@ tptp.ord_less_eq_int X2) A))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((A3 tptp.int) (B4 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A3) N2)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B4) N2) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B4) N2))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N2) K)) (and (=> (= K tptp.zero_zero_int) (@ P N2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P J3))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R2) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (=> (@ (@ tptp.ord_less_int R2) B) (= (@ (@ tptp.modulo_modulo_int A) B) R2))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) K)) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ (@ P I5) J3)))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) K)) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ (@ P I5) J3)))))))
% 6.31/6.61 (assert (forall ((B2 tptp.real) (A2 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B2) A2)) (@ (@ tptp.ord_less_real A2) B2))))
% 6.31/6.61 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B2) A2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 6.31/6.61 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B2) A2)) (@ (@ tptp.ord_less_num A2) B2))))
% 6.31/6.61 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B2) A2)) (@ (@ tptp.ord_less_nat A2) B2))))
% 6.31/6.61 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B2) A2)) (@ (@ tptp.ord_less_int A2) B2))))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.31/6.61 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R2)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q2)) R2)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R2) (@ (@ tptp.ord_less_int R2) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R2) (@ (@ tptp.ord_less_eq_int R2) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (assert (forall ((X2 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X2) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((X2 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X2) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R2)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R2)) tptp.one_one_int)))))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A4))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S))) (=> (= X2 _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S))) (=> (= X2 _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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 Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 6.31/6.61 (assert (forall ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))))
% 6.31/6.61 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 6.31/6.61 (assert (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 6.31/6.61 (assert (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 6.31/6.61 (assert (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 6.31/6.61 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L)))))
% 6.31/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L)))))
% 6.31/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_rat (@ (@ tptp.pow K) L)))))
% 6.31/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L)))))
% 6.31/6.61 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N2)) tptp.bot_bot_set_nat)))
% 6.31/6.61 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T)))))
% 6.31/6.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.31/6.61 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.31/6.61 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.31/6.61 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.31/6.61 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.31/6.61 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.61 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N2)) (not (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N2))) (@ _let_1 N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.31/6.61 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (= (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ _let_2 A))))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ _let_2 A))))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ _let_2 A))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N2) _let_1)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N2)) tptp.one_one_Code_integer)) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N2)) tptp.one_one_nat)) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N2)) tptp.one_one_int)) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.31/6.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) A)))) (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) B)))) (@ (@ tptp.dvd_dvd_real A) B))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.31/6.61 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (= A B) (= C D)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.31/6.61 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M) N2)) (=> (@ _let_1 N2) (@ _let_1 M))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) A)))) (@ tptp.collect_real (lambda ((C2 tptp.real)) (@ (@ tptp.dvd_dvd_real C2) B)))) (and (@ (@ tptp.dvd_dvd_real A) B) (not (@ (@ tptp.dvd_dvd_real B) A))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) A)))) (@ tptp.collect_nat (lambda ((C2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C2) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) A)))) (@ tptp.collect_int (lambda ((C2 tptp.int)) (@ (@ tptp.dvd_dvd_int C2) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) A)))) (@ tptp.collect_Code_integer (lambda ((C2 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C2) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 6.31/6.61 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.31/6.61 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.31/6.61 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.31/6.61 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.31/6.61 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.31/6.61 (assert (= (lambda ((X tptp.complex)) X) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.31/6.61 (assert (= (lambda ((X tptp.real)) X) (@ tptp.times_times_real tptp.one_one_real)))
% 6.31/6.61 (assert (= (lambda ((X tptp.rat)) X) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.31/6.61 (assert (= (lambda ((X tptp.nat)) X) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.31/6.61 (assert (= (lambda ((X tptp.int)) X) (@ tptp.times_times_int tptp.one_one_int)))
% 6.31/6.61 (assert (= tptp.ord_max_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A5) B5)) B5) A5))))
% 6.31/6.61 (assert (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B5)) B5) A5))))
% 6.31/6.61 (assert (= tptp.ord_max_num (lambda ((A5 tptp.num) (B5 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B5)) B5) A5))))
% 6.31/6.61 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B5)) B5) A5))))
% 6.31/6.61 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B5)) B5) A5))))
% 6.31/6.61 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X3 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X3) T2)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T2))))))))
% 6.31/6.61 (assert (forall ((D tptp.real) (D4 tptp.real) (T2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X3 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X3) T2)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K4) D4))) T2))))))))
% 6.31/6.61 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X3 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X3) T2)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K4) D4))) T2))))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (D4 tptp.int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X3 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X3) T2)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K4) D4))) T2))))))))
% 6.31/6.61 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X3 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X3) T2))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T2)))))))))
% 6.31/6.61 (assert (forall ((D tptp.real) (D4 tptp.real) (T2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X3 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X3) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K4) D4))) T2)))))))))
% 6.31/6.61 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X3 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X3) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K4) D4))) T2)))))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (D4 tptp.int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X3 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X3) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K4) D4))) T2)))))))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_complex (lambda ((A5 tptp.complex) (B5 tptp.complex)) (=> (= A5 tptp.zero_zero_complex) (= B5 tptp.zero_zero_complex)))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_real (lambda ((A5 tptp.real) (B5 tptp.real)) (=> (= A5 tptp.zero_zero_real) (= B5 tptp.zero_zero_real)))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (=> (= A5 tptp.zero_zero_rat) (= B5 tptp.zero_zero_rat)))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.31/6.61 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.complex) (Z2 tptp.complex)) (= Y4 Z2)) (lambda ((A5 tptp.complex) (B5 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A5) B5) tptp.zero_zero_complex))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A5 tptp.real) (B5 tptp.real)) (= (@ (@ tptp.minus_minus_real A5) B5) tptp.zero_zero_real))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((A5 tptp.rat) (B5 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A5) B5) tptp.zero_zero_rat))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A5 tptp.int) (B5 tptp.int)) (= (@ (@ tptp.minus_minus_int A5) B5) tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B5 tptp.code_integer) (A5 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A5 (@ (@ tptp.times_3573771949741848930nteger B5) K3))))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_real (lambda ((B5 tptp.real) (A5 tptp.real)) (exists ((K3 tptp.real)) (= A5 (@ (@ tptp.times_times_real B5) K3))))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (exists ((K3 tptp.rat)) (= A5 (@ (@ tptp.times_times_rat B5) K3))))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (exists ((K3 tptp.nat)) (= A5 (@ (@ tptp.times_times_nat B5) K3))))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_int (lambda ((B5 tptp.int) (A5 tptp.int)) (exists ((K3 tptp.int)) (= A5 (@ (@ tptp.times_times_int B5) K3))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (assert (forall ((P2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P2) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.times_times_nat X5) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X5) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.31/6.61 (assert (forall ((P2 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P2) (@ (@ tptp.times_times_int A) B)) (not (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.times_times_int X5) Y3)) (=> (@ (@ tptp.dvd_dvd_int X5) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B6 tptp.nat) (C4 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B6) C4)) (@ (@ tptp.dvd_dvd_nat B6) B) (@ (@ tptp.dvd_dvd_nat C4) C))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B6 tptp.int) (C4 tptp.int)) (and (= A (@ (@ tptp.times_times_int B6) C4)) (@ (@ tptp.dvd_dvd_int B6) B) (@ (@ tptp.dvd_dvd_int C4) C))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.31/6.61 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) D4))))) (forall ((X3 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (forall ((X3 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (forall ((X3 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) D4))))) (=> (forall ((X5 tptp.real) (K2 tptp.real)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_real X5) (@ (@ tptp.times_times_real K2) D4))))) (forall ((X3 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X3) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (=> (forall ((X5 tptp.rat) (K2 tptp.rat)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_rat X5) (@ (@ tptp.times_times_rat K2) D4))))) (forall ((X3 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (forall ((X3 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A3 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A3) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 6.31/6.61 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A3) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 6.31/6.61 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A3) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N2)) (@ (@ tptp.power_power_nat Y) N2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N2)) (@ (@ tptp.power_power_int Y) N2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N2)) (@ (@ tptp.power_power_real Y) N2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N2)) (@ (@ tptp.power_power_complex Y) N2)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N2)))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N2)))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N2)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B2) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A2) B2)) C))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X2) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X2) Z)) (@ (@ tptp.minus_minus_real Y) Z)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X2) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X2) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X2) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X2) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.31/6.61 (assert (= tptp.vEBT_set_vebt (lambda ((T tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T)))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri6519982836138164636nteger M) A)) (@ _let_1 A)))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int M) A)) (@ _let_1 A)))))
% 6.31/6.61 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.31/6.61 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.31/6.61 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.31/6.61 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.31/6.61 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A5) B5)) tptp.zero_zero_real))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A5) B5)) tptp.zero_zero_rat))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A5) B5)) tptp.zero_zero_int))))
% 6.31/6.61 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.31/6.61 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.31/6.61 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.31/6.61 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A5) B5)) tptp.zero_zero_real))))
% 6.31/6.61 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A5) B5)) tptp.zero_zero_rat))))
% 6.31/6.61 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A5) B5)) tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S2))))) (=> (@ (@ tptp.ord_less_real X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X3) S2))))) (=> (@ (@ tptp.ord_less_rat X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S2))))) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S2))))) (=> (@ (@ tptp.ord_less_int X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S2)))) (=> (@ (@ tptp.ord_less_real X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X3) S2)))) (=> (@ (@ tptp.ord_less_rat X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S2)))) (=> (@ (@ tptp.ord_less_nat X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S2)))) (=> (@ (@ tptp.ord_less_int X3) Z3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S2))))) (=> (@ (@ tptp.ord_less_real Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X3) S2))))) (=> (@ (@ tptp.ord_less_rat Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S2))))) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S2))))) (=> (@ (@ tptp.ord_less_int Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X3) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X3) S2)))) (=> (@ (@ tptp.ord_less_real Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X3 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X3) S2)))) (=> (@ (@ tptp.ord_less_rat Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X3) S2)))) (=> (@ (@ tptp.ord_less_nat Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X3) S2)))) (=> (@ (@ tptp.ord_less_int Z3) X3) (= _let_1 _let_1)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((I3 tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I3) K)) N2) (@ (@ tptp.ord_less_eq_real I3) (@ (@ tptp.minus_minus_real N2) K)))))
% 6.31/6.61 (assert (forall ((I3 tptp.rat) (K tptp.rat) (N2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I3) K)) N2) (@ (@ tptp.ord_less_eq_rat I3) (@ (@ tptp.minus_minus_rat N2) K)))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) K)) N2) (@ (@ tptp.ord_less_eq_nat I3) (@ (@ tptp.minus_minus_nat N2) K)))))
% 6.31/6.61 (assert (forall ((I3 tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I3) K)) N2) (@ (@ tptp.ord_less_eq_int I3) (@ (@ tptp.minus_minus_int N2) K)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((I3 tptp.real) (K tptp.real) (N2 tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N2) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I3) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))))
% 6.31/6.61 (assert (forall ((I3 tptp.rat) (K tptp.rat) (N2 tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N2) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I3) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N2) K)) J)))))))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (K tptp.nat) (N2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))))
% 6.31/6.61 (assert (forall ((I3 tptp.int) (K tptp.int) (N2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N2) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I3) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (= (@ (@ 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 X2) A)) B))))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (= (@ (@ 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 X2) A)) B))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (= (@ (@ 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 X2) A)) B))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.minus_minus_real X2) Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) Y)) (@ (@ tptp.minus_minus_rat X2) Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) Y)) (@ (@ tptp.minus_minus_int X2) Y)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N2) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.31/6.61 (assert (forall ((B tptp.nat) (A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N2) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A5 tptp.code_integer) (B5 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B5) A5) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B5) A5) tptp.zero_zero_nat))))
% 6.31/6.61 (assert (= tptp.dvd_dvd_int (lambda ((A5 tptp.int) (B5 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B5) A5) tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.31/6.61 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X2) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X2) N2)) (@ (@ tptp.power_power_nat Y) M))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X2) N2)) (@ (@ tptp.power_power_int Y) M))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X2) N2)) (@ (@ tptp.power_power_real Y) M))))))
% 6.31/6.61 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X2) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X2) N2)) (@ (@ tptp.power_power_complex Y) M))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 6.31/6.61 (assert (forall ((A tptp.complex) (N2 tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (@ _let_1 M))))))
% 6.31/6.61 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_int M) N2) (=> (@ (@ tptp.dvd_dvd_int N2) M) (= M N2))))))))
% 6.31/6.61 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N2) (not (@ (@ tptp.dvd_dvd_int N2) M))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (M tptp.int) (T2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T2)))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N2))))))
% 6.31/6.61 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X2) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X2) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_3 Y3)) D)) (= (@ _let_3 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D)))))))))))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X5) (@ (@ tptp.plus_plus_nat (@ _let_2 Y3)) D3)) (= (@ _let_2 X5) (@ (@ tptp.plus_plus_nat (@ _let_1 Y3)) D3))))))))))
% 6.31/6.61 (assert (forall ((I3 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P K) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I3))))))
% 6.31/6.61 (assert (forall ((I3 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I3))))))
% 6.31/6.61 (assert (forall ((K tptp.int) (N2 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N2) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N2)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (D tptp.int) (X2 tptp.int) (T2 tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X2))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T2)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T2))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.pow X2) tptp.one) X2)))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X))) (exists ((X tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.zero_z3403309356797280102nteger)) (@ P X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X))) (exists ((X tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X) tptp.zero_zero_complex)) (@ P X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X tptp.real)) (@ P (@ (@ tptp.times_times_real L) X))) (exists ((X tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X) tptp.zero_zero_real)) (@ P X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X))) (exists ((X tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X) tptp.zero_zero_rat)) (@ P X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X))) (exists ((X tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X) tptp.zero_zero_nat)) (@ P X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X tptp.int)) (@ P (@ (@ tptp.times_times_int L) X))) (exists ((X tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X) tptp.zero_zero_int)) (@ P X))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.31/6.61 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.31/6.61 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.31/6.61 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) Y)) Z)))))
% 6.31/6.61 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) Y)) Z)))))
% 6.31/6.61 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) Y)) Z)))))
% 6.31/6.61 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X2 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.31/6.61 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.31/6.61 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.31/6.61 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.31/6.61 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X2) X2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X2) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) X2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) X2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X2) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X2) X2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat K) N2)))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) D3))))))))
% 6.31/6.61 (assert (forall ((Z tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int Z) N2)))))
% 6.31/6.61 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.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))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P1 X5) (@ P1 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P1 X5))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (P5 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P5 X5) (@ P5 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (exists ((X_1 tptp.int)) (@ P5 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I3 tptp.int)) (=> (@ P K) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P I2) (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int))))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P I2) (@ P (@ (@ tptp.minus_minus_int I2) tptp.one_one_int))))) (@ P I3))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.31/6.61 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.31/6.61 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.31/6.61 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))))))))))))
% 6.31/6.61 (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)))))))))))))))
% 6.31/6.61 (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)))))))))))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B3))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B3))))))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B3 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B3))))))))
% 6.31/6.61 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.31/6.61 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.31/6.61 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.31/6.61 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.code_integer) (Z2 tptp.code_integer)) (= Y4 Z2)) (lambda ((A5 tptp.code_integer) (B5 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 A5) (@ _let_2 B5)) (= (@ (@ tptp.divide6298287555418463151nteger A5) _let_1) (@ (@ tptp.divide6298287555418463151nteger B5) _let_1))))))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A5 tptp.nat) (B5 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 A5) (@ _let_2 B5)) (= (@ (@ tptp.divide_divide_nat A5) _let_1) (@ (@ tptp.divide_divide_nat B5) _let_1))))))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A5 tptp.int) (B5 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 A5) (@ _let_2 B5)) (= (@ (@ tptp.divide_divide_int A5) _let_1) (@ (@ tptp.divide_divide_int B5) _let_1))))))))
% 6.31/6.61 (assert (forall ((Y tptp.real) (Z tptp.real) (X2 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X2) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X2 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X2) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X2) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.31/6.61 (assert (forall ((X2 tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X2))) (=> (not (= X2 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X2))) (=> (not (= X2 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X2) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (not (= X2 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X2 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X2) (@ (@ tptp.power_8256067586552552935nteger X2) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X2 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X2) (@ (@ tptp.power_power_rat X2) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X2 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X2) (@ (@ tptp.power_power_nat X2) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X2 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X2) (@ (@ tptp.power_power_int X2) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X2 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X2) (@ (@ tptp.power_power_real X2) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X2 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X2) (@ (@ tptp.power_power_complex X2) N2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X2) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X2)) _let_1)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X2)) _let_1)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X2) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X2)) _let_1)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X2) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X2)) _let_1)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N2) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N2)) M) (= N2 tptp.one_one_nat)))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M)) M) (= N2 tptp.one_one_nat)))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I3))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I3) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.61 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K) D))))))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_eq_real R2) S2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.minus_minus_real V) U))) S2))) V))))))
% 6.31/6.61 (assert (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R2) (=> (@ (@ tptp.ord_less_eq_rat R2) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R2) (@ (@ tptp.minus_minus_rat V) U))) S2))) V))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se8260200283734997820nteger M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2793503036327961859nteger M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1345352211410354436nteger M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.31/6.61 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.31/6.61 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList) S2)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (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))))))))))
% 6.31/6.61 (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))))))))))
% 6.31/6.61 (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))))))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (@ _let_1 A))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (@ _let_1 A))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (@ _let_1 A))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N2)))))
% 6.31/6.61 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.31/6.61 (assert (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList) Vd2)) X2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 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 X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X2) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary)) X2) (=> (not (= X2 Mi)) (=> (not (= X2 Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4))))))))))))))))
% 6.31/6.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Vc)) X2) (or (= X2 Mi) (= X2 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_3)) (@ (@ tptp.vEBT_VEBT_low X2) _let_2))) _let_4)))))))))
% 6.31/6.61 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.31/6.61 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.31/6.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.31/6.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((W tptp.real) (Y tptp.real) (X2 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X2))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 6.31/6.61 (assert (forall ((W tptp.rat) (Y tptp.rat) (X2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X2))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 6.31/6.61 (assert (forall ((W tptp.nat) (Y tptp.nat) (X2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X2))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 6.31/6.61 (assert (forall ((W tptp.int) (Y tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X2))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X2) (= Y Z)))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.31/6.61 (assert (forall ((X2 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 X2) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X2) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) Y)))))))
% 6.31/6.61 (assert (forall ((X2 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 X2) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) Y)))))))
% 6.31/6.61 (assert (forall ((X2 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 X2) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X2) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X2)) Y)))))))
% 6.31/6.61 (assert (forall ((X2 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 X2) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X2) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X2)) Y)))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ 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 (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A4) B3)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ 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)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((S tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList2) S))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (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)))))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ tptp.vEBT_Leaf A4) B3)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))) (not (forall ((Mi2 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 Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList2) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList2) Vd))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X2) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X2) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList)) (not (or (= X2 Mi) (= X2 Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X2) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ 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 (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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 Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 (@ (@ 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)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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 Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va))) TreeList2) Summary2))) (= Y (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.31/6.61 (assert (forall ((L tptp.num) (R2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q2) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R2))))))))))
% 6.31/6.61 (assert (forall ((L tptp.num) (R2 tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q2) R2)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R2))))))))))
% 6.31/6.61 (assert (forall ((L tptp.num) (R2 tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q2) R2)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R2))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R2) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R2))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat tptp.bot_bot_set_nat) X2) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.ord_max_set_int tptp.bot_bot_set_int) X2) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.ord_max_set_real tptp.bot_bot_set_real) X2) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.bot_bot_nat) X2) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat)) (= (@ (@ tptp.ord_max_set_nat X2) tptp.bot_bot_set_nat) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.set_int)) (= (@ (@ tptp.ord_max_set_int X2) tptp.bot_bot_set_int) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.set_real)) (= (@ (@ tptp.ord_max_set_real X2) tptp.bot_bot_set_real) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.ord_max_nat X2) tptp.bot_bot_nat) X2)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_int))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A3) tptp.bot_bot_set_real) (= A3 tptp.bot_bot_set_real))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_nat))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X2) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A4))) (let ((_let_2 (@ _let_1 B3))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B3))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S))) (=> (= X2 _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S))) (=> (= X2 _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary2))) (=> (= X2 _let_2) (=> (= Y (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xa2) Xa2))) _let_1) TreeList2) Summary2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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 Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (=> (= X2 _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 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 X2) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X2) (@ _let_2 Y)) (= X2 Y)))))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.31/6.61 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X2) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X2) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.num)) (@ (@ tptp.ord_less_eq_num X2) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X2) X2)))
% 6.31/6.61 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_eq_int X2) X2)))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N2)) K))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.31/6.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_complex) (B4 tptp.set_complex)) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X5))) (=> (@ _let_1 A3) (@ _let_1 B4)))) (@ (@ tptp.ord_le211207098394363844omplex A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real)) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ tptp.member_real X5))) (=> (@ _let_1 A3) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_real A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_set_nat) (B4 tptp.set_set_nat)) (=> (forall ((X5 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X5))) (=> (@ _let_1 A3) (@ _let_1 B4)))) (@ (@ tptp.ord_le6893508408891458716et_nat A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int)) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ tptp.member_int X5))) (=> (@ _let_1 A3) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_int A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X5))) (=> (@ _let_1 A3) (@ _let_1 B4)))) (@ (@ tptp.ord_less_eq_set_nat A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A3) (= A3 B4)))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ _let_1 (@ _let_1 I3)) I3)))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I3))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A3) B4) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A3) B4) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A3) B4) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A3) B4))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I3) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I3) K)) J)))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I3)) K)))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I3))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (not (= A3 B4)) (@ (@ tptp.ord_less_set_nat A3) B4)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I3) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I3))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I3) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I3) K)) (@ tptp.suc J))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (C5 tptp.set_nat) (D4 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C5) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B4) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B4)) (@ (@ tptp.minus_minus_set_nat C5) D4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B4)) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (= (@ (@ tptp.minus_minus_set_nat B4) (@ (@ tptp.minus_minus_set_nat C5) A3)) A3)))))
% 6.31/6.61 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I3 tptp.nat)) (=> (@ P K) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P (@ (@ tptp.minus_minus_nat K) I3))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))))
% 6.31/6.61 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.31/6.61 (assert (forall ((J tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N2)) K))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N2) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (or (@ (@ tptp.ord_less_nat N2) M) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M))))))
% 6.31/6.61 (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))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N2) L)))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M N2)))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 M)))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)))
% 6.31/6.61 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M) N2)))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X5)) (@ _let_2 Y3)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X5)) (@ _let_1 Y3)) D3)))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N2) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) M))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M) N2)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M) N2)) M))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I3) K)) J))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (= (= (@ (@ tptp.minus_minus_nat J) I3) K) (= J (@ (@ tptp.plus_plus_nat K) I3))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I3)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I3)))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I3))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I3) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I3) K)) J)))))
% 6.31/6.61 (assert (forall ((J tptp.nat) (K tptp.nat) (I3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I3) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I3) K)))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))))
% 6.31/6.61 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N3)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N3)) N3)))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N2) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M)) M) (@ (@ tptp.ord_max_nat N2) M))))
% 6.31/6.61 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X2 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X2))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))) N2))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D2)) (not (@ P D2)))))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D2)) (@ P D2)))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I3) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I3) K))))))
% 6.31/6.61 (assert (forall ((Y tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X2) (= (@ (@ tptp.ord_less_eq_set_nat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X2) (= (@ (@ tptp.ord_less_eq_rat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X2) (= (@ (@ tptp.ord_less_eq_num X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= (@ (@ tptp.ord_less_eq_nat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (= (@ (@ tptp.ord_less_eq_int X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X2) Y)) (@ (@ tptp.ord_less_eq_rat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X2) Y)) (@ (@ tptp.ord_less_eq_num Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X2) Y)) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_eq_rat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y) (@ (@ tptp.ord_less_eq_num Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_set_nat X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_num X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_nat X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (= X2 Y) (@ (@ tptp.ord_less_eq_int X2) Y))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (@ (@ tptp.ord_less_eq_set_nat B5) A5)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B5) (@ (@ tptp.ord_less_eq_rat B5) A5)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((A5 tptp.num) (B5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B5) (@ (@ tptp.ord_less_eq_num B5) A5)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B5) (@ (@ tptp.ord_less_eq_nat B5) A5)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A5 tptp.int) (B5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B5) (@ (@ tptp.ord_less_eq_int B5) A5)))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.31/6.61 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.31/6.61 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.31/6.61 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.31/6.61 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat A) B) (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B5) A5) (@ (@ tptp.ord_less_eq_set_nat A5) B5)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B5) A5) (@ (@ tptp.ord_less_eq_rat A5) B5)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((A5 tptp.num) (B5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B5) A5) (@ (@ tptp.ord_less_eq_num A5) B5)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A5) (@ (@ tptp.ord_less_eq_nat A5) B5)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A5 tptp.int) (B5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B5) A5) (@ (@ tptp.ord_less_eq_int A5) B5)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.rat) (B3 tptp.rat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ (@ tptp.ord_less_eq_set_nat A) C)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((X tptp.set_nat) (Y6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X) Y6) (@ (@ tptp.ord_less_eq_set_nat Y6) X)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((X tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y6) (@ (@ tptp.ord_less_eq_rat Y6) X)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((X tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y6) (@ (@ tptp.ord_less_eq_num Y6) X)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((X tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y6) (@ (@ tptp.ord_less_eq_nat Y6) X)))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((X tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y6) (@ (@ tptp.ord_less_eq_int Y6) X)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X2))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X2))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X2))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num B) A) (not (= B A))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= B A))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (not (= B A))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (@ (@ tptp.ord_less_rat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (@ (@ tptp.ord_less_num Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (@ (@ tptp.ord_less_int Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= Y X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (= Y X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (= Y X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= Y X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (= Y X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y) (@ (@ tptp.ord_less_real Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X2) Y) (= X2 Y) (@ (@ tptp.ord_less_rat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X2) Y) (= X2 Y) (@ (@ tptp.ord_less_num Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X2) Y) (= X2 Y) (@ (@ tptp.ord_less_nat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X2) Y) (= X2 Y) (@ (@ tptp.ord_less_int Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_real Y) X2) P))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X2) Y) (=> (@ (@ tptp.ord_less_rat Y) X2) P))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X2) Y) (=> (@ (@ tptp.ord_less_num Y) X2) P))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X2) Y) (=> (@ (@ tptp.ord_less_nat Y) X2) P))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X2) Y) (=> (@ (@ tptp.ord_less_int Y) X2) P))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (@ (@ tptp.ord_less_rat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (@ (@ tptp.ord_less_num Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (@ (@ tptp.ord_less_int Y) X2)))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real)) (not (@ (@ tptp.ord_less_real X2) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat)) (not (@ (@ tptp.ord_less_rat X2) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.num)) (not (@ (@ tptp.ord_less_num X2) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat)) (not (@ (@ tptp.ord_less_nat X2) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int)) (not (@ (@ tptp.ord_less_int X2) X2))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_rat X2) Y) (@ (@ tptp.ord_less_rat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_num X2) Y) (@ (@ tptp.ord_less_num Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_nat X2) Y) (@ (@ tptp.ord_less_nat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (not (= X2 Y)) (or (@ (@ tptp.ord_less_int X2) Y) (@ (@ tptp.ord_less_int Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (@ (@ tptp.ord_less_real Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (@ (@ tptp.ord_less_rat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (@ (@ tptp.ord_less_num Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (@ (@ tptp.ord_less_nat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (@ (@ tptp.ord_less_int Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (@ (@ tptp.ord_less_rat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_num X2) Y)) (@ (@ tptp.ord_less_num Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (= X2 Y)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (@ (@ tptp.ord_less_int Y) X2)))))
% 6.31/6.61 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (or (@ (@ tptp.ord_less_real Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y)) (or (@ (@ tptp.ord_less_rat Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y)) (or (@ (@ tptp.ord_less_num Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (or (@ (@ tptp.ord_less_nat Y) X2) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y)) (or (@ (@ tptp.ord_less_int Y) X2) (= X2 Y)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N3 tptp.nat)) (and (@ P4 N3) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N3) (not (@ P4 M6)))))))))
% 6.31/6.61 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.31/6.61 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.31/6.61 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.31/6.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.31/6.61 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.31/6.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_real Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_rat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_num Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_nat Y) X2)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (=> (not (= X2 Y)) (@ (@ tptp.ord_less_int Y) X2)))))
% 6.31/6.61 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X2)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X2)) (= (not (@ (@ tptp.ord_less_rat X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X2)) (= (not (@ (@ tptp.ord_less_num X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X2)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X2)) (= (not (@ (@ tptp.ord_less_int X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y5) X5) (@ P Y5))) (@ P X5))) (@ P A))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (not (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real X2) Z3) (@ (@ tptp.ord_less_real Z3) Y))))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (exists ((Z3 tptp.rat)) (and (@ (@ tptp.ord_less_rat X2) Z3) (@ (@ tptp.ord_less_rat Z3) Y))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X2) X_12))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X2) X_12))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X2) X_12))))
% 6.31/6.61 (assert (forall ((X2 tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X2) X_12))))
% 6.31/6.61 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X2))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I3)) U)) N2))))))
% 6.31/6.61 (assert (forall ((J tptp.nat) (I3 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I3) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I3) J)) U)) M)) N2)))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I3)) U)) N2))))))
% 6.31/6.61 (assert (forall ((J tptp.nat) (I3 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I3) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I3) J)) U)) M)) N2)))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I3)) U)) N2))))))
% 6.31/6.61 (assert (forall ((J tptp.nat) (I3 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I3) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I3) J)) U)) M) N2)))))
% 6.31/6.61 (assert (forall ((Q2 tptp.nat) (N2 tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R2) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 6.31/6.61 (assert (forall ((R2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R2) N2) (=> (@ (@ tptp.ord_less_eq_nat R2) M) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M) R2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) R2))))))
% 6.31/6.61 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N3)) N3)))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_complex) (B4 tptp.set_complex) (X2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X2))) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ tptp.member_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_set_nat) (B4 tptp.set_set_nat) (X2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ tptp.member_int X2))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X2))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_complex) (B4 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_le211207098394363844omplex A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_set_nat) (B4 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (@ _let_1 A3) (@ _let_1 B4))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A3) B4) (not (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (@ (@ tptp.ord_less_eq_set_nat B4) A3))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (= A3 B4) (not (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (not (@ (@ tptp.ord_less_eq_set_nat B4) A3)))))))
% 6.31/6.61 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B7 tptp.set_set_nat)) (forall ((X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (= A3 B4) (@ (@ tptp.ord_less_eq_set_nat A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (= A3 B4) (@ (@ tptp.ord_less_eq_set_nat B4) A3))))
% 6.31/6.61 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B7) (not (= A6 B7))))))
% 6.31/6.61 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (forall ((T tptp.complex)) (let ((_let_1 (@ tptp.member_complex T))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (forall ((T tptp.real)) (let ((_let_1 (@ tptp.member_real T))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B7 tptp.set_set_nat)) (forall ((T tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (forall ((T tptp.int)) (let ((_let_1 (@ tptp.member_int T))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (forall ((T tptp.nat)) (let ((_let_1 (@ tptp.member_nat T))) (=> (@ _let_1 A6) (@ _let_1 B7)))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A3) A3)))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (=> (forall ((X5 tptp.real)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X5 tptp.list_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X5 tptp.set_nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ Q X5))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A3))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (@ _let_1 C5))))))
% 6.31/6.61 (assert (= (lambda ((Y4 tptp.set_nat) (Z2 tptp.set_nat)) (= Y4 Z2)) (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B7) (@ (@ tptp.ord_less_eq_set_nat B7) A6)))))
% 6.31/6.61 (assert (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X tptp.real)) (=> (@ P X) (@ Q X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)) (forall ((X tptp.list_nat)) (=> (@ P X) (@ Q X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)) (forall ((X tptp.set_nat)) (=> (@ P X) (@ Q X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X tptp.int)) (=> (@ P X) (@ Q X))))))
% 6.31/6.61 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X tptp.nat)) (=> (@ P X) (@ Q X))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A3) B4) (@ (@ tptp.ord_less_eq_set_nat A3) B4))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A3))) (=> (@ _let_1 B4) (=> (@ (@ tptp.ord_less_eq_set_nat B4) C5) (@ _let_1 C5))))))
% 6.31/6.61 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A6) B7) (not (@ (@ tptp.ord_less_eq_set_nat B7) A6))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (=> (@ (@ tptp.ord_less_set_nat B4) C5) (@ (@ tptp.ord_less_set_nat A3) C5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A6) B7) (= A6 B7)))))
% 6.31/6.61 (assert (forall ((X2 tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M3 tptp.nat)) (not (= X2 (@ (@ tptp.product_Pair_nat_nat K2) M3)))))))
% 6.31/6.61 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= N2 (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.31/6.61 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N3) (= N3 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N3)) N3))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.31/6.61 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N3) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N3))))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I3)) U)) N2))))))
% 6.31/6.61 (assert (forall ((J tptp.nat) (I3 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I3) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I3) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I3) J)) U)) M)) N2)))))
% 6.31/6.61 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N3) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N3))))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A3) (@ P X))))) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A3) (@ P X))))) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) A3) (@ P X))))) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (and (@ (@ tptp.member_set_nat X) A3) (@ P X))))) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A3) (@ P X))))) A3)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A3) (@ P X))))) A3)))
% 6.31/6.61 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B7 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B7))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B7 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B7))))))
% 6.31/6.61 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B7 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) A6))) (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) B7))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B7 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B7))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B7 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B7))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_int))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.31/6.61 (assert (= tptp.power_power_complex (lambda ((P6 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P6) (@ (@ tptp.power_power_complex P6) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.61 (assert (= tptp.power_power_real (lambda ((P6 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P6) (@ (@ tptp.power_power_real P6) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.61 (assert (= tptp.power_power_rat (lambda ((P6 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P6) (@ (@ tptp.power_power_rat P6) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.61 (assert (= tptp.power_power_nat (lambda ((P6 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P6) (@ (@ tptp.power_power_nat P6) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.61 (assert (= tptp.power_power_int (lambda ((P6 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P6) (@ (@ tptp.power_power_int P6) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.31/6.61 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (or (@ (@ tptp.ord_less_real X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y) (or (@ (@ tptp.ord_less_set_nat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (or (@ (@ tptp.ord_less_rat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (or (@ (@ tptp.ord_less_num X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (or (@ (@ tptp.ord_less_nat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (or (@ (@ tptp.ord_less_int X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_real Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_rat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X2) Y) (@ (@ tptp.ord_less_num Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X2) Y) (@ (@ tptp.ord_less_nat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_int Y) X2))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_num (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_int (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_real (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.real) (Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.31/6.61 (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 ((X5 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Y3) (@ (@ tptp.ord_less_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_nat Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X2) Z)))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y) (=> (@ (@ tptp.ord_less_set_nat Y) Z) (@ (@ tptp.ord_less_set_nat X2) Z)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X2) Z)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X2) Z)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X2) Z)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X2) Z)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat X2) Y) (@ (@ tptp.ord_less_eq_set_nat X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Y) (@ (@ tptp.ord_less_eq_num X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Y) (@ (@ tptp.ord_less_eq_nat X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Y) (@ (@ tptp.ord_less_eq_int X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X2) Y)) (@ (@ tptp.ord_less_eq_rat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X2) Y)) (@ (@ tptp.ord_less_eq_num Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X2) Y)) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X2) Y)) (@ (@ tptp.ord_less_real Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X2) Y)) (@ (@ tptp.ord_less_rat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X2) Y)) (@ (@ tptp.ord_less_num Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X2) Y)) (@ (@ tptp.ord_less_nat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X2) Y)) (@ (@ tptp.ord_less_int Y) X2))))
% 6.31/6.61 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y6) (not (= X Y6))))))
% 6.31/6.61 (assert (= tptp.ord_less_set_nat (lambda ((X tptp.set_nat) (Y6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X) Y6) (not (= X Y6))))))
% 6.31/6.61 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y6) (not (= X Y6))))))
% 6.31/6.61 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y6) (not (= X Y6))))))
% 6.31/6.61 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y6) (not (= X Y6))))))
% 6.31/6.61 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y6) (not (= X Y6))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y6 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y6) (= X Y6)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((X tptp.set_nat) (Y6 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat X) Y6) (= X Y6)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y6 tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y6) (= X Y6)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_num (lambda ((X tptp.num) (Y6 tptp.num)) (or (@ (@ tptp.ord_less_num X) Y6) (= X Y6)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y6 tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y6) (= X Y6)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y6 tptp.int)) (or (@ (@ tptp.ord_less_int X) Y6) (= X Y6)))))
% 6.31/6.61 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.31/6.61 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.31/6.61 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.31/6.61 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.31/6.61 (assert (= tptp.ord_less_real (lambda ((B5 tptp.real) (A5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B5) A5) (not (@ (@ tptp.ord_less_eq_real A5) B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_set_nat (lambda ((B5 tptp.set_nat) (A5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B5) A5) (not (@ (@ tptp.ord_less_eq_set_nat A5) B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B5) A5) (not (@ (@ tptp.ord_less_eq_rat A5) B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_num (lambda ((B5 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B5) A5) (not (@ (@ tptp.ord_less_eq_num A5) B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A5) (not (@ (@ tptp.ord_less_eq_nat A5) B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_int (lambda ((B5 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B5) A5) (not (@ (@ tptp.ord_less_eq_int A5) B5))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (assert (= tptp.ord_less_real (lambda ((B5 tptp.real) (A5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B5) A5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_set_nat (lambda ((B5 tptp.set_nat) (A5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B5) A5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B5) A5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_num (lambda ((B5 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B5) A5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_int (lambda ((B5 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B5) A5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_real (lambda ((B5 tptp.real) (A5 tptp.real)) (or (@ (@ tptp.ord_less_real B5) A5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((B5 tptp.set_nat) (A5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat B5) A5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (or (@ (@ tptp.ord_less_rat B5) A5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_num (lambda ((B5 tptp.num) (A5 tptp.num)) (or (@ (@ tptp.ord_less_num B5) A5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (or (@ (@ tptp.ord_less_nat B5) A5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_int (lambda ((B5 tptp.int) (A5 tptp.int)) (or (@ (@ tptp.ord_less_int B5) A5) (= A5 B5)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.31/6.61 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X2) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X2) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.31/6.61 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X2) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X2) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.31/6.61 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A5) B5) (not (@ (@ tptp.ord_less_eq_real B5) A5))))))
% 6.31/6.61 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (@ (@ tptp.ord_less_eq_set_nat B5) A5))))))
% 6.31/6.61 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B5) (not (@ (@ tptp.ord_less_eq_rat B5) A5))))))
% 6.31/6.61 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B5) (not (@ (@ tptp.ord_less_eq_num B5) A5))))))
% 6.31/6.61 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B5) (not (@ (@ tptp.ord_less_eq_nat B5) A5))))))
% 6.31/6.61 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B5) (not (@ (@ tptp.ord_less_eq_int B5) A5))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (= tptp.ord_less_real (lambda ((A5 tptp.real) (B5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A5) B5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat A5) B5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B5) (not (= A5 B5))))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_real (lambda ((A5 tptp.real) (B5 tptp.real)) (or (@ (@ tptp.ord_less_real A5) B5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (or (@ (@ tptp.ord_less_set_nat A5) B5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (or (@ (@ tptp.ord_less_rat A5) B5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B5 tptp.num)) (or (@ (@ tptp.ord_less_num A5) B5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (or (@ (@ tptp.ord_less_nat A5) B5) (= A5 B5)))))
% 6.31/6.61 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B5 tptp.int)) (or (@ (@ tptp.ord_less_int A5) B5) (= A5 B5)))))
% 6.31/6.61 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X2)) (@ (@ tptp.ord_less_real X2) Y))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X2)) (@ (@ tptp.ord_less_rat X2) Y))))
% 6.31/6.61 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X2)) (@ (@ tptp.ord_less_num X2) Y))))
% 6.31/6.61 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X2)) (@ (@ tptp.ord_less_nat X2) Y))))
% 6.31/6.61 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X2)) (@ (@ tptp.ord_less_int X2) Y))))
% 6.31/6.61 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y6) (not (@ (@ tptp.ord_less_eq_real Y6) X))))))
% 6.31/6.61 (assert (= tptp.ord_less_set_nat (lambda ((X tptp.set_nat) (Y6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat X) Y6) (not (@ (@ tptp.ord_less_eq_set_nat Y6) X))))))
% 6.31/6.61 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y6 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y6) (not (@ (@ tptp.ord_less_eq_rat Y6) X))))))
% 6.31/6.61 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y6 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y6) (not (@ (@ tptp.ord_less_eq_num Y6) X))))))
% 6.31/6.61 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y6) (not (@ (@ tptp.ord_less_eq_nat Y6) X))))))
% 6.31/6.61 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y6) (not (@ (@ tptp.ord_less_eq_int Y6) X))))))
% 6.31/6.61 (assert (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Y) (@ (@ tptp.ord_less_eq_real X5) Z))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Y) (@ (@ tptp.ord_less_eq_rat X5) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.31/6.61 (assert (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X5) (@ (@ tptp.ord_less_eq_real Y) X5))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 6.31/6.61 (assert (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X5) (@ (@ tptp.ord_less_eq_rat Y) X5))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (= (not (@ (@ tptp.ord_less_real X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y) (= (not (@ (@ tptp.ord_less_set_nat X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (= (not (@ (@ tptp.ord_less_rat X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (= (not (@ (@ tptp.ord_less_num X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (= (not (@ (@ tptp.ord_less_nat X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (= (not (@ (@ tptp.ord_less_int X2) Y)) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (= (@ (@ tptp.ord_less_eq_real X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (=> (not (@ (@ tptp.ord_less_set_nat X2) Y)) (= (@ (@ tptp.ord_less_eq_set_nat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (= (@ (@ tptp.ord_less_eq_rat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y)) (= (@ (@ tptp.ord_less_eq_num X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (= (@ (@ tptp.ord_less_eq_nat X2) Y) (= X2 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (= (@ (@ tptp.ord_less_eq_int X2) Y) (= X2 Y)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X2) Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X2) Y)) (@ (@ tptp.ord_less_eq_rat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X2) Y)) (@ (@ tptp.ord_less_eq_num Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X2) Y)) (@ (@ tptp.ord_less_eq_nat Y) X2))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X2) Y)) (@ (@ tptp.ord_less_eq_int Y) X2))))
% 6.31/6.61 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (not (@ (@ tptp.ord_less_real X2) Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X2) (not (@ (@ tptp.ord_less_set_nat X2) Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X2) (not (@ (@ tptp.ord_less_rat X2) Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X2) (not (@ (@ tptp.ord_less_num X2) Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (not (@ (@ tptp.ord_less_nat X2) Y)))))
% 6.31/6.61 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (not (@ (@ tptp.ord_less_int X2) Y)))))
% 6.31/6.61 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.31/6.61 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.31/6.61 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.31/6.61 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.31/6.61 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.31/6.61 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.31/6.61 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.31/6.61 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.31/6.61 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.31/6.61 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.31/6.61 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.31/6.61 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_nat)) (not (forall ((N tptp.nat)) (not (= X2 (@ tptp.suc N))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y) (= (@ (@ tptp.ord_max_set_nat X2) Y) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (= (@ (@ tptp.ord_max_rat X2) Y) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X2) Y) (= (@ (@ tptp.ord_max_num X2) Y) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X2) Y) (= (@ (@ tptp.ord_max_nat X2) Y) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (= (@ (@ tptp.ord_max_int X2) Y) Y))))
% 6.31/6.61 (assert (forall ((Y tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X2) (= (@ (@ tptp.ord_max_set_nat X2) Y) X2))))
% 6.31/6.61 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X2) (= (@ (@ tptp.ord_max_rat X2) Y) X2))))
% 6.31/6.61 (assert (forall ((Y tptp.num) (X2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X2) (= (@ (@ tptp.ord_max_num X2) Y) X2))))
% 6.31/6.61 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (= (@ (@ tptp.ord_max_nat X2) Y) X2))))
% 6.31/6.61 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X2) (= (@ (@ tptp.ord_max_int X2) Y) X2))))
% 6.31/6.61 (assert (= tptp.ord_max_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ (@ tptp.if_set_nat (@ (@ tptp.ord_less_eq_set_nat A5) B5)) B5) A5))))
% 6.31/6.61 (assert (= tptp.ord_max_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A5) B5)) B5) A5))))
% 6.31/6.61 (assert (= tptp.ord_max_num (lambda ((A5 tptp.num) (B5 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A5) B5)) B5) A5))))
% 6.31/6.61 (assert (= tptp.ord_max_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A5) B5)) B5) A5))))
% 6.31/6.61 (assert (= tptp.ord_max_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A5) B5)) B5) A5))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) _let_3)) _let_2))))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X2) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _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) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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 Mi2) Ma2))) _let_1) TreeList2) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X2 _let_2) (=> (= Y (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (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))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A4) B3))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X2 _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) Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (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))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList2) S))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((A4 Bool) (B3 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A4) B3))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A4) (=> (not _let_2) (and (=> _let_1 B3) _let_1)))))))))) (not (forall ((Mi2 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 Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Summary2))) (=> (= X2 _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I3))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.31/6.61 (assert (forall ((C tptp.real)) (= (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C)) (@ tptp.times_times_real C))))
% 6.31/6.61 (assert (forall ((C tptp.rat)) (= (lambda ((X tptp.rat)) (@ (@ tptp.times_times_rat X) C)) (@ tptp.times_times_rat C))))
% 6.31/6.61 (assert (forall ((C tptp.nat)) (= (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C)) (@ tptp.times_times_nat C))))
% 6.31/6.61 (assert (forall ((C tptp.int)) (= (lambda ((X tptp.int)) (@ (@ tptp.times_times_int X) C)) (@ tptp.times_times_int C))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X2 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X2 _let_1) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (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 Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (=> (= X2 _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList2) Vc2))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd))) (=> (= X2 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.31/6.61 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X2) Y) (=> (=> (= X2 tptp.zero_zero_nat) _let_1) (=> (=> (= X2 (@ 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))) (=> (= X2 _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)))))))))))))))))))))))
% 6.31/6.61 (assert (= tptp.nat_triangle (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N3) (@ tptp.suc N3))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (=> (@ P X2) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X2)) I3))))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I3) N2) (=> (@ P X2) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X2)) I3))))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I3) N2) (=> (@ P X2) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X2)) I3))))))
% 6.31/6.61 (assert (forall ((I3 tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I3) (@ (@ tptp.set_or4548717258645045905et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I3) (@ (@ tptp.ord_less_eq_set_nat I3) U)))))
% 6.31/6.61 (assert (forall ((I3 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I3) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I3) (@ (@ tptp.ord_less_eq_rat I3) U)))))
% 6.31/6.61 (assert (forall ((I3 tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I3) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I3) (@ (@ tptp.ord_less_eq_num I3) U)))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I3) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I3) (@ (@ tptp.ord_less_eq_nat I3) U)))))
% 6.31/6.61 (assert (forall ((I3 tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I3) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I3) (@ (@ tptp.ord_less_eq_int I3) U)))))
% 6.31/6.61 (assert (forall ((I3 tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I3) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I3) (@ (@ tptp.ord_less_eq_real I3) U)))))
% 6.31/6.61 (assert (forall ((L tptp.set_nat) (H2 tptp.set_nat) (L3 tptp.set_nat) (H3 tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat L) H2) (@ (@ tptp.set_or4548717258645045905et_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (not (@ (@ tptp.ord_less_eq_set_nat L3) H3)))))))
% 6.31/6.61 (assert (forall ((L tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 6.31/6.61 (assert (forall ((L tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 6.31/6.61 (assert (forall ((L tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 6.31/6.61 (assert (forall ((L tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 6.31/6.61 (assert (forall ((L tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 6.31/6.61 (assert (forall ((M tptp.nat) (X2 tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X2) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M N2) (=> (not (= M tptp.zero_zero_nat)) (= X2 Y))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X2)) N2)))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N2) X2)) N2)))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N2) X2)) N2)))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X2)) N2)))
% 6.31/6.61 (assert (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.31/6.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.set_or4548717258645045905et_nat A) B) tptp.bot_bot_set_set_nat) (not (@ (@ tptp.ord_less_eq_set_nat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat) (D tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat A) B)) (@ (@ tptp.set_or4548717258645045905et_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_set_nat A) B)) (and (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat B) D))))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D))))))
% 6.31/6.61 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D))))))
% 6.31/6.61 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D))))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D))))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((X2 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X2) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N2) Y))) (and (= X2 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X2) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X2 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (N2 tptp.nat) (Y tptp.set_nat)) (= (@ (@ tptp.member_set_nat X2) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N2) Y))) (and (= X2 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X2) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X2 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X2) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X2 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((X2 tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X2 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (N2 tptp.nat) (X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X2)) I3) X2))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (N2 tptp.nat) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_nat I3) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X2)) I3) X2))))
% 6.31/6.61 (assert (forall ((I3 tptp.nat) (N2 tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I3) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X2)) I3) X2))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N2)) _let_1)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X))))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X))))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X2 tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (= X5 X2))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X2) Xs))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_o) (X2 Bool)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (= X5 X2))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs)) X2) Xs))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_nat) (X2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (= X5 X2))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X2) Xs))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_int) (X2 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (= X5 X2))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X2) Xs))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_complex) (N2 tptp.nat) (X2 tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs) N2) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs)) (= Y3 X2))) (= Xs (@ (@ tptp.replicate_complex N2) X2))))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_real) (N2 tptp.nat) (X2 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs)) (= Y3 X2))) (= Xs (@ (@ tptp.replicate_real N2) X2))))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_set_nat) (N2 tptp.nat) (X2 tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs) N2) (=> (forall ((Y3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y3) (@ tptp.set_set_nat2 Xs)) (= Y3 X2))) (= Xs (@ (@ tptp.replicate_set_nat N2) X2))))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N2 tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N2) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs)) (= Y3 X2))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N2) X2))))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_o) (N2 tptp.nat) (X2 Bool)) (=> (= (@ tptp.size_size_list_o Xs) N2) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs)) (= Y3 X2))) (= Xs (@ (@ tptp.replicate_o N2) X2))))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_nat) (N2 tptp.nat) (X2 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N2) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs)) (= Y3 X2))) (= Xs (@ (@ tptp.replicate_nat N2) X2))))))
% 6.31/6.61 (assert (forall ((Xs tptp.list_int) (N2 tptp.nat) (X2 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N2) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs)) (= Y3 X2))) (= Xs (@ (@ tptp.replicate_int N2) X2))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))))))))))))
% 6.31/6.61 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N3 tptp.nat) (A5 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A5) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N3 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A5) _let_1))))))))))
% 6.31/6.61 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (A5 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A5) _let_1))) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A5) _let_1))))))))))
% 6.31/6.61 (assert (forall ((N2 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 N2)) K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N2) (@ (@ tptp.divide_divide_int K) _let_1)) L)))))))
% 6.31/6.61 (assert (forall ((X2 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 X2) Y) (=> (@ _let_2 X2) (=> (=> (= X2 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X2 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((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))) (=> (= X2 _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)))))))))))))))))))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (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)))))))
% 6.31/6.61 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X2)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2)))))
% 6.31/6.61 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X2)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X2) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X2) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X2) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X2) Y))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.31/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) (@ tptp.uminus5710092332889474511et_nat B4)) (@ (@ tptp.ord_less_eq_set_nat B4) A3))))
% 6.31/6.61 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B4) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat B4)) (@ tptp.uminus5710092332889474511et_nat A3)))))
% 6.31/6.61 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) (@ tptp.uminus5710092332889474511et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat Y) X2))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.61 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.61 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.61 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.31/6.61 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.31/6.61 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= M N2))))
% 6.31/6.61 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= M N2))))
% 6.31/6.61 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= M N2))))
% 6.31/6.61 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (= M N2))))
% 6.31/6.61 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= M N2))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.31/6.61 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.31/6.61 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.31/6.61 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X2)) Y) (@ (@ tptp.dvd_dvd_real X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X2)) Y) (@ (@ tptp.dvd_dvd_int X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X2)) Y) (@ (@ tptp.dvd_dvd_complex X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X2)) Y) (@ (@ tptp.dvd_dvd_rat X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X2)) Y) (@ (@ tptp.dvd_dvd_Code_integer X2) Y))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X2))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X2))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X2))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X2))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))))
% 6.31/6.61 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.31/6.61 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.31/6.61 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.31/6.61 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.31/6.61 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.31/6.61 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.31/6.61 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.31/6.61 (assert (forall ((X2 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X2) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X2 A))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.31/6.61 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.31/6.61 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.31/6.61 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.31/6.61 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.31/6.61 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.31/6.61 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.31/6.61 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.31/6.61 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.31/6.61 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (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)))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.31/6.61 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.31/6.61 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.31/6.61 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (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))))
% 6.31/6.61 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.31/6.62 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.31/6.62 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.31/6.62 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.31/6.62 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.31/6.62 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.31/6.62 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.31/6.62 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.31/6.62 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.31/6.62 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.31/6.62 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.31/6.62 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.31/6.62 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.31/6.62 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.31/6.62 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.31/6.62 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.divide_divide_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X2))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N2) (@ tptp.zero_n2687167440665602831ol_nat (not (= N2 _let_1)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N2) _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((N2 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 N2) K) L)) (@ _let_1 L)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N2) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.31/6.62 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N2 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)))) (not (= M tptp.one)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)))) (not (= M tptp.one)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (not (= M tptp.one)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M tptp.one)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P2))) P2)))
% 6.31/6.62 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P2))) P2)))
% 6.31/6.62 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P2))) P2)))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.31/6.62 (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)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.31/6.62 (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))
% 6.31/6.62 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.31/6.62 (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))
% 6.31/6.62 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.31/6.62 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.31/6.62 (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)))
% 6.31/6.62 (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)))
% 6.31/6.62 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.power_power_real A) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.power_power_int A) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.power_power_complex A) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.power_power_rat A) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_real)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_complex)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_rat)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_Code_integer)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real _let_1) N2) _let_1)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int _let_1) N2) _let_1)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex _let_1) N2) _let_1)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_rat _let_1) N2) _let_1)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N2) _let_1)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2) tptp.one_one_complex))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2) tptp.one_one_rat))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2) tptp.one_one_Code_integer))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.62 (assert (forall ((Y tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) X2) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat X2)) Y))))
% 6.31/6.62 (assert (forall ((Y tptp.set_nat) (X2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X2)) (@ (@ tptp.ord_less_eq_set_nat X2) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat X2) Y) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) (@ tptp.uminus5710092332889474511et_nat X2)))))
% 6.31/6.62 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.31/6.62 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.31/6.62 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P2 Q2))))
% 6.31/6.62 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P2 Q2))))
% 6.31/6.62 (assert (forall ((P2 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) (@ tptp.zero_n356916108424825756nteger Q2)) (= P2 Q2))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.31/6.62 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.31/6.62 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.31/6.62 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.31/6.62 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A3 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A3 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A3) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 6.31/6.62 (assert (forall ((A3 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A3 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 6.31/6.62 (assert (forall ((A3 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A3 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A3) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.31/6.62 (assert (forall ((A3 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A3 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 6.31/6.62 (assert (forall ((A3 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A3 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int) (A2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A2) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A2)) B)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A2 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A2) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A2)) B)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R2 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R2)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 L)) R2)))))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.31/6.62 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P6 Bool)) (@ (@ (@ tptp.if_complex P6) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.31/6.62 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P6 Bool)) (@ (@ (@ tptp.if_real P6) tptp.one_one_real) tptp.zero_zero_real))))
% 6.31/6.62 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_rat P6) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.31/6.62 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P6 Bool)) (@ (@ (@ tptp.if_nat P6) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.31/6.62 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P6 Bool)) (@ (@ (@ tptp.if_int P6) tptp.one_one_int) tptp.zero_zero_int))))
% 6.31/6.62 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P6 Bool)) (@ (@ (@ tptp.if_Code_integer P6) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (assert (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (and (=> P2 (@ P tptp.one_one_complex)) (=> (not P2) (@ P tptp.zero_zero_complex))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (and (=> P2 (@ P tptp.one_one_real)) (=> (not P2) (@ P tptp.zero_zero_real))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (and (=> P2 (@ P tptp.one_one_rat)) (=> (not P2) (@ P tptp.zero_zero_rat))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (and (=> P2 (@ P tptp.one_one_nat)) (=> (not P2) (@ P tptp.zero_zero_nat))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (and (=> P2 (@ P tptp.one_one_int)) (=> (not P2) (@ P tptp.zero_zero_int))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (and (=> P2 (@ P tptp.one_one_Code_integer)) (=> (not P2) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.complex Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P2)) (not (or (and P2 (not (@ P tptp.one_one_complex))) (and (not P2) (not (@ P tptp.zero_zero_complex))))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.real Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P2)) (not (or (and P2 (not (@ P tptp.one_one_real))) (and (not P2) (not (@ P tptp.zero_zero_real))))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.rat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P2)) (not (or (and P2 (not (@ P tptp.one_one_rat))) (and (not P2) (not (@ P tptp.zero_zero_rat))))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.nat Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P2)) (not (or (and P2 (not (@ P tptp.one_one_nat))) (and (not P2) (not (@ P tptp.zero_zero_nat))))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.int Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P2)) (not (or (and P2 (not (@ P tptp.one_one_int))) (and (not P2) (not (@ P tptp.zero_zero_int))))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.code_integer Bool)) (P2 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P2)) (not (or (and P2 (not (@ P tptp.one_one_Code_integer))) (and (not P2) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.31/6.62 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.31/6.62 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.31/6.62 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.31/6.62 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.31/6.62 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.31/6.62 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.31/6.62 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.31/6.62 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.31/6.62 (assert (forall ((W tptp.num) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real X2) (@ tptp.uminus_uminus_real _let_1))))))
% 6.31/6.62 (assert (forall ((W tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X2)) (@ (@ tptp.times_times_int X2) (@ tptp.uminus_uminus_int _let_1))))))
% 6.31/6.62 (assert (forall ((W tptp.num) (X2 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex X2) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.31/6.62 (assert (forall ((W tptp.num) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat X2) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.31/6.62 (assert (forall ((W tptp.num) (X2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X2)) (@ (@ tptp.times_3573771949741848930nteger X2) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real N2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat N2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.times_times_real X2) X2) tptp.one_one_real) (or (= X2 tptp.one_one_real) (= X2 (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.times_times_int X2) X2) tptp.one_one_int) (or (= X2 tptp.one_one_int) (= X2 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X2) X2) tptp.one_one_complex) (or (= X2 tptp.one_one_complex) (= X2 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X2) X2) tptp.one_one_rat) (or (= X2 tptp.one_one_rat) (= X2 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X2) X2) tptp.one_one_Code_integer) (or (= X2 tptp.one_one_Code_integer) (= X2 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.31/6.62 (assert (forall ((B4 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B4 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.31/6.62 (assert (forall ((B4 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B4 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.31/6.62 (assert (forall ((B4 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B4 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.31/6.62 (assert (forall ((B4 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B4 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 6.31/6.62 (assert (forall ((B4 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B4 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B4) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.31/6.62 (assert (= tptp.minus_minus_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.plus_plus_real A5) (@ tptp.uminus_uminus_real B5)))))
% 6.31/6.62 (assert (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B5)))))
% 6.31/6.62 (assert (= tptp.minus_minus_complex (lambda ((A5 tptp.complex) (B5 tptp.complex)) (@ (@ tptp.plus_plus_complex A5) (@ tptp.uminus1482373934393186551omplex B5)))))
% 6.31/6.62 (assert (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B5)))))
% 6.31/6.62 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B5 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B5)))))
% 6.31/6.62 (assert (= tptp.minus_minus_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.plus_plus_real A5) (@ tptp.uminus_uminus_real B5)))))
% 6.31/6.62 (assert (= tptp.minus_minus_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.plus_plus_int A5) (@ tptp.uminus_uminus_int B5)))))
% 6.31/6.62 (assert (= tptp.minus_minus_complex (lambda ((A5 tptp.complex) (B5 tptp.complex)) (@ (@ tptp.plus_plus_complex A5) (@ tptp.uminus1482373934393186551omplex B5)))))
% 6.31/6.62 (assert (= tptp.minus_minus_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.uminus_uminus_rat B5)))))
% 6.31/6.62 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A5 tptp.code_integer) (B5 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.uminus1351360451143612070nteger B5)))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.uminus1532241313380277803et_int A3)) (= A3 tptp.bot_bot_set_int))))
% 6.31/6.62 (assert (forall ((A3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A3) (@ tptp.uminus612125837232591019t_real A3)) (= A3 tptp.bot_bot_set_real))))
% 6.31/6.62 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.uminus5710092332889474511et_nat A3)) (= A3 tptp.bot_bot_set_nat))))
% 6.31/6.62 (assert (forall ((U tptp.real) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X2) X2))))
% 6.31/6.62 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N2 tptp.one_one_int)) (and (= M _let_1) (= N2 _let_1)))))))
% 6.31/6.62 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.31/6.62 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L) (@ tptp.uminus_uminus_int L))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= tptp.minus_minus_real (lambda ((X tptp.real) (Y6 tptp.real)) (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real Y6)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.31/6.62 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.31/6.62 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.31/6.62 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.31/6.62 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.31/6.62 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.31/6.62 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.31/6.62 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.31/6.62 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.power_power_real A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ (@ tptp.power_power_complex A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ (@ tptp.power_power_rat A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) D4))))) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X3) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.minus_minus_int X5) D4))))) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X3) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (A3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.plus_plus_int X5) D4))))) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X3) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (and (@ P X3) (@ Q X3)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (A3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X5) (@ Q (@ (@ tptp.plus_plus_int X5) D4))))) (forall ((X3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X3) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (or (@ P X3) (@ Q X3)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ (@ tptp.power_power_real X2) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ (@ tptp.power_power_int X2) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ (@ tptp.power_power_complex X2) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ (@ tptp.power_power_rat X2) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X2)) Y))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X2) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X2) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X2)) Y))))
% 6.31/6.62 (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)))))))))
% 6.31/6.62 (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))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.31/6.62 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X2) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (X2 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X2) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.rat) (X2 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X2) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X2)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.31/6.62 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.31/6.62 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X2) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_real Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X2) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_int Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X2) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus1482373934393186551omplex Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X2) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_rat Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X2 Y) (= X2 (@ tptp.uminus1351360451143612070nteger Y)))))))
% 6.31/6.62 (assert (forall ((D tptp.int) (D4 tptp.int) (A3 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X3))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T2))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T2)))))))))))
% 6.31/6.62 (assert (forall ((D tptp.int) (D4 tptp.int) (A3 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X3))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_2 (@ _let_1 T2)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T2))))))))))
% 6.31/6.62 (assert (forall ((D tptp.int) (D4 tptp.int) (B4 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X3) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X3) D4)) T2))))))))))
% 6.31/6.62 (assert (forall ((D tptp.int) (D4 tptp.int) (B4 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X3) T2)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X3) D4)) T2)))))))))
% 6.31/6.62 (assert (forall ((A3 tptp.int) (B4 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B4) N2)) (@ (@ tptp.divide_divide_int A3) N2))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.modulo_modulo_nat A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.modulo_modulo_int A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n356916108424825756nteger (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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))))))))))))
% 6.31/6.62 (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))))))))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (= (exists ((X4 tptp.int)) (@ P X4)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (T2 tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T2) tptp.one_one_int)) B4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X3 T2) (= (@ (@ tptp.minus_minus_int X3) D4) T2))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (T2 tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) B4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X3 T2)) (not (= (@ (@ tptp.minus_minus_int X3) D4) T2)))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X3) T2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X3) D4)) T2)))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (T2 tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) B4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.minus_minus_int X3) D4))))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (T2 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T2) tptp.one_one_int)) A3) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X3 T2) (= (@ (@ tptp.plus_plus_int X3) D4) T2))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (T2 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) A3) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X3 T2)) (not (= (@ (@ tptp.plus_plus_int X3) D4) T2)))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (T2 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) A3) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X3) T2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X3) D4)) T2))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (A3 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.plus_plus_int X3) D4)))))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.31/6.62 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.62 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.62 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.62 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.62 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.62 (assert (forall ((U tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X2) _let_1)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))))))))
% 6.31/6.62 (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)))))))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R2 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R2))))))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A4 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.code_integer) (B3 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B3)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.31/6.62 (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))))))))))))
% 6.31/6.62 (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))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (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)))))))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (B4 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X3) T2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X3) D4)) T2)))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (T2 tptp.int) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T2) tptp.one_one_int)) B4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B4) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.minus_minus_int X3) D4))))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (T2 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T2) tptp.one_one_int)) A3) (forall ((X3 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X3) T2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X3) D4)) T2))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (A3 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T2))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X3) (@ _let_1 (@ (@ tptp.plus_plus_int X3) D4)))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (B4 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z4) (= (@ P X5) (@ P5 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B4) (not (= X5 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P5 X5) (@ P5 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P5 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) B4) (@ P (@ (@ tptp.plus_plus_int Y6) X))))))))))))))
% 6.31/6.62 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P5 (-> tptp.int Bool)) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X5) (= (@ P X5) (@ P5 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A3) (not (= X5 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P5 X5) (@ P5 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X4 tptp.int)) (@ P X4)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P5 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A3) (@ P (@ (@ tptp.minus_minus_int Y6) X))))))))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2) (=> (@ (@ tptp.ord_le3102999989581377725nteger X2) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X2) (=> (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X2) (=> (@ (@ tptp.ord_less_eq_int X2) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.31/6.62 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.62 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) _let_1))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) K))))
% 6.31/6.62 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))))
% 6.31/6.62 (assert (= tptp.nat_set_decode (lambda ((X tptp.nat)) (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat _let_1) N3))))))))))
% 6.31/6.62 (assert (forall ((Q2 tptp.int) (R2 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R2)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R2 tptp.zero_zero_int)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.31/6.62 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.31/6.62 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.31/6.62 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.31/6.62 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A5 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A5) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A5) _let_1)))))))
% 6.31/6.62 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A5) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A5) _let_1)))))))
% 6.31/6.62 (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))))))))))
% 6.31/6.62 (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)))))))))
% 6.31/6.62 (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))))))))))
% 6.31/6.62 (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))))))))))
% 6.31/6.62 (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))))))))))
% 6.31/6.62 (assert (forall ((X2 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 X2) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X2) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N2)) (= M N2))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real W) (@ tptp.ring_1_of_int_real Z)) (= W Z))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat W) (@ tptp.ring_1_of_int_rat Z)) (= W Z))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit1 N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.62 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sqrt X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.zero_zero_int) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.zero_zero_rat) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_complex (@ tptp.ring_17405671764205052669omplex Z)) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z)) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_rat (@ tptp.ring_1_of_int_rat Z)) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.zero_zero_int) tptp.zero_zero_complex))
% 6.31/6.62 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.62 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 6.31/6.62 (assert (= (@ tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.31/6.62 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.31/6.62 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.31/6.62 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.31/6.62 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int Z)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger Z)))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.31/6.62 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.31/6.62 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X2) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X2) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X2) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X2) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X2 (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X2)) (= (@ (@ tptp.power_power_int B) W) X2))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N2))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N2))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N2))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N2)) (@ tptp.bit0 (@ _let_1 N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ tptp.ring_1_of_int_real (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ tptp.ring_1_of_int_rat (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.31/6.62 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((P Bool)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.bit1 N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) tptp.one)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2) Y))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2) Y))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N2) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2) Y))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.power_power_int B) W)))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.31/6.62 (assert (forall ((B tptp.int) (W tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X2)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X2))))
% 6.31/6.62 (assert (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.31/6.62 (assert (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.31/6.62 (assert (forall ((N2 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 N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2) Y))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X2))) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2) Y))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N2) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2) Y))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N2) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2) Y))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N2))) _let_1)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X2))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X2))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)) A))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X2))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X2))) N2)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.31/6.62 (assert (forall ((H2 (-> Bool Bool)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> Bool tptp.int)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> tptp.int Bool)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> tptp.int tptp.int)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> tptp.product_prod_int_int Bool)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> tptp.product_prod_int_int tptp.int)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> Bool tptp.product_prod_int_int)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> tptp.int tptp.product_prod_int_int)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> tptp.product_prod_int_int tptp.product_prod_int_int)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H2 (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X15 tptp.int) (X24 tptp.int)) (@ H2 (@ (@ F X15) X24)))) Prod))))
% 6.31/6.62 (assert (forall ((H2 (-> (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat Bool)) (F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (= (@ H2 (@ (@ tptp.produc8739625826339149834_nat_o F) Prod)) (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X15 tptp.nat) (X24 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ H2 (@ (@ F X15) X24)) __flatten_var_0))) Prod))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 6.31/6.62 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 6.31/6.62 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.ord_max_int X2) Y)) (@ (@ tptp.ord_max_real (@ tptp.ring_1_of_int_real X2)) (@ tptp.ring_1_of_int_real Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.ord_max_int X2) Y)) (@ (@ tptp.ord_max_rat (@ tptp.ring_1_of_int_rat X2)) (@ tptp.ring_1_of_int_rat Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.ord_max_int X2) Y)) (@ (@ tptp.ord_max_int (@ tptp.ring_1_of_int_int X2)) (@ tptp.ring_1_of_int_int Y)))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int Bool)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int) (S2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ tptp.bit_concat_bit N2))) (= (= (@ (@ _let_2 K) L) (@ (@ _let_2 R2) S2)) (and (= (@ _let_1 K) (@ _let_1 R2)) (= L S2)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N2))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) B)) (@ _let_1 B)))))
% 6.31/6.62 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z)) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y3)) (not (@ Q (@ (@ P X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z)) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X5) Y3)) (not (@ Q (@ (@ P X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z)) (not (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X5) Y3)) (not (@ Q (@ (@ P X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z)) (not (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X5) Y3)) (not (@ Q (@ (@ P X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z)) (not (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X5) Y3)) (not (@ Q (@ (@ P X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X) Y6)) __flatten_var_0))) F)))
% 6.31/6.62 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X) Y6)) __flatten_var_0))) F)))
% 6.31/6.62 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X tptp.int) (Y6 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y6)))) F)))
% 6.31/6.62 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X tptp.int) (Y6 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y6)))) F)))
% 6.31/6.62 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X tptp.int) (Y6 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X) Y6)))) F)))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X5) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y3)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X5) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X5) Y3)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (= (@ (@ F X5) Y3) (@ G (@ (@ tptp.product_Pair_int_int X5) Y3)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (= (@ (@ F X5) Y3) (@ G (@ (@ tptp.product_Pair_int_int X5) Y3)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (= (@ (@ F X5) Y3) (@ G (@ (@ tptp.product_Pair_int_int X5) Y3)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (@ _let_1 (@ tptp.sqrt X2))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N2))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N2) M)) _let_2) _let_1) A))))))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y (@ tptp.bit1 X33)))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.product_prod_num_num)) (=> (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N))))) (=> (forall ((N tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N))))) (=> (forall ((M3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) tptp.one)))) (=> (forall ((M3 tptp.num) (N tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) (@ tptp.bit0 N))))) (=> (forall ((M3 tptp.num) (N tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M3)) (@ tptp.bit1 N))))) (=> (forall ((M3 tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) tptp.one)))) (=> (forall ((M3 tptp.num) (N tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) (@ tptp.bit0 N))))) (not (forall ((M3 tptp.num) (N tptp.num)) (not (= X2 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M3)) (@ tptp.bit1 N))))))))))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X2)) (@ tptp.sqrt Y))))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N2)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) A)) (@ _let_1 A))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X2) X2)) (@ (@ tptp.times_times_real Y) Y))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X2)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X2) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X2)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X2) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X2)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X2) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X2)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X2) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X2)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1))))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X2))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.31/6.62 (assert (forall ((D tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N2) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real D))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))))
% 6.31/6.62 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 6.31/6.62 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A) A)) A))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A) A)) A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A) A)) A))))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))))
% 6.31/6.62 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (= tptp.ord_less_eq_int (lambda ((N3 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N3)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))
% 6.31/6.62 (assert (= tptp.ord_less_int (lambda ((N3 tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N3)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 6.31/6.62 (assert (forall ((X2 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 X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X2) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X2) D))) _let_1))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A5 tptp.int)) (@ (@ tptp.modulo_modulo_int A5) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.62 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X2) (@ tptp.sqrt Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.62 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.62 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X2))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X2)))) tptp.one_one_real)))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N2) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M))))
% 6.31/6.62 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X2) Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X2)) Y)))))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X2 tptp.zero_zero_real)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X2) (= Y tptp.zero_zero_real)))))
% 6.31/6.62 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D) _let_1))))))))
% 6.31/6.62 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.31/6.62 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K)))))
% 6.31/6.62 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ _let_1 K)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.31/6.62 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X2)) Y)))))))
% 6.31/6.62 (assert (forall ((X2 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 X2) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X2) Y))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N2) (= (@ tptp.sqrt (@ _let_3 N2)) (@ _let_3 (@ (@ tptp.divide_divide_nat N2) _let_2)))))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ 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)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ 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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X2)) N2) (@ (@ tptp.power_power_real X2) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X2) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.31/6.62 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.31/6.62 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N3)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N2) 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) N2)) tptp.one_one_Code_integer))))))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N2) 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) N2)) tptp.one_one_int))))))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N2) 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) N2)) tptp.one_one_nat))))))))))
% 6.31/6.62 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.31/6.62 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.31/6.62 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (@ tptp.numeral_numeral_nat _let_1)) (= _let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y5)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X5)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X5)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X5) tptp.one_one_int))) (forall ((Y5 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y5)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y5) tptp.one_one_int)))) (= Y5 X5)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X2) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X2) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.31/6.62 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (C (-> tptp.code_integer Bool Bool))) (=> (forall ((A4 tptp.code_integer) (B3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A4) B3)) (@ (@ C A4) B3))) (@ (@ tptp.produc7828578312038201481er_o_o C) P2))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_num_num) (C (-> tptp.num tptp.num Bool))) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A4) B3)) (@ (@ C A4) B3))) (@ (@ tptp.produc5703948589228662326_num_o C) P2))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_nat_num) (C (-> tptp.nat tptp.num Bool))) (=> (forall ((A4 tptp.nat) (B3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A4) B3)) (@ (@ C A4) B3))) (@ (@ tptp.produc4927758841916487424_num_o C) P2))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat Bool))) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat A4) B3)) (@ (@ C A4) B3))) (@ (@ tptp.produc6081775807080527818_nat_o C) P2))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (= P2 (@ (@ tptp.product_Pair_int_int A4) B3)) (@ (@ C A4) B3))) (@ (@ tptp.produc4947309494688390418_int_o C) P2))))
% 6.31/6.62 (assert (forall ((F (-> tptp.code_integer Bool Bool)) (A tptp.code_integer) (B Bool)) (=> (@ (@ F A) B) (@ (@ tptp.produc7828578312038201481er_o_o F) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))
% 6.31/6.62 (assert (forall ((F (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (@ (@ F A) B) (@ (@ tptp.produc5703948589228662326_num_o F) (@ (@ tptp.product_Pair_num_num A) B)))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ F A) B) (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ tptp.product_Pair_nat_num A) B)))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ F A) B) (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.31/6.62 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex))) (=> (forall ((A4 tptp.code_integer) (B3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A4) B3)) (@ (@ tptp.member_complex Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real))) (=> (forall ((A4 tptp.code_integer) (B3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A4) B3)) (@ (@ tptp.member_real Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat))) (=> (forall ((A4 tptp.code_integer) (B3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A4) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.produc6271795597528267376eger_o) (Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int))) (=> (forall ((A4 tptp.code_integer) (B3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o A4) B3)) (@ (@ tptp.member_int Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex))) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A4) B3)) (@ (@ tptp.member_complex Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real))) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A4) B3)) (@ (@ tptp.member_real Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat))) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A4) B3)) (@ (@ tptp.member_nat Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_num_num) (Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int))) (=> (forall ((A4 tptp.num) (B3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num A4) B3)) (@ (@ tptp.member_int Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_nat_num) (Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex))) (=> (forall ((A4 tptp.nat) (B3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A4) B3)) (@ (@ tptp.member_complex Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P2)))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_nat_num) (Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real))) (=> (forall ((A4 tptp.nat) (B3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num A4) B3)) (@ (@ tptp.member_real Z) (@ (@ C A4) B3)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P2)))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1043322548047392435omplex C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc242741666403216561t_real C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc5431169771168744661et_nat C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (A tptp.code_integer) (B Bool)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1253318751659547953et_int C) (@ (@ tptp.produc6677183202524767010eger_o A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc2866383454006189126omplex C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8296048397933160132t_real C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1361121860356118632et_nat C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6406642877701697732et_int C) (@ (@ tptp.product_Pair_num_num A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6231982587499038204omplex C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (A tptp.nat) (B tptp.num)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc1435849484188172666t_real C) (@ (@ tptp.product_Pair_nat_num A) B)))))))
% 6.31/6.62 (assert (forall ((P2 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X2 tptp.product_prod_nat_nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A4) B3) P2) (@ (@ (@ C A4) B3) X2))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P2) X2))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.31/6.62 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.31/6.62 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.31/6.62 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.31/6.62 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))))
% 6.31/6.62 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K)))))
% 6.31/6.62 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N2))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K)))))
% 6.31/6.62 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.pred_numeral K)))))
% 6.31/6.62 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) (@ tptp.pred_numeral K))))))
% 6.31/6.62 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N2)))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.31/6.62 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.31/6.62 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.31/6.62 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.31/6.62 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N2) M)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N2) M)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N2) M)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))
% 6.31/6.62 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q4) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q4) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (C (-> tptp.code_integer Bool tptp.set_complex)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc1043322548047392435omplex C) P2)) (not (forall ((X5 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X5) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (C (-> tptp.code_integer Bool tptp.set_real)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc242741666403216561t_real C) P2)) (not (forall ((X5 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X5) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.nat) (C (-> tptp.code_integer Bool tptp.set_nat)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc5431169771168744661et_nat C) P2)) (not (forall ((X5 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X5) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (C (-> tptp.code_integer Bool tptp.set_int)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc1253318751659547953et_int C) P2)) (not (forall ((X5 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X5) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (C (-> tptp.num tptp.num tptp.set_complex)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2866383454006189126omplex C) P2)) (not (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X5) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (C (-> tptp.num tptp.num tptp.set_real)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc8296048397933160132t_real C) P2)) (not (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X5) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.nat) (C (-> tptp.num tptp.num tptp.set_nat)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc1361121860356118632et_nat C) P2)) (not (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X5) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.int) (C (-> tptp.num tptp.num tptp.set_int)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc6406642877701697732et_int C) P2)) (not (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X5) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.complex) (C (-> tptp.nat tptp.num tptp.set_complex)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc6231982587499038204omplex C) P2)) (not (forall ((X5 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X5) Y3)) (not (@ (@ tptp.member_complex Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (C (-> tptp.nat tptp.num tptp.set_real)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc1435849484188172666t_real C) P2)) (not (forall ((X5 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X5) Y3)) (not (@ (@ tptp.member_real Z) (@ (@ C X5) Y3)))))))))
% 6.31/6.62 (assert (forall ((C (-> tptp.code_integer Bool Bool)) (P2 tptp.produc6271795597528267376eger_o)) (=> (@ (@ tptp.produc7828578312038201481er_o_o C) P2) (not (forall ((X5 tptp.code_integer) (Y3 Bool)) (=> (= P2 (@ (@ tptp.produc6677183202524767010eger_o X5) Y3)) (not (@ (@ C X5) Y3))))))))
% 6.31/6.62 (assert (forall ((C (-> tptp.num tptp.num Bool)) (P2 tptp.product_prod_num_num)) (=> (@ (@ tptp.produc5703948589228662326_num_o C) P2) (not (forall ((X5 tptp.num) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_num_num X5) Y3)) (not (@ (@ C X5) Y3))))))))
% 6.31/6.62 (assert (forall ((C (-> tptp.nat tptp.num Bool)) (P2 tptp.product_prod_nat_num)) (=> (@ (@ tptp.produc4927758841916487424_num_o C) P2) (not (forall ((X5 tptp.nat) (Y3 tptp.num)) (=> (= P2 (@ (@ tptp.product_Pair_nat_num X5) Y3)) (not (@ (@ C X5) Y3))))))))
% 6.31/6.62 (assert (forall ((C (-> tptp.nat tptp.nat Bool)) (P2 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o C) P2) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat X5) Y3)) (not (@ (@ C X5) Y3))))))))
% 6.31/6.62 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P2 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P2) (not (forall ((X5 tptp.int) (Y3 tptp.int)) (=> (= P2 (@ (@ tptp.product_Pair_int_int X5) Y3)) (not (@ (@ C X5) Y3))))))))
% 6.31/6.62 (assert (forall ((F (-> tptp.code_integer Bool Bool)) (A tptp.code_integer) (B Bool)) (=> (@ (@ tptp.produc7828578312038201481er_o_o F) (@ (@ tptp.produc6677183202524767010eger_o A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((F (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (@ (@ tptp.produc5703948589228662326_num_o F) (@ (@ tptp.product_Pair_num_num A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.num Bool)) (A tptp.nat) (B tptp.num)) (=> (@ (@ tptp.produc4927758841916487424_num_o F) (@ (@ tptp.product_Pair_nat_num A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.produc6081775807080527818_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.31/6.62 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P2 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P2) Z) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (=> (= P2 (@ (@ tptp.product_Pair_nat_nat X5) Y3)) (not (@ (@ (@ C X5) Y3) Z))))))))
% 6.31/6.62 (assert (forall ((R (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o R) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R A) B) C))))
% 6.31/6.62 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.31/6.62 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.31/6.62 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N3))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.31/6.62 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q4 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q4) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 6.31/6.62 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N3))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.31/6.62 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N3))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.31/6.62 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N3))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.31/6.62 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.31/6.62 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.31/6.62 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.31/6.62 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (exists ((N tptp.nat)) (and (not (@ P N)) (@ P (@ tptp.suc N))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.ring_1_of_int_real Z3)))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.ring_1_of_int_rat Z3)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z3)) X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z3)) X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_real X2) (@ tptp.ring_1_of_int_real Z3)))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (exists ((Z3 tptp.int)) (@ (@ tptp.ord_less_rat X2) (@ tptp.ring_1_of_int_rat Z3)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X2 (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X2) Z)))))
% 6.31/6.62 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N3)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N3) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N3)))))))
% 6.31/6.62 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N3)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N3) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N3)))))))
% 6.31/6.62 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N3 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N3)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N3) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N3)))))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N3))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q4 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q4)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N3)) N3))))))
% 6.31/6.62 (assert (forall ((X2 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 X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X2) _let_1)) (= (@ tptp.archim8280529875227126926d_real X2) Y)))))))
% 6.31/6.62 (assert (forall ((X2 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 X2) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X2) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X2) Y)))))))
% 6.31/6.62 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.62 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.62 (assert (forall ((P Bool) (Q (-> tptp.int tptp.int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (B5 tptp.int)) (and P (@ (@ Q A5) B5)))) (lambda ((Ab tptp.product_prod_int_int)) (and P (@ (@ tptp.produc4947309494688390418_int_o Q) Ab))))))
% 6.31/6.62 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 6.31/6.62 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.62 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.31/6.62 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))))
% 6.31/6.62 (assert (forall ((Prod tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((Uu3 tptp.int) (Uv3 tptp.int)) true)) Prod)))
% 6.31/6.62 (assert (forall ((A3 (-> tptp.int tptp.int Bool)) (B4 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_le6741204236512500942_int_o A3) B4) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o A3))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o B4))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.num Bool)) (X2 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X5 tptp.num)) (=> (@ P X5) (@ P (@ tptp.inc X5)))) (@ P X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X2))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.31/6.62 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X2)) (@ tptp.bit1 X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X2)) (@ tptp.bit0 (@ tptp.inc X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.plus_plus_num X2) tptp.one) (@ tptp.inc X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X2) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X2)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X2))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X2)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X2)) tptp.one_one_complex))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X2)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X2)) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X2)) tptp.one_one_rat))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X2)) tptp.one_one_nat))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X2)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X2)) tptp.one_one_int))))
% 6.31/6.62 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N3)) (@ (@ tptp.modulo_modulo_nat M6) N3)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) (@ (@ tptp.plus_plus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.31/6.62 (assert (= tptp.artanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.31/6.62 (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))))))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) B) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) B) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) A) A)))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) A) A)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.zero_zero_int) A) A)))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.zero_zero_nat) A) A)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.zero_zero_int) A)))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger X2) _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int X2) _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_se1080825931792720795nteger _let_1) X2) _let_1))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) X2) _let_1))))
% 6.31/6.62 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.31/6.62 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.62 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.31/6.62 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (= (@ _let_1 (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (= (@ tptp.ln_ln_real X2) tptp.zero_zero_real) (= X2 tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ 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_se1409905431419307370or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ 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_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ 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_se1409905431419307370or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ 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_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ 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_se1409905431419307370or_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ 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_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.31/6.62 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int B))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.31/6.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat B))) (let ((_let_2 (@ tptp.bit_se1412395901928357646or_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.31/6.62 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int B5) A5))))
% 6.31/6.62 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat B5) A5))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int A))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int B) C))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se1412395901928357646or_nat A))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat B) C))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.bit_se1409905431419307370or_int A) B) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.bit_se1412395901928357646or_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int X2) tptp.zero_zero_int) X2)))
% 6.31/6.62 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X2) Y)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N2)) (@ tptp.bit1 (@ tptp.bitM N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.inc (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.inc N2)) (@ tptp.bit1 N2))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X2)) tptp.zero_zero_real)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X2)) (=> (@ _let_1 X2) (@ (@ tptp.ord_less_real tptp.one_one_real) X2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N2)) tptp.one) (@ tptp.bit0 N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1080825931792720795nteger A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) (and (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X2)) (@ tptp.ln_ln_real Y))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (= (@ tptp.ln_ln_real X2) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (= X2 tptp.one_one_real)))))
% 6.31/6.62 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.31/6.62 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.31/6.62 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.31/6.62 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2))) tptp.one_one_complex))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N2))) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2))) tptp.one_one_rat))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.31/6.62 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))))
% 6.31/6.62 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2))) (@ tptp.uminus_uminus_real X2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ tptp.sqrt X2)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger tptp.one_one_Code_integer) A) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) A) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) A) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1080825931792720795nteger A) tptp.one_one_Code_integer) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int A) tptp.one_one_int) (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))))))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat A) tptp.one_one_nat) (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X2) Y)) _let_1)))))))
% 6.31/6.62 (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)))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (= (@ tptp.arcosh_real X2) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X2) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr448751882837621926eger_o) (S3 tptp.set_Pr448751882837621926eger_o)) (= (@ (@ tptp.ord_le2162486998276636481er_o_o (lambda ((X tptp.code_integer) (Y6 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y6)) R))) (lambda ((X tptp.code_integer) (Y6 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y6)) S3))) (@ (@ tptp.ord_le8980329558974975238eger_o R) S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr8218934625190621173um_num) (S3 tptp.set_Pr8218934625190621173um_num)) (= (@ (@ tptp.ord_le6124364862034508274_num_o (lambda ((X tptp.num) (Y6 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y6)) R))) (lambda ((X tptp.num) (Y6 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y6)) S3))) (@ (@ tptp.ord_le880128212290418581um_num R) S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr6200539531224447659at_num) (S3 tptp.set_Pr6200539531224447659at_num)) (= (@ (@ tptp.ord_le3404735783095501756_num_o (lambda ((X tptp.nat) (Y6 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y6)) R))) (lambda ((X tptp.nat) (Y6 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y6)) S3))) (@ (@ tptp.ord_le8085105155179020875at_num R) S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le2646555220125990790_nat_o (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y6)) R))) (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y6)) S3))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (@ (@ tptp.ord_le6741204236512500942_int_o (lambda ((X tptp.int) (Y6 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y6)) R))) (lambda ((X tptp.int) (Y6 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y6)) S3))) (@ (@ tptp.ord_le2843351958646193337nt_int R) S3))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.31/6.62 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.31/6.62 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.31/6.62 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.31/6.62 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M)) K) (@ (@ tptp.dvd_dvd_Code_integer M) K))))
% 6.31/6.62 (assert (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 6.31/6.62 (assert (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 6.31/6.62 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ tptp.ring_1_of_int_real (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat X2)))))
% 6.31/6.62 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.31/6.62 (assert (= (@ tptp.tanh_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.62 (assert (= (@ tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.31/6.62 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X2) X2)) (@ tptp.abs_abs_real X2))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X2))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) (or (not (= A tptp.zero_zero_real)) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2)) (or (not (= A tptp.zero_zero_rat)) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2)) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 6.31/6.62 (assert (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1))))))
% 6.31/6.62 (assert (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1))))))
% 6.31/6.62 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X2))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.31/6.62 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X2) (@ tptp.abs_abs_real Y)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_real Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X2) (@ tptp.abs_abs_int Y)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_int Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X2) (@ tptp.abs_abs_rat Y)) (or (= X2 Y) (= X2 (@ tptp.uminus_uminus_rat Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X2) (@ tptp.abs_abs_Code_integer Y)) (or (= X2 Y) (= X2 (@ tptp.uminus1351360451143612070nteger Y))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.31/6.62 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))))
% 6.31/6.62 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 6.31/6.62 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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))))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X2)) tptp.one_one_real)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) tptp.one) tptp.one)))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) E))) (= X2 tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) E))) (= X2 tptp.zero_zero_rat))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X2) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X2) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X2) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X2) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X2) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X2) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X2))))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))))
% 6.31/6.62 (assert (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))))
% 6.31/6.62 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.31/6.62 (assert (forall ((Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X2)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X2) Y))))))
% 6.31/6.62 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X2)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X2) Y))))))
% 6.31/6.62 (assert (= tptp.abs_abs_real (lambda ((A5 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A5) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A5)) A5))))
% 6.31/6.62 (assert (= tptp.abs_abs_int (lambda ((A5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A5) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A5)) A5))))
% 6.31/6.62 (assert (= tptp.abs_abs_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A5) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A5)) A5))))
% 6.31/6.62 (assert (= tptp.abs_abs_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A5) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A5)) A5))))
% 6.31/6.62 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.31/6.62 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.31/6.62 (assert (= tptp.abs_abs_real (lambda ((A5 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A5) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A5)) A5))))
% 6.31/6.62 (assert (= tptp.abs_abs_int (lambda ((A5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A5) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A5)) A5))))
% 6.31/6.62 (assert (= tptp.abs_abs_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A5) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A5)) A5))))
% 6.31/6.62 (assert (= tptp.abs_abs_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A5) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A5)) A5))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R2) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X2) (@ (@ tptp.ord_le3102999989581377725nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R2) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R2)) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R2) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R2)) X2) (@ (@ tptp.ord_less_eq_rat X2) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R2) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R2)) X2) (@ (@ tptp.ord_less_eq_int X2) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X2) A))) R2) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R2)) X2) (@ (@ tptp.ord_le6747313008572928689nteger X2) (@ (@ tptp.plus_p5714425477246183910nteger A) R2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (A tptp.real) (R2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) A))) R2) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R2)) X2) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real A) R2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) A))) R2) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R2)) X2) (@ (@ tptp.ord_less_rat X2) (@ (@ tptp.plus_plus_rat A) R2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (A tptp.int) (R2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) A))) R2) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R2)) X2) (@ (@ tptp.ord_less_int X2) (@ (@ tptp.plus_plus_int A) R2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.31/6.62 (assert (= tptp.abs_abs_real (lambda ((A5 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A5) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A5)) A5))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X2 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 X2) U)) Y))) V)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X2)))))
% 6.31/6.62 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X2) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X2) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X2) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X2) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X2) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X2) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X2) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X2) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.31/6.62 (assert (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 6.31/6.62 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 6.31/6.62 (assert (= tptp.bot_bo4731626569425807221er_o_o (lambda ((X tptp.code_integer) (Y6 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y6)) tptp.bot_bo5379713665208646970eger_o))))
% 6.31/6.62 (assert (= tptp.bot_bot_num_num_o (lambda ((X tptp.num) (Y6 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y6)) tptp.bot_bo9056780473022590049um_num))))
% 6.31/6.62 (assert (= tptp.bot_bot_nat_num_o (lambda ((X tptp.nat) (Y6 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y6)) tptp.bot_bo7038385379056416535at_num))))
% 6.31/6.62 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y6)) tptp.bot_bo2099793752762293965at_nat))))
% 6.31/6.62 (assert (= tptp.bot_bot_int_int_o (lambda ((X tptp.int) (Y6 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y6)) tptp.bot_bo1796632182523588997nt_int))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr448751882837621926eger_o) (S3 tptp.set_Pr448751882837621926eger_o)) (= (= (lambda ((X tptp.code_integer) (Y6 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y6)) R)) (lambda ((X tptp.code_integer) (Y6 Bool)) (@ (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X) Y6)) S3))) (= R S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr8218934625190621173um_num) (S3 tptp.set_Pr8218934625190621173um_num)) (= (= (lambda ((X tptp.num) (Y6 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y6)) R)) (lambda ((X tptp.num) (Y6 tptp.num)) (@ (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X) Y6)) S3))) (= R S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr6200539531224447659at_num) (S3 tptp.set_Pr6200539531224447659at_num)) (= (= (lambda ((X tptp.nat) (Y6 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y6)) R)) (lambda ((X tptp.nat) (Y6 tptp.num)) (@ (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X) Y6)) S3))) (= R S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (= (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y6)) R)) (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y6)) S3))) (= R S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (= (lambda ((X tptp.int) (Y6 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y6)) R)) (lambda ((X tptp.int) (Y6 tptp.int)) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X) Y6)) S3))) (= R S3))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 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 X2)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X2) tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X2) tptp.one_one_rat))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (= (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X2) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X2) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2) (@ (@ tptp.power_power_int A) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2) (@ (@ tptp.power_power_real A) N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X2) Xa2) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M3)) (not (= Y (@ tptp.bit1 M3)))))) (=> (=> _let_3 (forall ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit1 M3))) (=> (= Xa2 _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N tptp.num)) (= X2 (@ tptp.bit0 N))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N tptp.num)) (=> (= X2 (@ tptp.bit0 N)) (forall ((M3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M3)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M3)))))))) (=> (forall ((N tptp.num)) (=> (= X2 (@ tptp.bit0 N)) (forall ((M3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M3)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M3)))))))) (=> (=> (exists ((N tptp.num)) (= X2 (@ tptp.bit1 N))) _let_2) (=> (forall ((N tptp.num)) (=> (= X2 (@ tptp.bit1 N)) (forall ((M3 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M3)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M3)))))))) (not (forall ((N tptp.num)) (=> (= X2 (@ tptp.bit1 N)) (forall ((M3 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M3)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M3)))))))))))))))))))))))
% 6.31/6.62 (assert (forall ((Y tptp.code_integer) (X2 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 X2) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) Y))))))
% 6.31/6.62 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) Y))))))
% 6.31/6.62 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) Y))))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X2)) tptp.one_one_Code_integer))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X2)) tptp.one_one_rat))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X2)) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 6.31/6.62 (assert (forall ((X2 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 X2)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.31/6.62 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real Y))))))
% 6.31/6.62 (assert (forall ((R2 tptp.set_Pr448751882837621926eger_o) (S2 tptp.set_Pr448751882837621926eger_o)) (=> (forall ((X5 tptp.code_integer) (Y3 Bool)) (let ((_let_1 (@ tptp.member1379723562493234055eger_o (@ (@ tptp.produc6677183202524767010eger_o X5) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le8980329558974975238eger_o R2) S2))))
% 6.31/6.62 (assert (forall ((R2 tptp.set_Pr8218934625190621173um_num) (S2 tptp.set_Pr8218934625190621173um_num)) (=> (forall ((X5 tptp.num) (Y3 tptp.num)) (let ((_let_1 (@ tptp.member7279096912039735102um_num (@ (@ tptp.product_Pair_num_num X5) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le880128212290418581um_num R2) S2))))
% 6.31/6.62 (assert (forall ((R2 tptp.set_Pr6200539531224447659at_num) (S2 tptp.set_Pr6200539531224447659at_num)) (=> (forall ((X5 tptp.nat) (Y3 tptp.num)) (let ((_let_1 (@ tptp.member9148766508732265716at_num (@ (@ tptp.product_Pair_nat_num X5) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le8085105155179020875at_num R2) S2))))
% 6.31/6.62 (assert (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X5) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le3146513528884898305at_nat R2) S2))))
% 6.31/6.62 (assert (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X5 tptp.int) (Y3 tptp.int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X5) Y3)))) (=> (@ _let_1 R2) (@ _let_1 S2)))) (@ (@ tptp.ord_le2843351958646193337nt_int R2) S2))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.62 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N3))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.31/6.62 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N3) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1))))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X2))) X2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X2))) X2))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X2) (@ tptp.ring_1_of_int_real N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X2) N2))))
% 6.31/6.62 (assert (forall ((X2 tptp.rat) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X2) (@ tptp.ring_1_of_int_rat N2)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X2) N2))))
% 6.31/6.62 (assert (forall ((X2 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 X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 6.31/6.62 (assert (forall ((X2 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 X2)) _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 X2) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 6.31/6.62 (assert (forall ((R tptp.set_complex) (S3 tptp.set_complex)) (= (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) R))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) S3))) (@ (@ tptp.ord_le211207098394363844omplex R) S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_real) (S3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) R))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) S3))) (@ (@ tptp.ord_less_eq_set_real R) S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_set_nat) (S3 tptp.set_set_nat)) (= (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) R))) (lambda ((X tptp.set_nat)) (@ (@ tptp.member_set_nat X) S3))) (@ (@ tptp.ord_le6893508408891458716et_nat R) S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_int) (S3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) R))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) S3))) (@ (@ tptp.ord_less_eq_set_int R) S3))))
% 6.31/6.62 (assert (forall ((R tptp.set_nat) (S3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) R))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) S3))) (@ (@ tptp.ord_less_eq_set_nat R) S3))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2))) X2))) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X2 tptp.code_integer)) (=> (forall ((X5 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X5) (@ (@ P X5) (@ (@ tptp.power_8256067586552552935nteger X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X2)) (@ (@ tptp.power_8256067586552552935nteger X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X2 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ P X5) (@ (@ tptp.power_power_real X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X2 tptp.rat)) (=> (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X5) (@ (@ P X5) (@ (@ tptp.power_power_rat X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X2)) (@ (@ tptp.power_power_rat X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X2 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X5) (@ (@ P X5) (@ (@ tptp.power_power_int X5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X2)) (@ (@ tptp.power_power_int X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X2)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.31/6.62 (assert (= tptp.arctan (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.31/6.62 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z5 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z5) (@ (@ tptp.ord_less_int Z5) Z6))))))))
% 6.31/6.62 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z5 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z6) (@ (@ tptp.ord_less_int Z5) Z6))))))))
% 6.31/6.62 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ 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) N3))))))))
% 6.31/6.62 (assert (= (@ tptp.bit_se1146084159140164899it_int tptp.zero_zero_int) tptp.bot_bot_nat_o))
% 6.31/6.62 (assert (= (@ tptp.bit_se1148574629649215175it_nat tptp.zero_zero_nat) tptp.bot_bot_nat_o))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.dvd_dvd_int X2) tptp.one_one_int) (= (@ tptp.abs_abs_int X2) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.31/6.62 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N2))))
% 6.31/6.62 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))))
% 6.31/6.62 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))))
% 6.31/6.62 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N2))))
% 6.31/6.62 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))))
% 6.31/6.62 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))))
% 6.31/6.62 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N2)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N2)))))
% 6.31/6.62 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.31/6.62 (assert (forall ((M tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (= _let_1 _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) B)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int A) B)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se1412395901928357646or_nat A) B)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (= M N2))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (= M N2))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N2) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N2) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (=> (forall ((N tptp.nat)) (or (not (@ (@ tptp.bit_se1146084159140164899it_int A) N)) (not (@ (@ tptp.bit_se1146084159140164899it_int B) N)))) (= (@ (@ tptp.plus_plus_int A) B) (@ (@ tptp.bit_se1409905431419307370or_int A) B)))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (forall ((N tptp.nat)) (or (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N)) (not (@ (@ tptp.bit_se1148574629649215175it_nat B) N)))) (= (@ (@ tptp.plus_plus_nat A) B) (@ (@ tptp.bit_se1412395901928357646or_nat A) B)))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.31/6.62 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) A) (@ (@ tptp.bit_se2923211474154528505it_int N2) A)))))
% 6.31/6.62 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N2)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X2) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X2) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X2)) (@ tptp.abs_abs_int Y))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.31/6.62 (assert (= tptp.abs_abs_int (lambda ((I5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I5) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I5)) I5))))
% 6.31/6.62 (assert (forall ((I3 tptp.int) (D tptp.int)) (=> (not (= I3 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I3) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I3))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N3 tptp.nat) (A5 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A5) N3)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N3) A5))))
% 6.31/6.62 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N3 tptp.nat) (A5 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A5) N3)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N3) A5))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.31/6.62 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N2)) M) (= (@ tptp.abs_abs_int N2) tptp.one_one_int)))))
% 6.31/6.62 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N3) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N3)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N2))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (=> (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (=> (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N) (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))))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (=> (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N) (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))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 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) N2) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (N2 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) N2) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.31/6.62 (assert (forall ((K tptp.int)) (not (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N) M2) (= (@ _let_1 M2) (@ _let_1 N))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (not (@ _let_1 N)))))))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L))) (@ _let_2 (@ _let_1 L)))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 6.31/6.62 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A5 tptp.code_integer) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A5) (@ (@ tptp.power_8256067586552552935nteger _let_1) N3))))))))
% 6.31/6.62 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A5 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A5) (@ (@ tptp.power_power_int _let_1) N3))))))))
% 6.31/6.62 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A5 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A5) (@ (@ tptp.power_power_nat _let_1) N3))))))))
% 6.31/6.62 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N3))))))))
% 6.31/6.62 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ (@ tptp.ord_less_nat I2) N2)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ F I2) K)))))))))
% 6.31/6.62 (assert (forall ((D tptp.int) (X2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 6.31/6.62 (assert (forall ((D tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X2) Z))) tptp.one_one_int)) D))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 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)) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 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)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (N2 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)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I2))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ F I2) K))))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N2))))))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int) (N2 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 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N2))))))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 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 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N2))))))))))
% 6.31/6.62 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A5 tptp.code_integer) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A5))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A5) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 6.31/6.62 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A5 tptp.int) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A5))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A5) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 6.31/6.62 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A5 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A5))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A5) _let_1)) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat))) (@ F I2)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ F I2) K))))))))
% 6.31/6.62 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N3)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))))))
% 6.31/6.62 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N3))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X2)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X2) Y)))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.31/6.62 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int M) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N2)) (@ (@ 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 N2)))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N2)) (@ (@ 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 N2)))))))
% 6.31/6.62 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.31/6.62 (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))))))))))))
% 6.31/6.62 (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))))))))))))))))
% 6.31/6.62 (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)))))))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) B) _let_1))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B))) (= (@ (@ tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ _let_1 N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X2) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.62 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.31/6.62 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.31/6.62 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.31/6.62 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.31/6.62 (assert (forall ((X2 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X2)))
% 6.31/6.62 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X2) (@ tptp.uminus_uminus_int tptp.one_one_int)) X2)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N2) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.31/6.62 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.exp_real X2) tptp.one_one_real) (= X2 tptp.zero_zero_real))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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)))))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.31/6.62 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.31/6.62 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.31/6.62 (assert (forall ((F (-> tptp.complex tptp.int)) (A3 tptp.set_complex)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.groups5690904116761175830ex_int F) A3)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ tptp.ring_17405671764205052669omplex (@ F X)))) A3))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups3539618377306564664at_int F) A3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X)))) A3))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X tptp.int)) (@ tptp.ring_1_of_int_real (@ F X)))) A3))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X)))) A3))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ tptp.ring_1_of_int_int (@ F X)))) A3))))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int)))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X2)) (@ tptp.numeral_numeral_int Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X2)) (@ tptp.numeral_numeral_nat Y))))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X2))) (@ 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 X2)) (@ tptp.numeral_numeral_int Y)))))))
% 6.31/6.62 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ 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 X2)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.31/6.62 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.31/6.62 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N3 tptp.nat) (A5 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A5) (@ tptp.bit_se2000444600071755411sk_int N3)))))
% 6.31/6.62 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N3 tptp.nat) (A5 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A5) (@ tptp.bit_se2002935070580805687sk_nat N3)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int B) C))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat B) C))))))
% 6.31/6.62 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B5) A5))))
% 6.31/6.62 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B5) A5))))
% 6.31/6.62 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int B))) (let ((_let_2 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.31/6.62 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex)) (not (= (@ tptp.exp_complex X2) tptp.zero_zero_complex))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (not (= (@ tptp.exp_real X2) tptp.zero_zero_real))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X2))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int Y) Z)) (@ (@ tptp.bit_se1409905431419307370or_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se1409905431419307370or_int X2))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int Y) Z)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (Z tptp.int) (X2 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y) Z)) X2) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) X2)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X2)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (Z tptp.int) (X2 tptp.int)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Z)) X2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se1409905431419307370or_int Y) X2)) (@ (@ tptp.bit_se1409905431419307370or_int Z) X2)))))
% 6.31/6.62 (assert (forall ((A3 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A3))) (= (@ (@ tptp.times_times_complex _let_1) A3) (@ (@ tptp.times_times_complex A3) _let_1)))))
% 6.31/6.62 (assert (forall ((A3 tptp.real)) (let ((_let_1 (@ tptp.exp_real A3))) (= (@ (@ tptp.times_times_real _let_1) A3) (@ (@ tptp.times_times_real A3) _let_1)))))
% 6.31/6.62 (assert (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A3 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A3)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) A))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A3 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I5)) A))) A3)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) A))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X2) Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) X2))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) Y))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) Z)))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X2) Y) (@ (@ tptp.times_times_complex Y) X2)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X2) Y) (@ (@ tptp.times_times_real Y) X2)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X2)) (@ tptp.exp_complex Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X2)) (@ tptp.exp_real Y)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X2) Y)) (@ (@ tptp.plus_plus_int X2) Y))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))))
% 6.31/6.62 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.31/6.62 (assert (forall ((Y tptp.int) (Z tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X2) Y)) Z)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))) tptp.one_one_real)))
% 6.31/6.62 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X2)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X2))) tptp.one_one_complex)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.31/6.62 (assert (forall ((A tptp.code_integer) (X2 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ tptp.bit_se1080825931792720795nteger A))) (let ((_let_3 (@ tptp.bit_se3949692690581998587nteger A))) (=> (= (@ _let_3 X2) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 X2) _let_1) (=> (= (@ _let_3 Y) tptp.zero_z3403309356797280102nteger) (=> (= (@ _let_2 Y) _let_1) (= X2 Y))))))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ tptp.bit_se1409905431419307370or_int A))) (let ((_let_3 (@ tptp.bit_se725231765392027082nd_int A))) (=> (= (@ _let_3 X2) tptp.zero_zero_int) (=> (= (@ _let_2 X2) _let_1) (=> (= (@ _let_3 Y) tptp.zero_zero_int) (=> (= (@ _let_2 Y) _let_1) (= X2 Y))))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ tptp.exp_real X2)))))
% 6.31/6.62 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 6.31/6.62 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ (@ tptp.minus_minus_real Y) tptp.one_one_real)) (= (@ tptp.exp_real X5) Y))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X2)) X2))))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.31/6.62 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N2)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.31/6.62 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.31/6.62 (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)))
% 6.31/6.62 (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)))
% 6.31/6.62 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ tptp.exp_real X))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.31/6.62 (assert (= tptp.tanh_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (@ tptp.exp_complex X))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.31/6.62 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.31/6.62 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.62 (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)))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.62 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N3))))))))
% 6.31/6.62 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.31/6.62 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.31/6.62 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.31/6.62 (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))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N2)) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2)) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N2)) (= N2 tptp.zero_zero_nat))))
% 6.31/6.62 (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))))))
% 6.31/6.62 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.31/6.62 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))
% 6.31/6.62 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_int))))
% 6.31/6.62 (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))
% 6.31/6.62 (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))))))
% 6.31/6.62 (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))))
% 6.31/6.62 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))
% 6.31/6.62 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_int))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N2)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N2)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_se2000444600071755411sk_int N2)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.31/6.62 (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)))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X2)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X2))))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc N2)) (@ (@ tptp.bit_se1412395901928357646or_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc N2)) (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N2))))))
% 6.31/6.62 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X2))))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A3))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A3))))
% 6.31/6.62 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A3))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A3))))
% 6.31/6.62 (assert (forall ((F (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A3))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A3))))
% 6.31/6.62 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups2073611262835488442omplex G) tptp.bot_bot_set_nat) tptp.zero_zero_complex)))
% 6.31/6.62 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G) tptp.bot_bot_set_nat) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((G (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups3049146728041665814omplex G) tptp.bot_bot_set_int) tptp.zero_zero_complex)))
% 6.31/6.62 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups8778361861064173332t_real G) tptp.bot_bot_set_int) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups3906332499630173760nt_rat G) tptp.bot_bot_set_int) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) tptp.bot_bot_set_int) tptp.zero_zero_nat)))
% 6.31/6.62 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups5754745047067104278omplex G) tptp.bot_bot_set_real) tptp.zero_zero_complex)))
% 6.31/6.62 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G) tptp.bot_bot_set_real) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups1300246762558778688al_rat G) tptp.bot_bot_set_real) tptp.zero_zero_rat)))
% 6.31/6.62 (assert (forall ((I6 tptp.set_complex) (X2 (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X2) I6) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I5 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_real) (X2 (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X2) I6) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I5 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_nat) (X2 (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X2) I6) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_int) (X2 (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X2 I2)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X2) I6) tptp.one_one_Code_integer) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I2)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I5 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_complex) (X2 (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X2) I6) tptp.one_one_real) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_real (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_real) (X2 (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X2) I6) tptp.one_one_real) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_real (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_int) (X2 (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X2 I2)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X2) I6) tptp.one_one_real) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ (@ tptp.times_times_real (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_complex) (X2 (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X2) I6) tptp.one_one_rat) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_real) (X2 (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X2) I6) tptp.one_one_rat) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((I6 tptp.set_nat) (X2 (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X2 I2)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X2) I6) tptp.one_one_rat) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I2)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X2 I5)))) I6)) B))) Delta))))))
% 6.31/6.62 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A3) tptp.zero_zero_int)))
% 6.31/6.62 (assert (forall ((A3 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A3) tptp.zero_zero_complex)))
% 6.31/6.62 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A3) tptp.zero_zero_nat)))
% 6.31/6.62 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A3) tptp.zero_zero_real)))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X2)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X2) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) 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 X2) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.31/6.62 (assert (forall ((X2 tptp.complex) (A3 tptp.set_complex) (B4 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.insert_complex X2) A3)) B4) (and (@ (@ tptp.member_complex X2) B4) (@ (@ tptp.ord_le211207098394363844omplex A3) B4)))))
% 6.31/6.62 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (B4 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X2) A3)) B4) (and (@ (@ tptp.member_real X2) B4) (@ (@ tptp.ord_less_eq_set_real A3) B4)))))
% 6.31/6.62 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat) (B4 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X2) A3)) B4) (and (@ (@ tptp.member_set_nat X2) B4) (@ (@ tptp.ord_le6893508408891458716et_nat A3) B4)))))
% 6.31/6.62 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (B4 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X2) A3)) B4) (and (@ (@ tptp.member_int X2) B4) (@ (@ tptp.ord_less_eq_set_int A3) B4)))))
% 6.31/6.62 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B4 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X2) A3)) B4) (and (@ (@ tptp.member_nat X2) B4) (@ (@ tptp.ord_less_eq_set_nat A3) B4)))))
% 6.31/6.62 (assert (forall ((A tptp.int) (A3 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A3) _let_1))))))
% 6.31/6.62 (assert (forall ((A tptp.real) (A3 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= (@ (@ tptp.insert_real A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A3) _let_1))))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (A3 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A3) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A3) _let_1))))))
% 6.31/6.63 (assert (forall ((B tptp.int) (A tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A) A3)) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A3) _let_1))))))
% 6.31/6.63 (assert (forall ((B tptp.real) (A tptp.real) (A3 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= _let_1 (@ (@ tptp.insert_real A) A3)) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A3) _let_1))))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (A tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A3)) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A3) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.31/6.63 (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)))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex A3) (@ tptp.uminus8566677241136511917omplex (@ (@ tptp.insert_complex B) tptp.bot_bot_set_complex))) (not (@ (@ tptp.member_complex B) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat A3) (@ tptp.uminus613421341184616069et_nat (@ (@ tptp.insert_set_nat B) tptp.bot_bot_set_set_nat))) (not (@ (@ tptp.member_set_nat B) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A3) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B) A3)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.31/6.63 (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)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.vEBT_VEBT)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X2)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X2)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.int)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X2)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X2)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((C5 tptp.set_int) (D4 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C5) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C5)) (@ _let_1 D4))))))
% 6.31/6.63 (assert (forall ((C5 tptp.set_real) (D4 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C5) D4) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C5)) (@ _let_1 D4))))))
% 6.31/6.63 (assert (forall ((C5 tptp.set_nat) (D4 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C5) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C5)) (@ _let_1 D4))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (A3 tptp.set_complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A3))) (=> (not (@ (@ tptp.member_complex X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_complex X2) B4)) (@ _let_1 B4))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (A3 tptp.set_real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A3))) (=> (not (@ (@ tptp.member_real X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_real X2) B4)) (@ _let_1 B4))))))
% 6.31/6.63 (assert (forall ((X2 tptp.set_nat) (A3 tptp.set_set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A3))) (=> (not (@ (@ tptp.member_set_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_set_nat X2) B4)) (@ _let_1 B4))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (A3 tptp.set_int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (=> (not (@ (@ tptp.member_int X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_int X2) B4)) (@ _let_1 B4))))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (A3 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A3))) (=> (not (@ (@ tptp.member_nat X2) A3)) (= (@ _let_1 (@ (@ tptp.insert_nat X2) B4)) (@ _let_1 B4))))))
% 6.31/6.63 (assert (forall ((B4 tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B4) (@ (@ tptp.insert_int A) B4))))
% 6.31/6.63 (assert (forall ((B4 tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B4) (@ (@ tptp.insert_real A) B4))))
% 6.31/6.63 (assert (forall ((B4 tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B4) (@ (@ tptp.insert_nat A) B4))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_int B) B4))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A3))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_real B) B4))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A3))) (=> (@ _let_1 B4) (@ _let_1 (@ (@ tptp.insert_nat B) B4))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.suc X5))) (=> (@ (@ tptp.member_nat _let_1) A3) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A3) (@ (@ tptp.groups3542108847815614940at_nat G) A3))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ tptp.suc X5))) (=> (@ (@ tptp.member_nat _let_1) A3) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A3) (@ (@ tptp.groups6591440286371151544t_real G) A3))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A3)) (@ (@ tptp.groups5693394587270226106ex_nat G) A3))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A3)) (@ (@ tptp.groups1935376822645274424al_nat G) A3))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_set_nat) (G (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A3)) (@ (@ tptp.groups8294997508430121362at_nat G) A3))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4541462559716669496nt_nat G) A3))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat G) A3))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A3) (@ tptp.suc N2)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))))
% 6.31/6.63 (assert (forall ((X8 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X8) _let_1) (or (= X8 tptp.bot_bot_set_int) (= X8 _let_1))))))
% 6.31/6.63 (assert (forall ((X8 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (= (@ (@ tptp.ord_less_eq_set_real X8) _let_1) (or (= X8 tptp.bot_bot_set_real) (= X8 _let_1))))))
% 6.31/6.63 (assert (forall ((X8 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X8) _let_1) (or (= X8 tptp.bot_bot_set_nat) (= X8 _let_1))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (X2 tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A3) _let_1) (or (= A3 tptp.bot_bot_set_int) (= A3 _let_1))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A3) _let_1) (or (= A3 tptp.bot_bot_set_real) (= A3 _let_1))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) _let_1) (or (= A3 tptp.bot_bot_set_nat) (= A3 _let_1))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (B4 tptp.set_complex) (X2 tptp.complex) (C5 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex B4))) (let ((_let_2 (@ tptp.ord_le211207098394363844omplex A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_complex X2) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_complex X2) A3))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (B4 tptp.set_real) (X2 tptp.real) (C5 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B4))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X2) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_real X2) A3))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_set_nat) (B4 tptp.set_set_nat) (X2 tptp.set_nat) (C5 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat B4))) (let ((_let_2 (@ tptp.ord_le6893508408891458716et_nat A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_set_nat X2) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_set_nat X2) A3))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (B4 tptp.set_int) (X2 tptp.int) (C5 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B4))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X2) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_int X2) A3))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (B4 tptp.set_nat) (X2 tptp.nat) (C5 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B4))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A3))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X2) C5))) (and (@ _let_2 (@ _let_1 C5)) (not (@ (@ tptp.member_nat X2) A3))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int X2))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) (@ _let_1 tptp.bot_bot_set_int))) B4) (@ (@ tptp.ord_less_eq_set_int A3) (@ _let_1 B4))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real X2))) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A3) (@ _let_1 tptp.bot_bot_set_real))) B4) (@ (@ tptp.ord_less_eq_set_real A3) (@ _let_1 B4))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat X2))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) (@ _let_1 tptp.bot_bot_set_nat))) B4) (@ (@ tptp.ord_less_eq_set_nat A3) (@ _let_1 B4))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A3))) (let ((_let_2 (@ (@ tptp.member_complex X2) A3))) (let ((_let_3 (@ tptp.insert_complex X2))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.minus_811609699411566653omplex A3) (@ _let_3 tptp.bot_bot_set_complex))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A3))) (let ((_let_2 (@ (@ tptp.member_set_nat X2) A3))) (let ((_let_3 (@ tptp.insert_set_nat X2))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ _let_3 tptp.bot_bot_set_set_nat))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (let ((_let_2 (@ (@ tptp.member_int X2) A3))) (let ((_let_3 (@ tptp.insert_int X2))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) (@ _let_3 tptp.bot_bot_set_int))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A3))) (let ((_let_2 (@ (@ tptp.member_real X2) A3))) (let ((_let_3 (@ tptp.insert_real X2))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A3) (@ _let_3 tptp.bot_bot_set_real))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A3))) (let ((_let_2 (@ (@ tptp.member_nat X2) A3))) (let ((_let_3 (@ tptp.insert_nat X2))) (= (@ _let_1 (@ _let_3 B4)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) (@ _let_3 tptp.bot_bot_set_nat))) B4)) (=> (not _let_2) (@ _let_1 B4)))))))))
% 6.31/6.63 (assert (forall ((Xs tptp.list_real) (I3 tptp.nat) (X2 tptp.real)) (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) I3) X2))) (@ (@ tptp.insert_real X2) (@ tptp.set_real2 Xs)))))
% 6.31/6.63 (assert (forall ((Xs tptp.list_int) (I3 tptp.nat) (X2 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) I3) X2))) (@ (@ tptp.insert_int X2) (@ tptp.set_int2 Xs)))))
% 6.31/6.63 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I3 tptp.nat) (X2 tptp.vEBT_VEBT)) (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I3) X2))) (@ (@ tptp.insert_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 6.31/6.63 (assert (forall ((Xs tptp.list_nat) (I3 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) I3) X2))) (@ (@ tptp.insert_nat X2) (@ tptp.set_nat2 Xs)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I6))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (X2 tptp.complex) (B4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_complex X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_complex A3))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A3) (@ _let_3 tptp.bot_bot_set_complex))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A3) B4)))))))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_set_nat) (X2 tptp.set_nat) (B4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_set_nat X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_set_nat A3))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) (@ _let_3 tptp.bot_bot_set_set_nat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_le6893508408891458716et_nat A3) B4)))))))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (X2 tptp.int) (B4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_int X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_int A3))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A3) (@ _let_3 tptp.bot_bot_set_int))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A3) B4)))))))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (X2 tptp.real) (B4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_real X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_real A3))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A3) (@ _let_3 tptp.bot_bot_set_real))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A3) B4)))))))))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (X2 tptp.nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat X2))) (let ((_let_2 (@ _let_1 A3))) (let ((_let_3 (@ tptp.insert_nat X2))) (let ((_let_4 (@ _let_1 B4))) (let ((_let_5 (@ tptp.ord_less_set_nat A3))) (= (@ _let_5 (@ _let_3 B4)) (and (=> _let_4 (@ _let_5 B4)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A3) (@ _let_3 tptp.bot_bot_set_nat))) B4)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A3) B4)))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N2)) X2)) (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N2)) X2)) (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N2)) X2)) (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N2)) X2)) (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) X2)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X2) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) X2)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X2) tptp.bot_bot_set_nat))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) X2)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X2) tptp.bot_bot_set_int))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) X2)))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X2) tptp.bot_bot_set_real))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.31/6.63 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N2))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N2))))))))
% 6.31/6.63 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I5)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I5) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F M))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (= (@ G X5) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G) A3) tptp.zero_zero_int))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (= (@ G X5) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7754918857620584856omplex G) A3) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (= (@ G X5) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G) A3) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (= (@ G X5) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G) A3) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.complex)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups5754745047067104278omplex G) A3) tptp.zero_zero_complex)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A3) (= (@ G A4) tptp.zero_zero_complex)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.complex)) (A3 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2073611262835488442omplex G) A3) tptp.zero_zero_complex)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (= (@ G A4) tptp.zero_zero_complex)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.complex)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3049146728041665814omplex G) A3) tptp.zero_zero_complex)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (= (@ G A4) tptp.zero_zero_complex)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.complex tptp.real)) (A3 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5808333547571424918x_real G) A3) tptp.zero_zero_real)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A3) (= (@ G A4) tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.real)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups8097168146408367636l_real G) A3) tptp.zero_zero_real)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A3) (= (@ G A4) tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.real)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G) A3) tptp.zero_zero_real)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (= (@ G A4) tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.complex tptp.rat)) (A3 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5058264527183730370ex_rat G) A3) tptp.zero_zero_rat)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A3) (= (@ G A4) tptp.zero_zero_rat)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.rat)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1300246762558778688al_rat G) A3) tptp.zero_zero_rat)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A3) (= (@ G A4) tptp.zero_zero_rat)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (A3 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2906978787729119204at_rat G) A3) tptp.zero_zero_rat)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (= (@ G A4) tptp.zero_zero_rat)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.rat)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3906332499630173760nt_rat G) A3) tptp.zero_zero_rat)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (= (@ G A4) tptp.zero_zero_rat)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.31/6.63 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N3 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.31/6.63 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N3))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q4 tptp.nat)) (@ (@ tptp.ord_less_nat Q4) N2))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K5) (@ (@ tptp.ord_less_eq_rat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) K5) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 6.31/6.63 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) K5) (@ (@ tptp.ord_less_eq_int (@ F I2)) (@ G I2)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.31/6.63 (assert (forall ((R2 tptp.int) (F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.times_times_int R2) (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N3 tptp.int)) (@ (@ tptp.times_times_int R2) (@ F N3)))) A3))))
% 6.31/6.63 (assert (forall ((R2 tptp.complex) (F (-> tptp.complex tptp.complex)) (A3 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R2) (@ (@ tptp.groups7754918857620584856omplex F) A3)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.times_times_complex R2) (@ F N3)))) A3))))
% 6.31/6.63 (assert (forall ((R2 tptp.nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R2) (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_nat R2) (@ F N3)))) A3))))
% 6.31/6.63 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (= (@ (@ tptp.times_times_real R2) (@ (@ tptp.groups6591440286371151544t_real F) A3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ F N3)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (R2 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) R2) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N3 tptp.int)) (@ (@ tptp.times_times_int (@ F N3)) R2))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.complex tptp.complex)) (A3 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A3)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N3)) R2))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (R2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) R2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N3)) R2))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (A3 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A3)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) R2))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (G (-> tptp.int tptp.int)) (B4 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups4538972089207619220nt_int G) B4)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I5)) (@ G J3)))) B4))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.complex tptp.complex)) (A3 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B4 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A3)) (@ (@ tptp.groups7754918857620584856omplex G) B4)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I5)) (@ G J3)))) B4))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B4 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat G) B4)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I5)) (@ G J3)))) B4))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (A3 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B4 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A3)) (@ (@ tptp.groups6591440286371151544t_real G) B4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ G J3)))) B4))) A3))))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A3)) (@ (@ tptp.groups4538972089207619220nt_int H2) A3)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A3 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A3)) (@ (@ tptp.groups7754918857620584856omplex H2) A3)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A3)) (@ (@ tptp.groups3542108847815614940at_nat H2) A3)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A3)) (@ (@ tptp.groups6591440286371151544t_real H2) A3)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.complex tptp.complex)) (A3 tptp.set_complex) (R2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A3)) R2) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N3 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) R2))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (A3 tptp.set_nat) (R2 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A3)) R2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) R2))) A3))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I5) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N2) D)))) _let_1)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A3)) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A3)) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_real (@ F X5)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A3)) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A3)) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A3)) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A3)) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A3)) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A3)) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_nat (@ F X5)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) tptp.zero_zero_nat))))
% 6.31/6.63 (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))))))))))))
% 6.31/6.63 (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))))))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X2) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X2)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X2) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X2) Xa2) 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 X2) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X2 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X2)))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X2 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X2)))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X2 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X2)))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X2)) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((N2 tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N2)) (= M N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)) (and (= N2 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri5074537144036343181t_real N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri681578069525770553at_rat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.31/6.63 (assert (= (@ tptp.cot_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.63 (assert (= (@ tptp.cot_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))))
% 6.31/6.63 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.31/6.63 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.31/6.63 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.31/6.63 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.31/6.63 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6690914467698888265omplex N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_real N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_rat N2))))
% 6.31/6.63 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.31/6.63 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))))
% 6.31/6.63 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.31/6.63 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.31/6.63 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.31/6.63 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.31/6.63 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X2) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X2) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X2) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X2) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X2) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (= X2 (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W) (@ tptp.semiri681578069525770553at_rat X2)) (= (@ (@ tptp.power_power_nat B) W) X2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat M)) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.31/6.63 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.31/6.63 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.31/6.63 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.31/6.63 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.complex tptp.nat)) (A3 tptp.set_complex)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.groups5693394587270226106ex_nat F) A3)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ tptp.semiri8010041392384452111omplex (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat W)))))
% 6.31/6.63 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) M))))
% 6.31/6.63 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat B) W)))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (W tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X2))))
% 6.31/6.63 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)))))
% 6.31/6.63 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)))))
% 6.31/6.63 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)))))
% 6.31/6.63 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 6.31/6.63 (assert (forall ((Y tptp.nat) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X2)) N2) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X2)) N2) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X2)) N2) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X2)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X2)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X2)) N2)) (or (@ _let_1 X2) (= N2 tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X2)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (I3 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I3)) N2)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (I3 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I3)) N2)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (I3 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_nat X2) _let_1)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (I3 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I3)) N2)) (@ (@ tptp.ord_less_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (N2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I3)) N2)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)) X2))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (N2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I3)) N2)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)) X2))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (N2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (N2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I3)) N2)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)) X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (I3 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I3)) N2)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (I3 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I3)) N2)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (I3 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X2)) _let_1) (@ (@ tptp.ord_less_eq_nat X2) _let_1)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (I3 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I3)) N2)) (@ (@ tptp.ord_less_eq_nat X2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (N2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I3)) N2)) (@ tptp.semiri5074537144036343181t_real X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)) X2))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (N2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I3)) N2)) (@ tptp.semiri681578069525770553at_rat X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)) X2))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (N2 tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X2)) (@ _let_1 X2)))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (N2 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I3)) N2)) (@ tptp.semiri1314217659103216013at_int X2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I3)) N2)) X2))))
% 6.31/6.63 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.one_one_real)))
% 6.31/6.63 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.cos_real X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X2))))
% 6.31/6.63 (assert (forall ((N2 tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N2))) tptp.one_one_real)))
% 6.31/6.63 (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))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat X2) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_rat X2) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X2))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X2))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X2))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.31/6.63 (assert (forall ((Z tptp.int)) (=> (forall ((N tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N)))) (not (forall ((N tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)))))))))
% 6.31/6.63 (assert (forall ((Z tptp.int)) (not (forall ((M3 tptp.nat) (N tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X2)) (@ _let_1 X2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ring_1_of_int_real X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.ring_1_of_int_rat X2)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I3)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I3)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I3)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I3)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X2)) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.31/6.63 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.31/6.63 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.31/6.63 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5)))))
% 6.31/6.63 (assert (forall ((P (-> tptp.int Bool)) (Z tptp.int)) (=> (forall ((N tptp.nat)) (@ P (@ tptp.semiri1314217659103216013at_int N))) (=> (forall ((N tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))) (@ P Z)))))
% 6.31/6.63 (assert (forall ((Z tptp.int)) (=> (forall ((N tptp.nat)) (not (= Z (@ tptp.semiri1314217659103216013at_int N)))) (not (forall ((N tptp.nat)) (not (= Z (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))))
% 6.31/6.63 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.31/6.63 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.31/6.63 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2))) Z))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.31/6.63 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N3 tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N3)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X)))) A3))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X2) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X2) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X2)) (@ tptp.semiri5074537144036343181t_real Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X2) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X2)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X2) Y)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X2)) (@ tptp.semiri681578069525770553at_rat Y)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se1412395901928357646or_nat M) N2)) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se1412395901928357646or_nat M) N2)) (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))))
% 6.31/6.63 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.31/6.63 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X2))) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) X2)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X2)) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X2) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X2)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X2) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.exp_real X2)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (forall ((Y5 tptp.real)) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real Y5) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X2)))))))
% 6.31/6.63 (assert (forall ((M tptp.int)) (=> (forall ((N tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N)))) (not (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X2))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N2 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))
% 6.31/6.63 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.31/6.63 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N3 tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N2) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_int)))
% 6.31/6.63 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)))))))))
% 6.31/6.63 (assert (forall ((D tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real D))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (or (exists ((X tptp.nat)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X tptp.nat)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.31/6.63 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.31/6.63 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.31/6.63 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= K (@ tptp.semiri1314217659103216013at_int N)))))))
% 6.31/6.63 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))))
% 6.31/6.63 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))))))
% 6.31/6.63 (assert (= tptp.ord_less_nat (lambda ((N3 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 6.31/6.63 (assert (= tptp.ord_less_eq_nat (lambda ((N3 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 6.31/6.63 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I3) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I3)) (@ _let_1 J)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) tptp.zero_zero_int) (exists ((N tptp.nat)) (= X2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)))
% 6.31/6.63 (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))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X2)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X2) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X2) D))) _let_1))))))
% 6.31/6.63 (assert (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) E2)))))))
% 6.31/6.63 (assert (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (not (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)))) E2)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.31/6.63 (assert (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X5) tptp.zero_zero_real) (forall ((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 X5))))))
% 6.31/6.63 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (or (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N2))))))))
% 6.31/6.63 (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 ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_eq_real X5) tptp.pi) (= (@ tptp.cos_real X5) 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 X5)))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X2) (@ tptp.semiri8010041392384452111omplex N2)))) N2) (@ tptp.exp_complex X2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N2)))) N2) (@ tptp.exp_real X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 C) (=> (forall ((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)) X2)) C))) (= X2 tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))))
% 6.31/6.63 (assert (forall ((P (-> tptp.int Bool)) (X2 tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X2) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X2) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X2)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X2) Y) (@ P tptp.zero_zero_int))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X2) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ln_ln_real X2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X2))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X2)))) tptp.one_one_real)))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N2))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N2) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) Z)) (@ (@ tptp.insert_nat N2) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X2))) tptp.one_one_real))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X2)))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.one_one_real) (exists ((X tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.cos_real X2))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X2)))))))
% 6.31/6.63 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A12)))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (D tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))))
% 6.31/6.63 (assert (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (D tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D))))))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (D tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.31/6.63 (assert (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X2)))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X2)))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X2)))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N2)) (@ tptp.exp_real X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.cos_real X2) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.31/6.63 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_complex (= N3 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M6)))) (@ (@ (@ tptp.if_complex (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M6)))) (@ (@ (@ tptp.if_int (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_real (= N3 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M6)))) (@ (@ (@ tptp.if_real (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M6)))) (@ (@ (@ tptp.if_nat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.if_rat (= N3 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M6 tptp.nat) (Q4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M6)))) (@ (@ (@ tptp.if_rat (= Q4 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X2)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X2) tptp.one_one_real)) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))))))
% 6.31/6.63 (assert (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N2)) (@ _let_4 N2))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 6.31/6.63 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N2)) (@ _let_3 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X2) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ tptp.suc N3))))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3)))) (@ F tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3)))) (@ F tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X2))))))
% 6.31/6.63 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 6.31/6.63 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 6.31/6.63 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.31/6.63 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arctan X2) (@ tptp.suminf_real (lambda ((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 X2) _let_1))))))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.31/6.63 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 6.31/6.63 (assert (forall ((W tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) (@ tptp.real_V1022390504157884413omplex A)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.zero_zero_real) (= X2 tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_complex))))
% 6.31/6.63 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.63 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.31/6.63 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.31/6.63 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.31/6.63 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.31/6.63 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X2)) (not (= X2 tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X2)) (not (= X2 tptp.zero_zero_complex)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X2)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X2)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (N2 tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N2) (@ (@ tptp.power_power_real Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (N2 tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N2) (@ (@ tptp.power_power_complex Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (R2 tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (R2 tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y))) (@ (@ tptp.times_times_real R2) S2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X2) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X2) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y))) E2))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y))) E2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (R2 tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (R2 tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) R2) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y))) E2))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y))) E2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X2) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R2) S2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X2) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X2)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X2) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X2)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X2) Y))) E2))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y))) E2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X2) Y))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X2)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X2) Y))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((W tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N2) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N2) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (= (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X2) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X2) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real Z) M)) (@ (@ tptp.power_power_real W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Z) W))))))))
% 6.31/6.63 (assert (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z) M)) (@ (@ tptp.power_power_complex W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W))))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 6.31/6.63 (assert (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.31/6.63 (assert (= (@ tptp.suminf_nat (lambda ((N3 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.31/6.63 (assert (= (@ tptp.suminf_int (lambda ((N3 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))))
% 6.31/6.63 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I2 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I2) J2) (@ (@ P (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J2)) (@ (@ P I2) J2)))) (@ (@ P A0) A12)))))
% 6.31/6.63 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q4)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.31/6.63 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P6 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q4)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.31/6.63 (assert (forall ((H2 tptp.real) (Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N2)) (@ _let_2 N2))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q4 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q4)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q4))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.31/6.63 (assert (forall ((I3 tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I3) (@ tptp.set_or890127255671739683et_nat K)) (@ (@ tptp.ord_less_set_nat I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I3) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I3) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I3) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I3) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I3) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I3) K))))
% 6.31/6.63 (assert (= (@ tptp.sin_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.63 (assert (= (@ tptp.sin_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X2)) (@ tptp.set_ord_lessThan_rat Y)) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X2)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X2)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X2)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X2)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))
% 6.31/6.63 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X2))) (let ((_let_2 (@ tptp.cos_complex X2))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (let ((_let_2 (@ tptp.cos_real X2))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) tptp.zero_zero_real)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.31/6.63 (assert (forall ((N2 tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)))
% 6.31/6.63 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.31/6.63 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) tptp.one_one_complex))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1)) tptp.one_one_complex))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.zero_zero_real)))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X2)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)))
% 6.31/6.63 (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)))
% 6.31/6.63 (assert (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X) U2))))))
% 6.31/6.63 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_rat X) U2))))))
% 6.31/6.63 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_num X) U2))))))
% 6.31/6.63 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_int X) U2))))))
% 6.31/6.63 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) U2))))))
% 6.31/6.63 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_real X) U2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((M tptp.rat) (N2 tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N2)) (@ (@ tptp.ord_less_rat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.31/6.63 (assert (forall ((M tptp.real) (N2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N2)) (@ (@ tptp.ord_less_real M) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (and (= X2 (@ _let_1 (@ tptp.cos_real A4))) (= Y (@ _let_1 (@ tptp.sin_real A4))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (=> (= (@ tptp.cos_complex X2) tptp.one_one_complex) (= (@ tptp.sin_complex X2) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.cos_real X2) tptp.one_one_real) (= (@ tptp.sin_real X2) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.sin_real Y))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X2))) tptp.one_one_real)))
% 6.31/6.63 (assert (= tptp.cot_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X)) (@ tptp.sin_complex X)))))
% 6.31/6.63 (assert (= tptp.cot_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))))
% 6.31/6.63 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.31/6.63 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N2 tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N2))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.31/6.63 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X2)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (=> (= (@ tptp.sin_complex X2) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X2)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X2)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I5 tptp.int)) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) tptp.pi))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (R2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) R2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I5)) R2))) _let_1)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (R2 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) R2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I5)) R2))) _let_1)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (R2 tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) R2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I5)) R2))) _let_1)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N3))) (@ F N3)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N3))) (@ F N3)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N3))) (@ F N3)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N3)) (@ F (@ tptp.suc N3))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N3)) (@ F (@ tptp.suc N3))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N3)) (@ F (@ tptp.suc N3))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X2)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X2))) (@ tptp.cos_complex X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X2)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X2))) (@ tptp.cos_real X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_rat (@ _let_2 X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (not (= X2 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X2) tptp.one_one_complex)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (not (= X2 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X2) tptp.one_one_rat)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (not (= X2 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X2) tptp.one_one_real)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 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 X2)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X2)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X2))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X2 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X2)))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X2))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X2 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N2))) (@ _let_1 X2)))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X2))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X2 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X2)))))))))))
% 6.31/6.63 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P6))) (@ _let_1 P6))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P6))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P6)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.31/6.63 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P6))) (@ _let_1 P6))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P6))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P6)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.31/6.63 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P6))) (@ _let_1 P6))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P6))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P6)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.31/6.63 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P6))) (@ _let_1 P6))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P6))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P6)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_complex X2) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) N2)) (@ (@ tptp.power_power_rat Y) N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_rat X2) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_int X2) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5)))) (@ (@ tptp.power_power_real X2) I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X2) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X2) P6)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X2) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X2) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X2) P6)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X2) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X2) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X2) P6)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X2) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X2) P6)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P6))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) K5))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) K5))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) K5))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) K5))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 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 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X2) (@ tptp.sin_real Y)) (= X2 Y))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 6.31/6.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X2))))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X2) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X2) N2)) (@ (@ tptp.times_times_rat (@ _let_1 X2)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_rat X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X2) N2)) (@ (@ tptp.times_times_int (@ _let_1 X2)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N2)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z) W)) _let_1)))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z) W)) _let_1)))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X2)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X2)) _let_2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X2)) _let_2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((X2 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 X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X2)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X2) Y))))))))))
% 6.31/6.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X2))))))))
% 6.31/6.63 (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 ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X5) (@ (@ tptp.ord_less_eq_real X5) _let_1) (= (@ tptp.sin_real X5) 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 X5)))))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ F I5)) (@ G I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) tptp.one_one_nat)))) _let_1))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X2)) (@ (@ tptp.divide_divide_real X2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.31/6.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _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) (= X2 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.sin_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5) (= X2 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (= (@ tptp.sin_real X2) tptp.zero_zero_real) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real X2) tptp.zero_zero_real) (or (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X2 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X2 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X2))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 6.31/6.63 (assert (forall ((X2 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 X2) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _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)))) (= X2 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real 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)) (= X2 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real 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)) (=> (= X2 (@ tptp.cos_real T3)) (not (= Y (@ tptp.sin_real T3))))))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (Mm tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) 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 X2) _let_1)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_complex X2) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X2))) (=> (not (= (@ tptp.cos_real X2) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X2))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X2) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.31/6.63 (assert (= (@ tptp.tan_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.63 (assert (= (@ tptp.tan_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (= R5 I3)) (@ F R5)) tptp.zero_zero_complex)))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I3)) (@ F R5)) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (F (-> tptp.nat tptp.nat))) (@ tptp.summable_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I3)) (@ F R5)) tptp.zero_zero_nat)))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I3)) (@ F R5)) tptp.zero_zero_int)))))
% 6.31/6.63 (assert (@ tptp.summable_complex (lambda ((N3 tptp.nat)) tptp.zero_zero_complex)))
% 6.31/6.63 (assert (@ tptp.summable_real (lambda ((N3 tptp.nat)) tptp.zero_zero_real)))
% 6.31/6.63 (assert (@ tptp.summable_nat (lambda ((N3 tptp.nat)) tptp.zero_zero_nat)))
% 6.31/6.63 (assert (@ tptp.summable_int (lambda ((N3 tptp.nat)) tptp.zero_zero_int)))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))) (@ tptp.summable_real F))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) tptp.pi)) (@ tptp.tan_real X2))))
% 6.31/6.63 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.31/6.63 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N3)))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.31/6.63 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) tptp.zero_zero_real)))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N2)) tptp.pi))) (@ tptp.tan_real X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi))) (@ tptp.tan_real X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (I3 tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) tptp.pi))) (@ tptp.tan_real X2))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X2) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X2))))
% 6.31/6.63 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (lambda ((Uu3 tptp.nat)) C)) (= C tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N))) (@ G N)))) (@ tptp.summable_real F)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N))) (@ G N)))) (@ tptp.summable_complex F)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N))) (@ G N))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N))) (@ G N))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) C))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N3)) (@ G N3))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N3)) (@ G N3))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N3)) (@ G N3))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) C))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) C))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) (@ tptp.summable_real F))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X2) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex X2) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N)) (@ G N))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ G N))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ G N))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))))
% 6.31/6.63 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N3)))) (=> (not (= C tptp.zero_zero_complex)) (@ tptp.summable_complex F)))))
% 6.31/6.63 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (=> (not (= C tptp.zero_zero_real)) (@ tptp.summable_real F)))))
% 6.31/6.63 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.31/6.63 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.31/6.63 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real F)) C) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) C)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (@ (@ tptp.times_times_real C) (@ tptp.suminf_real F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N3)) (@ G N3)))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N3)) (@ G N3)))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N3)) (@ G N3)))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_nat)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N3 tptp.nat)) (= (@ F N3) tptp.zero_zero_int)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_int (@ F N3)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N3))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N3) M))) (@ (@ tptp.power_power_complex Z) N3)))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N3) M))) (@ (@ tptp.power_power_real Z) N3)))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N))) (@ G N))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N3))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N))) (@ G N))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ tptp.abs_abs_real (@ F N3))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (I3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N))) (=> (@ _let_1 (@ F I3)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (I3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N))) (=> (@ _let_1 (@ F I3)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (I3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N))) (=> (@ _let_1 (@ F I3)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I5))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I5))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I5 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I5))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (@ tptp.summable_int F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) X2)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X2)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) X2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X2)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real F) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X2)))))
% 6.31/6.63 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex X)))))
% 6.31/6.63 (assert (= tptp.tan_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X)) (@ tptp.cos_real X)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X2) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X2)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (X2 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex X2) N3)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X2)) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N))) X2)) (@ tptp.summable_int F)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N))) X2)) (@ tptp.summable_nat F)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N))) X2)) (@ tptp.summable_real F)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X2)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real F) (@ (@ tptp.plus_plus_real (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N3) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M3)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))) (= (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3))))) Z))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))) (= (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3))))) Z))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) (@ (@ tptp.power_power_complex Z) N3))))) (@ F tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real Z) N3))))) (@ F tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N7 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) M2) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N8)))) E2)))))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N7 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) M2) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N8)))) E2)))))))))))
% 6.31/6.63 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_real F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N8) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N8)))))) R2))))))))
% 6.31/6.63 (assert (forall ((R2 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (=> (@ tptp.summable_complex F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N8) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N8)))))) R2))))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I2)) tptp.one_one_real)) (=> (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ (@ tptp.power_power_real Z) I5))))))))))
% 6.31/6.63 (assert (forall ((R2 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R2) (=> (@ (@ tptp.ord_less_real R2) R0) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N))) (@ (@ tptp.power_power_real R0) N))) M7)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N3))) (@ (@ tptp.power_power_real R2) N3)))))))))
% 6.31/6.63 (assert (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N)))))) (@ tptp.summable_real F)))))
% 6.31/6.63 (assert (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N)))))) (@ tptp.summable_complex F)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I3 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (I3 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (I3 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I3) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))))
% 6.31/6.63 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y) (@ tptp.tan_real X5)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 6.31/6.63 (assert (forall ((Y tptp.real)) (exists ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) Y))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X2) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 6.31/6.63 (assert (forall ((Y tptp.real) (X2 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 X2) (=> (@ (@ tptp.ord_less_real X2) _let_2) (= (@ _let_1 X2) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X2))))))))))))
% 6.31/6.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X2))))))))
% 6.31/6.63 (assert (forall ((Y tptp.real)) (exists ((X5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X5) (@ (@ tptp.ord_less_real X5) _let_1) (= (@ tptp.tan_real X5) 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 X5)))))))))
% 6.31/6.63 (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)))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X2) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.cot_real X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X2)))))))
% 6.31/6.63 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X5) Y))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X2)) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((X2 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 X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))))))))
% 6.31/6.63 (assert (forall ((X2 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)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X2))) tptp.one_one_real))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X2)) X2))))))
% 6.31/6.63 (assert (forall ((X2 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)) X2) (=> (@ (@ tptp.ord_less_real X2) _let_1) (=> (= (@ tptp.tan_real X2) Y) (= (@ tptp.arctan Y) X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X2) Y))) (=> (not (= (@ tptp.cos_complex X2) 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))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.plus_plus_real X2) Y))) (=> (not (= (@ tptp.cos_real X2) 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))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X2))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X2) Y))) (=> (not (= (@ tptp.cos_complex X2) 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))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X2))) (let ((_let_3 (@ (@ tptp.minus_minus_real X2) Y))) (=> (not (= (@ tptp.cos_real X2) 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))))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X2))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X2)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X2) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X2))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X2)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X2) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (exists ((Z3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z3) (@ (@ tptp.ord_less_real Z3) _let_1) (= (@ tptp.tan_real Z3) X2)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D3))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F (@ _let_2 _let_1))) (@ F (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real F))))))
% 6.31/6.63 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.31/6.63 (assert (= tptp.tan_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X2)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X2) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X2) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ tptp.cos_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2))))))))
% 6.31/6.63 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (=> (@ (@ tptp.ord_less_real T3) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T3)) (@ tptp.sin_real T3)))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (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 X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))))))))))
% 6.31/6.63 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.31/6.63 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.31/6.63 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.31/6.63 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.31/6.63 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.31/6.63 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.31/6.63 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.31/6.63 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.31/6.63 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.31/6.63 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.31/6.63 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.31/6.63 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.31/6.63 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.31/6.63 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.31/6.63 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_rat _let_1))))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.31/6.63 (assert (forall ((T2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T2)) (@ tptp.sin_real T2))) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5044797733671781792omplex N2) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri773545260158071498ct_rat N2) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1406184849735516958ct_int N2) tptp.zero_zero_int))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri2265585572941072030t_real N2) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1408675320244567234ct_nat N2) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N2)) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real M)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N2))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N2))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N2))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N2))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N2))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N2) N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.31/6.63 (assert (forall ((K tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K))))))
% 6.31/6.63 (assert (forall ((K tptp.num)) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ tptp.pred_numeral K))))))
% 6.31/6.63 (assert (forall ((K tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K))))))
% 6.31/6.63 (assert (forall ((K tptp.num)) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real K)) (@ tptp.semiri2265585572941072030t_real (@ tptp.pred_numeral K))))))
% 6.31/6.63 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.semiri1408675320244567234ct_nat (@ tptp.pred_numeral K)))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.31/6.63 (assert (= tptp.semiri5044797733671781792omplex (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M6)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M6)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (= tptp.semiri2265585572941072030t_real (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M6)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M6)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1406184849735516958ct_int N2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri773545260158071498ct_rat N2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri2265585572941072030t_real N2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1408675320244567234ct_nat N2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X2) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X2 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.31/6.63 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ tptp.exp_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X2) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2))))))))
% 6.31/6.63 (assert (= tptp.cos_coeff (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N3)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N3) _let_1))) (@ tptp.semiri2265585572941072030t_real N3))) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X2) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))))))
% 6.31/6.63 (assert (= tptp.sin_coeff (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N3)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N3) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N3)))))))
% 6.31/6.63 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N2))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N2)))))))))
% 6.31/6.63 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R2)))) (@ (@ tptp.power_power_nat N2) R2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N2)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N2))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.sin_real X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X2)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.31/6.63 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))) (@ (@ tptp.power_power_real Z) N3)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N3))) (@ (@ tptp.power_power_complex Z) N3)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) tptp.zero_zero_complex)) tptp.zero_zero_complex))
% 6.31/6.63 (assert (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) tptp.zero_zero_real)) tptp.zero_zero_real))
% 6.31/6.63 (assert (@ (@ tptp.sums_nat (lambda ((N3 tptp.nat)) tptp.zero_zero_nat)) tptp.zero_zero_nat))
% 6.31/6.63 (assert (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) tptp.zero_zero_int)) tptp.zero_zero_int))
% 6.31/6.63 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.31/6.63 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3)))) X2) (= (@ A tptp.zero_zero_nat) X2))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.real)) (X2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ A N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3)))) X2) (= (@ A tptp.zero_zero_nat) X2))))
% 6.31/6.63 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.31/6.63 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S2 tptp.real) (T2 tptp.real)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N)) (@ G N))) (=> (@ (@ tptp.sums_real F) S2) (=> (@ (@ tptp.sums_real G) T2) (@ (@ tptp.ord_less_eq_real S2) T2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S2 tptp.nat) (T2 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ G N))) (=> (@ (@ tptp.sums_nat F) S2) (=> (@ (@ tptp.sums_nat G) T2) (@ (@ tptp.ord_less_eq_nat S2) T2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S2 tptp.int) (T2 tptp.int)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ G N))) (=> (@ (@ tptp.sums_int F) S2) (=> (@ (@ tptp.sums_int G) T2) (@ (@ tptp.ord_less_eq_int S2) T2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_real)) (@ (@ tptp.sums_real F) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_nat)) (@ (@ tptp.sums_nat F) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_int)) (@ (@ tptp.sums_int F) tptp.zero_zero_int))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (F (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_complex (= R5 I3)) (@ F R5)) tptp.zero_zero_complex))) (@ F I3))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (F (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_real (= R5 I3)) (@ F R5)) tptp.zero_zero_real))) (@ F I3))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (F (-> tptp.nat tptp.nat))) (@ (@ tptp.sums_nat (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_nat (= R5 I3)) (@ F R5)) tptp.zero_zero_nat))) (@ F I3))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (F (-> tptp.nat tptp.int))) (@ (@ tptp.sums_int (lambda ((R5 tptp.nat)) (@ (@ (@ tptp.if_int (= R5 I3)) (@ F R5)) tptp.zero_zero_int))) (@ F I3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (@ (@ tptp.times_times_real C) A)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) C))) (@ (@ tptp.times_times_real A) C)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N3)) (@ G N3)))) (@ (@ tptp.plus_plus_real A) B))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N3)) (@ G N3)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N3)) (@ G N3)))) (@ (@ tptp.plus_plus_int A) B))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N3)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N3)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.31/6.63 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N3)))) (@ (@ tptp.times_times_complex C) D)) (@ (@ tptp.sums_complex F) D)))))
% 6.31/6.63 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) (@ (@ tptp.times_times_real C) D)) (@ (@ tptp.sums_real F) D)))))
% 6.31/6.63 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N3)) C))) (@ (@ tptp.times_times_complex D) C)) (@ (@ tptp.sums_complex F) D)))))
% 6.31/6.63 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) C))) (@ (@ tptp.times_times_real D) C)) (@ (@ tptp.sums_real F) D)))))
% 6.31/6.63 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N3)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.31/6.63 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N3)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ F tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) L) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L) (@ F tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) L) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L) (@ F tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) (@ F (@ tptp.suc N3)))) L) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L) (@ F tptp.zero_zero_nat))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.complex)) (S2 tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ F I2) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S2) (@ (@ tptp.sums_complex F) S2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (S2 tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ F I2) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S2) (@ (@ tptp.sums_real F) S2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X2) (@ tptp.arccos Y)) (= X2 Y)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X2)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X2)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X2) (@ tptp.arcsin Y)) (= X2 Y))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N3 M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N3)))) (@ (@ tptp.power_power_complex Z) M))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N3 M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N3)))) (@ (@ tptp.power_power_real Z) M))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N3 M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N3)))) (@ (@ tptp.power_power_int Z) M))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A N3)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N3)))) (@ A tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ A N3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N3)))) (@ A tptp.zero_zero_nat))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) S2) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (S2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.sums_real F) S2) (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S2 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I5) N2)))) (@ (@ tptp.minus_minus_real S2) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_real F) S2))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X2)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X2))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X2)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X2) Y))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X2)) tptp.zero_zero_real))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X2)) tptp.zero_zero_real))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N3)))) tptp.one_one_real))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X2)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N3)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) _let_1)))))) X2))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (X2 tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X2) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N3)) (@ F (@ (@ tptp.divide_divide_nat N3) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X2) Y))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X2)) X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.cos_real X2))))
% 6.31/6.63 (assert (forall ((X2 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)) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X2)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X2))))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X2))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X2)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X2) N3)))) (@ (@ tptp.sums_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N3)) (@ C N3))) (@ (@ tptp.power_power_complex X2) (@ (@ tptp.minus_minus_nat N3) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X2) N3))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X2) N3)))) (@ (@ tptp.sums_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ C N3))) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N3) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X2) N3))))))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_real (@ X8 M3)) (@ X8 N)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_set_nat (@ X8 M3)) (@ X8 N)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_rat (@ X8 M3)) (@ X8 N)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_num (@ X8 M3)) (@ X8 N)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_nat (@ X8 M3)) (@ X8 N)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_int (@ X8 M3)) (@ X8 N)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_real (@ X8 N)) (@ X8 M3)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N)) (@ X8 M3)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_rat (@ X8 N)) (@ X8 M3)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_num (@ X8 N)) (@ X8 M3)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_nat (@ X8 N)) (@ X8 M3)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((M3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.ord_less_eq_int (@ X8 N)) (@ X8 M3)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.31/6.63 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_real (@ X4 M6)) (@ X4 N3)))) (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_real (@ X4 N3)) (@ X4 M6))))))))
% 6.31/6.63 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X4 (-> tptp.nat tptp.set_nat))) (or (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X4 M6)) (@ X4 N3)))) (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_set_nat (@ X4 N3)) (@ X4 M6))))))))
% 6.31/6.63 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_rat (@ X4 M6)) (@ X4 N3)))) (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_rat (@ X4 N3)) (@ X4 M6))))))))
% 6.31/6.63 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_num (@ X4 M6)) (@ X4 N3)))) (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_num (@ X4 N3)) (@ X4 M6))))))))
% 6.31/6.63 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_nat (@ X4 M6)) (@ X4 N3)))) (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_nat (@ X4 N3)) (@ X4 M6))))))))
% 6.31/6.63 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_int (@ X4 M6)) (@ X4 N3)))) (forall ((M6 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.ord_less_eq_int (@ X4 N3)) (@ X4 M6))))))))
% 6.31/6.63 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N2))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N2))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))))
% 6.31/6.63 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N2))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N2))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N2)))))))))
% 6.31/6.63 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N2))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N2))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N2)))))))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.31/6.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X2) N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X2) N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X2) N2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X2) N2))))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_complex)))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_rat)))))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N2) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 6.31/6.63 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.31/6.63 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.31/6.63 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.31/6.63 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.31/6.63 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X2) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X2) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X2) N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X2) N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N2)))))
% 6.31/6.63 (assert (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))))
% 6.31/6.63 (assert (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))))
% 6.31/6.63 (assert (= tptp.diffs_rat (lambda ((C2 (-> tptp.nat tptp.rat)) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ C2 _let_1))))))
% 6.31/6.63 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N2)))))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2)))))))
% 6.31/6.63 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))))
% 6.31/6.63 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) (@ _let_1 N2))))))
% 6.31/6.63 (assert (forall ((Z tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))))
% 6.31/6.63 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) (@ _let_1 N2))))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N2) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N2) K))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N2) K))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N2) K))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N2) K))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat)))))
% 6.31/6.63 (assert (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) M))))))
% 6.31/6.63 (assert (forall ((Z tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) M))))))
% 6.31/6.63 (assert (forall ((Z tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) M))))))
% 6.31/6.63 (assert (forall ((Z tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) M))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (forall ((X5 tptp.complex)) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N3)) (@ (@ tptp.power_power_complex X5) N3))))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X2) N3)))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((X5 tptp.real)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ C N3)) (@ (@ tptp.power_power_real X5) N3))))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X2) N3)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.31/6.63 (assert (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R2) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R2) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.31/6.63 (assert (forall ((R2 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R2) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R2) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.31/6.63 (assert (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R2))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R2) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R2) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.31/6.63 (assert (forall ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.31/6.63 (assert (forall ((R2 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R2) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R2) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ tptp.semiri5044797733671781792omplex N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X2)) K5) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X5)) K5) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ C N3)) (@ (@ tptp.power_power_real X5) N3)))))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N3)) (@ (@ tptp.power_power_real X2) N3))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X2)) K5) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X5)) K5) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C N3)) (@ (@ tptp.power_power_complex X5) N3)))))) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N3)) (@ (@ tptp.power_power_complex X2) N3))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N2))) (@ tptp.semiri5044797733671781792omplex N2))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N2))) (@ tptp.semiri773545260158071498ct_rat N2))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N2))) (@ tptp.semiri2265585572941072030t_real N2))))))))
% 6.31/6.63 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X4 (-> tptp.nat tptp.real))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 N3)) (@ X4 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X4 (@ tptp.suc N3))) (@ X4 N3)))))))
% 6.31/6.63 (assert (= tptp.topolo7278393974255667507et_nat (lambda ((X4 (-> tptp.nat tptp.set_nat))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X4 N3)) (@ X4 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X4 (@ tptp.suc N3))) (@ X4 N3)))))))
% 6.31/6.63 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X4 (-> tptp.nat tptp.rat))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X4 N3)) (@ X4 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X4 (@ tptp.suc N3))) (@ X4 N3)))))))
% 6.31/6.63 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X4 (-> tptp.nat tptp.num))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 N3)) (@ X4 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X4 (@ tptp.suc N3))) (@ X4 N3)))))))
% 6.31/6.63 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X4 (-> tptp.nat tptp.nat))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 N3)) (@ X4 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X4 (@ tptp.suc N3))) (@ X4 N3)))))))
% 6.31/6.63 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X4 (-> tptp.nat tptp.int))) (or (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 N3)) (@ X4 (@ tptp.suc N3)))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X4 (@ tptp.suc N3))) (@ X4 N3)))))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 (@ tptp.suc N))) (@ X8 N))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 (@ tptp.suc N))) (@ X8 N))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 (@ tptp.suc N))) (@ X8 N))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 (@ tptp.suc N))) (@ X8 N))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 (@ tptp.suc N))) (@ X8 N))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 (@ tptp.suc N))) (@ X8 N))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 N)) (@ X8 (@ tptp.suc N)))) (@ tptp.topolo6980174941875973593q_real X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.set_nat))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat (@ X8 N)) (@ X8 (@ tptp.suc N)))) (@ tptp.topolo7278393974255667507et_nat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.rat))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X8 N)) (@ X8 (@ tptp.suc N)))) (@ tptp.topolo4267028734544971653eq_rat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.num))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X8 N)) (@ X8 (@ tptp.suc N)))) (@ tptp.topolo1459490580787246023eq_num X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.nat))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X8 N)) (@ X8 (@ tptp.suc N)))) (@ tptp.topolo4902158794631467389eq_nat X8))))
% 6.31/6.63 (assert (forall ((X8 (-> tptp.nat tptp.int))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X8 N)) (@ X8 (@ tptp.suc N)))) (@ tptp.topolo4899668324122417113eq_int X8))))
% 6.31/6.63 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.31/6.63 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.31/6.63 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.31/6.63 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A5 tptp.complex) (N3 tptp.nat)) (@ (@ (@ tptp.if_complex (= N3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A5) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.31/6.63 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N3 tptp.nat)) (@ (@ (@ tptp.if_int (= N3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.31/6.63 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A5 tptp.real) (N3 tptp.nat)) (@ (@ (@ tptp.if_real (= N3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A5) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.31/6.63 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N3 tptp.nat)) (@ (@ (@ tptp.if_rat (= N3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.31/6.63 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N3 tptp.nat)) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.31/6.63 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.plus_plus_complex I5) tptp.one_one_complex))) N3) tptp.zero_zero_complex))))
% 6.31/6.63 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I5 tptp.int)) (@ (@ tptp.plus_plus_int I5) tptp.one_one_int))) N3) tptp.zero_zero_int))))
% 6.31/6.63 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I5 tptp.real)) (@ (@ tptp.plus_plus_real I5) tptp.one_one_real))) N3) tptp.zero_zero_real))))
% 6.31/6.63 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat I5) tptp.one_one_nat))) N3) tptp.zero_zero_nat))))
% 6.31/6.63 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I5 tptp.rat)) (@ (@ tptp.plus_plus_rat I5) tptp.one_one_rat))) N3) tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((R2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R2) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R2) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex R2) _let_1))))))
% 6.31/6.63 (assert (forall ((R2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R2) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R2) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R2) _let_1))))))
% 6.31/6.63 (assert (forall ((R2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real R2) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real R2) _let_1))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) N2)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_1) N2) _let_1))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) N2) tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A3) tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A3) tptp.one_one_int)))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A3) tptp.one_one_int)))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A3)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups705719431365010083at_int F) A3)) (@ (@ tptp.groups129246275422532515t_real (lambda ((X tptp.nat)) (@ tptp.ring_1_of_int_real (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups705719431365010083at_int F) A3)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X tptp.nat)) (@ tptp.ring_1_of_int_rat (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups705719431365010083at_int F) A3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ tptp.ring_1_of_int_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.groups1705073143266064639nt_int F) A3)) (@ (@ tptp.groups2316167850115554303t_real (lambda ((X tptp.int)) (@ tptp.ring_1_of_int_real (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups1705073143266064639nt_int F) A3)) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups1705073143266064639nt_int F) A3)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ tptp.ring_1_of_int_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups6464643781859351333omplex G) tptp.bot_bot_set_nat) tptp.one_one_complex)))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real))) (= (@ (@ tptp.groups129246275422532515t_real G) tptp.bot_bot_set_nat) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups7440179247065528705omplex G) tptp.bot_bot_set_int) tptp.one_one_complex)))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups2316167850115554303t_real G) tptp.bot_bot_set_int) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) tptp.bot_bot_set_int) tptp.one_one_rat)))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups1707563613775114915nt_nat G) tptp.bot_bot_set_int) tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups713298508707869441omplex G) tptp.bot_bot_set_real) tptp.one_one_complex)))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups1681761925125756287l_real G) tptp.bot_bot_set_real) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups4061424788464935467al_rat G) tptp.bot_bot_set_real) tptp.one_one_rat)))
% 6.31/6.63 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.31/6.63 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.31/6.63 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.31/6.63 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.31/6.63 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) (@ tptp.suc tptp.zero_zero_nat)) N2)))
% 6.31/6.63 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.31/6.63 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N2))) (= (@ (@ tptp.binomial (@ tptp.suc N2)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.one_one_nat) N2)))
% 6.31/6.63 (assert (forall ((G (-> tptp.complex tptp.complex)) (A3 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups3708469109370488835omplex G) A3) tptp.one_one_complex)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A3) (= (@ G A4) tptp.one_one_complex)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.complex)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups713298508707869441omplex G) A3) tptp.one_one_complex)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A3) (= (@ G A4) tptp.one_one_complex)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.complex)) (A3 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups6464643781859351333omplex G) A3) tptp.one_one_complex)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (= (@ G A4) tptp.one_one_complex)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.complex)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups7440179247065528705omplex G) A3) tptp.one_one_complex)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (= (@ G A4) tptp.one_one_complex)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.complex tptp.real)) (A3 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A3) tptp.one_one_real)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A3) (= (@ G A4) tptp.one_one_real)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.real)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A3) tptp.one_one_real)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A3) (= (@ G A4) tptp.one_one_real)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (A3 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A3) tptp.one_one_real)) (not (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (= (@ G A4) tptp.one_one_real)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.real)) (A3 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A3) tptp.one_one_real)) (not (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (= (@ G A4) tptp.one_one_real)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.complex tptp.rat)) (A3 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups225925009352817453ex_rat G) A3) tptp.one_one_rat)) (not (forall ((A4 tptp.complex)) (=> (@ (@ tptp.member_complex A4) A3) (= (@ G A4) tptp.one_one_rat)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.real tptp.rat)) (A3 tptp.set_real)) (=> (not (= (@ (@ tptp.groups4061424788464935467al_rat G) A3) tptp.one_one_rat)) (not (forall ((A4 tptp.real)) (=> (@ (@ tptp.member_real A4) A3) (= (@ G A4) tptp.one_one_rat)))))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (= (@ G X5) tptp.one_one_nat))) (= (@ (@ tptp.groups708209901874060359at_nat G) A3) tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (= (@ G X5) tptp.one_one_int))) (= (@ (@ tptp.groups705719431365010083at_int G) A3) tptp.one_one_int))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (= (@ G X5) tptp.one_one_int))) (= (@ (@ tptp.groups1705073143266064639nt_int G) A3) tptp.one_one_int))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A3)) (@ (@ tptp.groups708209901874060359at_nat H2) A3)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (H2 (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A3)) (@ (@ tptp.groups705719431365010083at_int H2) A3)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.times_times_int (@ G X)) (@ H2 X)))) A3) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A3)) (@ (@ tptp.groups1705073143266064639nt_int H2) A3)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) N2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.power_power_nat (@ F X)) N2))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A3)) N2) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.power_power_int (@ F X)) N2))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A3)) N2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.power_power_int (@ F X)) N2))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A3 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I5)) A))) A3)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) A))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A3 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A3)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A3)) A))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A3 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A3)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A3)) A))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A3) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups766887009212190081x_real F) A3)) (@ (@ tptp.groups766887009212190081x_real G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A3) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups1681761925125756287l_real F) A3)) (@ (@ tptp.groups1681761925125756287l_real G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A3) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups129246275422532515t_real F) A3)) (@ (@ tptp.groups129246275422532515t_real G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A3) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups2316167850115554303t_real F) A3)) (@ (@ tptp.groups2316167850115554303t_real G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups225925009352817453ex_rat F) A3)) (@ (@ tptp.groups225925009352817453ex_rat G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups4061424788464935467al_rat F) A3)) (@ (@ tptp.groups4061424788464935467al_rat G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I2 tptp.nat)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_nat I2) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A3)) (@ (@ tptp.groups73079841787564623at_rat G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I2 tptp.int)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_int I2) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A3)) (@ (@ tptp.groups1072433553688619179nt_rat G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I2 tptp.complex)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_complex I2) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups861055069439313189ex_nat F) A3)) (@ (@ tptp.groups861055069439313189ex_nat G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I2 tptp.real)) (let ((_let_1 (@ F I2))) (=> (@ (@ tptp.member_real I2) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I2)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4696554848551431203al_nat F) A3)) (@ (@ tptp.groups4696554848551431203al_nat G) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X5)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups766887009212190081x_real F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups1681761925125756287l_real F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups129246275422532515t_real F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.groups2316167850115554303t_real F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups225925009352817453ex_rat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups4061424788464935467al_rat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X5)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups861055069439313189ex_nat F) A3)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X5)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups4696554848551431203al_nat F) A3)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_complex))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_real))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) K)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R2))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))))
% 6.31/6.63 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R2) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R2)) (@ (@ tptp.power_power_nat N2) R2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.power_power_real C) (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups129246275422532515t_real (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_real C) (@ F A5)))) A3))))
% 6.31/6.63 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.power_power_complex C) (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_complex C) (@ F A5)))) A3))))
% 6.31/6.63 (assert (forall ((C tptp.nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.power_power_nat C) (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A5)))) A3))))
% 6.31/6.63 (assert (forall ((C tptp.int) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A5)))) A3))))
% 6.31/6.63 (assert (forall ((C tptp.int) (F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A5 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A5)))) A3))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_complex X5) A3) (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) A3)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A3) (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) A3)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A3) (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) A3)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A3) (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) A3)) tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_complex X5) A3) (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) A3)) tptp.one_one_rat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A3) (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) A3)) tptp.one_one_rat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X5 tptp.nat)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_nat X5) A3) (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) A3)) tptp.one_one_rat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X5 tptp.int)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_int X5) A3) (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) A3)) tptp.one_one_rat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X5 tptp.complex)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_complex X5) A3) (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) A3)) tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X5 tptp.real)) (let ((_let_1 (@ F X5))) (=> (@ (@ tptp.member_real X5) A3) (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) A3)) tptp.one_one_nat))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K))) _let_1))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I5)))) _let_1)))))
% 6.31/6.63 (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 ((I5 tptp.nat)) (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri5044797733671781792omplex _let_1))))))
% 6.31/6.63 (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 ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.31/6.63 (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 ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2265585572941072030t_real _let_1))))))
% 6.31/6.63 (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 ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.31/6.63 (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 ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) K))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.binomial N2) K)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups129246275422532515t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G M)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ G M)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.31/6.63 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N3 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.31/6.63 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.31/6.63 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N3 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N2)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N2) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups129246275422532515t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_real (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P2))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.nat) (Xb3 tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X2))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb3) Xa2))) (=> (= (@ (@ (@ _let_1 Xa2) Xb3) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb3) (@ (@ X2 Xa2) Xc))))))))))
% 6.31/6.63 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B5) A5)) Acc2) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) B5) (@ (@ F3 A5) Acc2))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.gbinomial_real A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real M)) K)) (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_complex) (Z (-> tptp.complex tptp.real)) (W (-> tptp.complex tptp.real))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups766887009212190081x_real Z) I6)) (@ (@ tptp.groups766887009212190081x_real W) I6)))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_real) (Z (-> tptp.real tptp.real)) (W (-> tptp.real tptp.real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups1681761925125756287l_real Z) I6)) (@ (@ tptp.groups1681761925125756287l_real W) I6)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_set_nat) (Z (-> tptp.set_nat tptp.real)) (W (-> tptp.set_nat tptp.real))) (=> (forall ((I2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups3619160379726066777t_real Z) I6)) (@ (@ tptp.groups3619160379726066777t_real W) I6)))) (@ (@ tptp.groups5107569545109728110t_real (lambda ((I5 tptp.set_nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_int) (Z (-> tptp.int tptp.real)) (W (-> tptp.int tptp.real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups2316167850115554303t_real Z) I6)) (@ (@ tptp.groups2316167850115554303t_real W) I6)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_complex) (Z (-> tptp.complex tptp.complex)) (W (-> tptp.complex tptp.complex))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.complex)) (=> (@ (@ tptp.member_complex I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups3708469109370488835omplex Z) I6)) (@ (@ tptp.groups3708469109370488835omplex W) I6)))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_real) (Z (-> tptp.real tptp.complex)) (W (-> tptp.real tptp.complex))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.real)) (=> (@ (@ tptp.member_real I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups713298508707869441omplex Z) I6)) (@ (@ tptp.groups713298508707869441omplex W) I6)))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_set_nat) (Z (-> tptp.set_nat tptp.complex)) (W (-> tptp.set_nat tptp.complex))) (=> (forall ((I2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups1092910753850256091omplex Z) I6)) (@ (@ tptp.groups1092910753850256091omplex W) I6)))) (@ (@ tptp.groups5107569545109728110t_real (lambda ((I5 tptp.set_nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_int) (Z (-> tptp.int tptp.complex)) (W (-> tptp.int tptp.complex))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.int)) (=> (@ (@ tptp.member_int I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7440179247065528705omplex Z) I6)) (@ (@ tptp.groups7440179247065528705omplex W) I6)))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_nat) (Z (-> tptp.nat tptp.real)) (W (-> tptp.nat tptp.real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups129246275422532515t_real Z) I6)) (@ (@ tptp.groups129246275422532515t_real W) I6)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((I6 tptp.set_nat) (Z (-> tptp.nat tptp.complex)) (W (-> tptp.nat tptp.complex))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ Z I2))) tptp.one_one_real))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.member_nat I2) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ W I2))) tptp.one_one_real))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups6464643781859351333omplex Z) I6)) (@ (@ tptp.groups6464643781859351333omplex W) I6)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ Z I5)) (@ W I5))))) I6))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.31/6.63 (assert (= tptp.gbinomial_complex (lambda ((A5 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 A5) (@ 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))))))
% 6.31/6.63 (assert (= tptp.gbinomial_rat (lambda ((A5 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 A5) (@ 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))))))
% 6.31/6.63 (assert (= tptp.gbinomial_real (lambda ((A5 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 A5) (@ 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))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N2) _let_1))) (let ((_let_3 (@ tptp.binomial N2))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.binomial N2) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N2))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N2))))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N2))))))
% 6.31/6.63 (assert (= tptp.gbinomial_complex (lambda ((A5 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)) A5)) tptp.one_one_complex)) K3)))))
% 6.31/6.63 (assert (= tptp.gbinomial_real (lambda ((A5 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)) A5)) tptp.one_one_real)) K3)))))
% 6.31/6.63 (assert (= tptp.gbinomial_rat (lambda ((A5 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)) A5)) tptp.one_one_rat)) K3)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I5)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.63 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A5 tptp.real) (N3 tptp.nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A5) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N3) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.31/6.63 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N3 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N3) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.31/6.63 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N3) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.31/6.63 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N3) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N3)))))
% 6.31/6.63 (assert (= tptp.binomial (lambda ((N3 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N3) K3))) (let ((_let_2 (@ tptp.ord_less_nat N3))) (@ (@ (@ 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 N3) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N3) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) _let_1)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups129246275422532515t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A5)) __flatten_var_0))) A) B) tptp.zero_zero_complex))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A5)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A5)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A5)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.31/6.63 (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 ((A5 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A5)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I5))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.63 (assert (= tptp.gbinomial_complex (lambda ((A5 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 A5)) K3))) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.31/6.63 (assert (= tptp.gbinomial_rat (lambda ((A5 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 A5)) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.31/6.63 (assert (= tptp.gbinomial_real (lambda ((A5 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 A5)) K3))) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.31/6.63 (assert (= tptp.gbinomial_complex (lambda ((A5 tptp.complex) (K3 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex A5) (@ tptp.semiri8010041392384452111omplex K3))) tptp.one_one_complex)) K3)) (@ tptp.semiri5044797733671781792omplex K3)))))
% 6.31/6.63 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat K3))) tptp.one_one_rat)) K3)) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.31/6.63 (assert (= tptp.gbinomial_real (lambda ((A5 tptp.real) (K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A5) (@ tptp.semiri5074537144036343181t_real K3))) tptp.one_one_real)) K3)) (@ tptp.semiri2265585572941072030t_real K3)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.31/6.63 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N3 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.31/6.63 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((N3 tptp.nat)) (@ tptp.semiri681578069525770553at_rat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.31/6.63 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N3 tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.31/6.63 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N3 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3) tptp.one_one_nat)))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ tptp.semiri8010041392384452111omplex K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_complex A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.semiri5074537144036343181t_real K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_real A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I5))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (= (@ (@ tptp.groups2073611262835488442omplex (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) (@ tptp.semiri8010041392384452111omplex M))) tptp.one_one_complex))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_complex _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ (@ tptp.groups6591440286371151544t_real (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) (@ tptp.semiri5074537144036343181t_real M))) tptp.one_one_real))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_real _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X2)) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A)))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A)))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A)))
% 6.31/6.63 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.63 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.63 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex B)))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.inverse_inverse_real X2) tptp.one_one_real) (= X2 tptp.one_one_real))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X2) tptp.one_one_complex) (= X2 tptp.one_one_complex))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X2) tptp.one_one_rat) (= X2 tptp.one_one_rat))))
% 6.31/6.63 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.31/6.63 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.31/6.63 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.31/6.63 (assert (forall ((I3 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I3) (@ tptp.set_ord_atMost_real K)) (@ (@ tptp.ord_less_eq_real I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I3) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I3) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I3) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I3) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I3) K))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I3) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I3) K))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat B) A))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A)))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A)))))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A)))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A)))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.abs_abs_complex A)))))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_or4236626031148496127et_nat X2)) (@ tptp.set_or4236626031148496127et_nat Y)) (@ (@ tptp.ord_less_eq_set_nat X2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X2)) (@ tptp.set_ord_atMost_rat Y)) (@ (@ tptp.ord_less_eq_rat X2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X2)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X2)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X2) Y))))
% 6.31/6.63 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X2)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X2) Y))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((L tptp.set_nat) (H2 tptp.set_nat) (H3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.set_or4548717258645045905et_nat L) H2)) (@ tptp.set_or4236626031148496127et_nat H3)) (or (not (@ (@ tptp.ord_less_eq_set_nat L) H2)) (@ (@ tptp.ord_less_eq_set_nat H2) H3)))))
% 6.31/6.63 (assert (forall ((L tptp.rat) (H2 tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H2)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L) H2)) (@ (@ tptp.ord_less_eq_rat H2) H3)))))
% 6.31/6.63 (assert (forall ((L tptp.num) (H2 tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H2)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L) H2)) (@ (@ tptp.ord_less_eq_num H2) H3)))))
% 6.31/6.63 (assert (forall ((L tptp.nat) (H2 tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H2)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H2)) (@ (@ tptp.ord_less_eq_nat H2) H3)))))
% 6.31/6.63 (assert (forall ((L tptp.int) (H2 tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H2)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H2)) (@ (@ tptp.ord_less_eq_int H2) H3)))))
% 6.31/6.63 (assert (forall ((L tptp.real) (H2 tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H2)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H2)) (@ (@ tptp.ord_less_eq_real H2) H3)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.31/6.63 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A3)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X)))) A3))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) (@ tptp.inverse_inverse_rat B)) (= A B))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A))))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.31/6.63 (assert (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.31/6.63 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.31/6.63 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.31/6.63 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.31/6.63 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real A)) N2) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real A) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N2) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N2)))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat A)) N2) (@ tptp.inverse_inverse_rat (@ (@ tptp.power_power_rat A) N2)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((Y tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y))) (let ((_let_2 (@ tptp.times_times_real X2))) (=> (= (@ (@ tptp.times_times_real Y) X2) (@ _let_2 Y)) (= (@ (@ tptp.times_times_real _let_1) X2) (@ _let_2 _let_1)))))))
% 6.31/6.63 (assert (forall ((Y tptp.complex) (X2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y))) (let ((_let_2 (@ tptp.times_times_complex X2))) (=> (= (@ (@ tptp.times_times_complex Y) X2) (@ _let_2 Y)) (= (@ (@ tptp.times_times_complex _let_1) X2) (@ _let_2 _let_1)))))))
% 6.31/6.63 (assert (forall ((Y tptp.rat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat Y))) (let ((_let_2 (@ tptp.times_times_rat X2))) (=> (= (@ (@ tptp.times_times_rat Y) X2) (@ _let_2 Y)) (= (@ (@ tptp.times_times_rat _let_1) X2) (@ _let_2 _let_1)))))))
% 6.31/6.63 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) U2))))))
% 6.31/6.63 (assert (= tptp.set_or4236626031148496127et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) U2))))))
% 6.31/6.63 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) U2))))))
% 6.31/6.63 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) U2))))))
% 6.31/6.63 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) U2))))))
% 6.31/6.63 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) U2))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 6.31/6.63 (assert (let ((_let_1 (@ tptp.numeral_numeral_rat tptp.one))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1)))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))))
% 6.31/6.63 (assert (= tptp.divide_divide_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.times_times_real A5) (@ tptp.inverse_inverse_real B5)))))
% 6.31/6.63 (assert (= tptp.divide1717551699836669952omplex (lambda ((A5 tptp.complex) (B5 tptp.complex)) (@ (@ tptp.times_times_complex A5) (@ tptp.invers8013647133539491842omplex B5)))))
% 6.31/6.63 (assert (= tptp.divide_divide_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.times_times_rat A5) (@ tptp.inverse_inverse_rat B5)))))
% 6.31/6.63 (assert (= tptp.divide_divide_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.times_times_real A5) (@ tptp.inverse_inverse_real B5)))))
% 6.31/6.63 (assert (= tptp.divide1717551699836669952omplex (lambda ((A5 tptp.complex) (B5 tptp.complex)) (@ (@ tptp.times_times_complex A5) (@ tptp.invers8013647133539491842omplex B5)))))
% 6.31/6.63 (assert (= tptp.divide_divide_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.times_times_rat A5) (@ tptp.inverse_inverse_rat B5)))))
% 6.31/6.63 (assert (= tptp.divide_divide_real (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B5)) A5))))
% 6.31/6.63 (assert (= tptp.divide1717551699836669952omplex (lambda ((A5 tptp.complex) (B5 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B5)) A5))))
% 6.31/6.63 (assert (= tptp.divide_divide_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.times_times_rat (@ tptp.inverse_inverse_rat B5)) A5))))
% 6.31/6.63 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 6.31/6.63 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 6.31/6.63 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X2))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X2))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) M))) (let ((_let_2 (@ tptp.inverse_inverse_rat X2))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X2) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X2)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X2) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X2)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X2) M))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X2)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_2) (@ (@ tptp.times_times_rat _let_2) _let_1))))))
% 6.31/6.63 (assert (forall ((Xa2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X2) (@ (@ tptp.times_times_real X2) _let_1)))))
% 6.31/6.63 (assert (forall ((Xa2 tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X2) (@ (@ tptp.times_times_complex X2) _let_1)))))
% 6.31/6.63 (assert (forall ((Xa2 tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat Xa2)))) (= (@ (@ tptp.times_times_rat _let_1) X2) (@ (@ tptp.times_times_rat X2) _let_1)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((Xa2 tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.ring_1_of_int_real Xa2)))) (= (@ (@ tptp.times_times_real _let_1) X2) (@ (@ tptp.times_times_real X2) _let_1)))))
% 6.31/6.63 (assert (forall ((Xa2 tptp.int) (X2 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.ring_17405671764205052669omplex Xa2)))) (= (@ (@ tptp.times_times_complex _let_1) X2) (@ (@ tptp.times_times_complex X2) _let_1)))))
% 6.31/6.63 (assert (forall ((Xa2 tptp.int) (X2 tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat (@ tptp.ring_1_of_int_rat Xa2)))) (= (@ (@ tptp.times_times_rat _let_1) X2) (@ (@ tptp.times_times_rat X2) _let_1)))))
% 6.31/6.63 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 6.31/6.63 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.31/6.63 (assert (= tptp.divide_divide_real (lambda ((X tptp.real) (Y6 tptp.real)) (@ (@ tptp.times_times_real X) (@ tptp.inverse_inverse_real Y6)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H2)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))))
% 6.31/6.63 (assert (forall ((H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H2)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X2)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X2)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X2)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X2)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_rat X2) tptp.one_one_rat)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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))))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat A)) (@ tptp.set_ord_lessThan_rat B)) (@ (@ tptp.ord_less_rat A) B))))
% 6.31/6.63 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num A)) (@ tptp.set_ord_lessThan_num B)) (@ (@ tptp.ord_less_num A) B))))
% 6.31/6.63 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int A)) (@ tptp.set_ord_lessThan_int B)) (@ (@ tptp.ord_less_int A) B))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat A)) (@ tptp.set_ord_lessThan_nat B)) (@ (@ tptp.ord_less_nat A) B))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real A)) (@ tptp.set_or5984915006950818249n_real B)) (@ (@ tptp.ord_less_real A) B))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M)))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X2)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X2)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (@ (@ tptp.ord_less_eq_rat X2) tptp.one_one_rat)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X2)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X2)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X2) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X2)))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (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)))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) X2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)))) X2)))))
% 6.31/6.63 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E) (=> (@ P D3) (@ P E)))) (=> (forall ((N tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 6.31/6.63 (assert (forall ((E2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3)))) (and (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E2)))))))
% 6.31/6.63 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E) (=> (@ P D3) (@ P E)))) (=> (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (I3 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I3)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I3))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (I3 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I3)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I3))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (I3 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I5)) (@ F (@ tptp.suc I5))))) (@ tptp.set_ord_atMost_nat I3)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I3))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X) I5)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I5)) (@ (@ tptp.power_power_complex X) I5)))) _let_1)))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) (@ D I5)))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X) I5)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ D I5)) (@ (@ tptp.power_power_real X) I5)))) _let_1)))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) (@ D I5)))))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.int)) (B4 tptp.int)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int A) (@ tptp.set_ord_atMost_nat N))) B4)) (@ tptp.summable_int A)))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.nat)) (B4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat A) (@ tptp.set_ord_atMost_nat N))) B4)) (@ tptp.summable_nat A)))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.real)) (B4 tptp.real)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real A) (@ tptp.set_ord_atMost_nat N))) B4)) (@ tptp.summable_real A)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.63 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I3) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I3) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I3)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (@ tptp.summable_complex (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex (@ tptp.semiri5044797733671781792omplex N3))) (@ (@ tptp.power_power_complex X2) N3))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N3))) (@ (@ tptp.power_power_real X2) N3))))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I5)) (@ tptp.set_ord_lessThan_nat I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ (@ A I5) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((R2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R2) K3)) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R2) N2))) N2))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) M))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N))) X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X2) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N))) X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (=> (not (= X2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X2)) M))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (=> (not (= X2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X2)) M))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (=> (not (= X2 tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X2)) M))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex W2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_complex)))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real W2) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (forall ((X tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) tptp.zero_zero_complex))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (forall ((X tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I5) N2) (= (@ C I5) tptp.zero_zero_real))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.31/6.63 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) N2))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) N2))))
% 6.31/6.63 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) N2))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N2)) M)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R2) K3))))) (@ tptp.set_ord_atMost_nat R2)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N2)) R2))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X2)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X2)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X2)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X2)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex) (not (forall ((B3 (-> tptp.nat tptp.complex))) (not (forall ((Z4 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z4) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I5)) (@ (@ tptp.power_power_complex Z4) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat) (not (forall ((B3 (-> tptp.nat tptp.rat))) (not (forall ((Z4 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat Z4) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z4) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ B3 I5)) (@ (@ tptp.power_power_rat Z4) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int) (not (forall ((B3 (-> tptp.nat tptp.int))) (not (forall ((Z4 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int Z4) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I5)) (@ (@ tptp.power_power_int Z4) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real A) I5)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real) (not (forall ((B3 (-> tptp.nat tptp.real))) (not (forall ((Z4 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z4) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I5)) (@ (@ tptp.power_power_real Z4) I5)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (A tptp.complex)) (exists ((B3 (-> tptp.nat tptp.complex))) (forall ((Z4 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex Z4) I5)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z4) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ B3 I5)) (@ (@ tptp.power_power_complex Z4) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex A) I5)))) _let_1))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.rat)) (N2 tptp.nat) (A tptp.rat)) (exists ((B3 (-> tptp.nat tptp.rat))) (forall ((Z4 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat Z4) I5)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z4) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ B3 I5)) (@ (@ tptp.power_power_rat Z4) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat A) I5)))) _let_1))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.int)) (N2 tptp.nat) (A tptp.int)) (exists ((B3 (-> tptp.nat tptp.int))) (forall ((Z4 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int Z4) I5)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z4) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ B3 I5)) (@ (@ tptp.power_power_int Z4) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ C I5)) (@ (@ tptp.power_power_int A) I5)))) _let_1))))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (A tptp.real)) (exists ((B3 (-> tptp.nat tptp.real))) (forall ((Z4 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real Z4) I5)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z4) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ B3 I5)) (@ (@ tptp.power_power_real Z4) I5)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real A) I5)))) _let_1))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X2))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups4567486121110086003t_real (@ tptp.produc1703576794950452218t_real G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I5) J3)) N2))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ G I5) (@ (@ tptp.minus_minus_nat K3) I5)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (@ tptp.summable_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N2)) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.complex)) (B (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ B K3)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex A)) (@ tptp.suminf_complex B)) (@ tptp.suminf_complex (lambda ((K3 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.31/6.63 (assert (forall ((A (-> tptp.nat tptp.real)) (B (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ A K3)))) (=> (@ tptp.summable_real (lambda ((K3 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ B K3)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real A)) (@ tptp.suminf_real B)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ B (@ (@ tptp.minus_minus_nat K3) I5))))) (@ tptp.set_ord_atMost_nat K3)))))))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N2 tptp.nat) (B (-> tptp.nat tptp.complex)) (X2 tptp.complex)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A I2) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I5)) (@ (@ tptp.power_power_complex X2) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B J3)) (@ (@ tptp.power_power_complex X2) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_complex X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.rat)) (N2 tptp.nat) (B (-> tptp.nat tptp.rat)) (X2 tptp.rat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A I2) tptp.zero_zero_rat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_rat))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ (@ tptp.power_power_rat X2) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B J3)) (@ (@ tptp.power_power_rat X2) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_rat X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N2 tptp.nat) (B (-> tptp.nat tptp.int)) (X2 tptp.int)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A I2) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ A I5)) (@ (@ tptp.power_power_int X2) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B J3)) (@ (@ tptp.power_power_int X2) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_int X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N2 tptp.nat) (B (-> tptp.nat tptp.real)) (X2 tptp.real)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A I2) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ A I5)) (@ (@ tptp.power_power_real X2) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B J3)) (@ (@ tptp.power_power_real X2) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_real X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups129246275422532515t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups129246275422532515t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.complex)) (= (forall ((X tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex X) I5)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X) tptp.zero_zero_complex)))))))
% 6.31/6.63 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.real)) (= (forall ((X tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real X) I5)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X) tptp.zero_zero_real)))))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (M tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex A) K3)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) M)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) tptp.one_one_complex)) M)))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) M)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.gbinomial_real A) K3)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) M)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real A) tptp.one_one_real)) M)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X2)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X2)))))
% 6.31/6.63 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N2 tptp.nat) (B (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I2) (= (@ A I2) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I5)) (@ (@ tptp.power_power_nat X2) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X2) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K3)) (@ B (@ (@ tptp.minus_minus_nat R5) K3))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X2) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N2) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.exp_real X2))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat I5) (@ (@ tptp.binomial N2) I5)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.31/6.63 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N3 tptp.nat)) N3)))
% 6.31/6.63 (assert (= tptp.divide1717551699836669952omplex (lambda ((X tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.times_times_complex X) (@ tptp.invers8013647133539491842omplex Y6)))))
% 6.31/6.63 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.31/6.63 (assert (forall ((R2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.real_V2046097035970521341omplex R2) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 6.31/6.63 (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)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.log _let_1) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X2)))))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.31/6.63 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X2)) (@ tptp.uminus1482373934393186551omplex X2)))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) A) tptp.one_one_real)))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X2) Y)))))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) A))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_real A) X2)))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X2) (= (@ _let_2 (@ (@ tptp.log A) X2)) (@ _let_1 X2))))))))
% 6.31/6.63 (assert (forall ((Z tptp.complex) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ (@ tptp.divide1717551699836669952omplex Z) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))))
% 6.31/6.63 (assert (forall ((X2 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X2) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X2))))
% 6.31/6.63 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X2) Y)))))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) A))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real A) X2))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X2)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 6.31/6.63 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.31/6.63 (assert (not (= tptp.imaginary_unit tptp.one_one_complex)))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X2))))
% 6.31/6.63 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W) Z) (= W (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z)))))))
% 6.31/6.63 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.31/6.63 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X2) Y) tptp.imaginary_unit) (and (= X2 tptp.zero_zero_real) (= Y tptp.one_one_real)))))
% 6.31/6.63 (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))))
% 6.31/6.63 (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))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X2) (@ (@ tptp.divide_divide_real (@ _let_1 X2)) (@ _let_1 B))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log B) _let_1)))))))
% 6.31/6.63 (assert (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X2)) (@ _let_1 Y)))))))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X2) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X2)) (@ _let_1 Y)))))))))))
% 6.31/6.63 (assert (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 (@ (@ tptp.power_power_real X2) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_1 X2)))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ _let_1 (@ tptp.inverse_inverse_real X2)) (@ tptp.uminus_uminus_real (@ _let_1 X2))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.31/6.63 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.log A) X2) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X2)))))))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.31/6.63 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ _let_1 X2) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X2)))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X2) (@ tptp.inverse_inverse_real X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.31/6.63 (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)))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.31/6.63 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.31/6.63 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N2) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (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))))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))))))
% 6.31/6.63 (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)))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X2) (@ (@ tptp.ord_less_eq_real X2) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N2)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.31/6.63 (assert (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N2))))))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.31/6.63 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.31/6.63 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 6.31/6.63 (assert (forall ((A tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X2) tptp.one_one_real) (= X2 tptp.zero_zero_real)))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real)) (= (= (@ (@ tptp.powr_real X2) tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2))))
% 6.31/6.63 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.31/6.63 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N2))))))
% 6.31/6.64 (assert (= (@ tptp.cis tptp.pi) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.31/6.64 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X2) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X2)) X2)))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y)) Y)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N2))))))
% 6.31/6.64 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X2)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real A) B))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.plus_plus_real A) B)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X2) Y)))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (X2 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 X2) (@ _let_1 Y)) (= X2 Y)))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A)) tptp.one_one_real)))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (X2 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) X2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y) B))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X2) A)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X2) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X2) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X2) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X2))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X2 tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X2) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X2)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X2)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X2) (@ (@ tptp.ord_less_real X2) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X2))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y) (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y)))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real X2) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X2)) Y))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X2) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X2)))))))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((N2 tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N2))))))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real R2) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2))) tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R2)))))
% 6.31/6.64 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X2))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.times_times_real X2) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X2))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y) (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y)))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real X2) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X2)) Y))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X2) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.int) (X2 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X2) (=> (@ (@ tptp.ord_less_real X2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X2) N2))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X2) A)) A))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X2)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X2))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real (@ _let_1 X2)) Y) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) Y)))))))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X2))))))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X2)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X2))))))))))
% 6.31/6.64 (assert (forall ((B tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X2) (= (@ (@ tptp.minus_minus_real (@ _let_1 X2)) Y) (@ _let_1 (@ (@ tptp.times_times_real X2) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.powr_real X2) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat N2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N2) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) _let_2))))) tptp.one_one_int))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N2))))) (@ tptp.set_ord_lessThan_nat N2)) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))))))
% 6.31/6.64 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.31/6.64 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.31/6.64 (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))
% 6.31/6.64 (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))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (exists ((A4 tptp.complex) (R3 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ tptp.exp_complex A4))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X2) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X2) R2)) (@ (@ tptp.times_times_real Y) R2)))))
% 6.31/6.64 (assert (forall ((R2 tptp.real) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X2) Y)) (@ (@ tptp.complex2 (@ _let_1 X2)) (@ _let_1 Y))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real) (R2 tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X2) Y)) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X2) R2)) Y))))
% 6.31/6.64 (assert (forall ((R2 tptp.real) (X2 tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 X2) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R2) X2)) Y))))
% 6.31/6.64 (assert (= tptp.cis (lambda ((B5 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B5))))))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R2))))
% 6.31/6.64 (assert (= tptp.complex2 (lambda ((A5 tptp.real) (B5 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A5)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B5))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A4 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R3)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A4))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A4)))))))))
% 6.31/6.64 (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)))
% 6.31/6.64 (assert (forall ((R2 tptp.real) (A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A)))))) (@ tptp.abs_abs_real R2))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (= tptp.arctan (lambda ((Y6 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.tan_real X) Y6))))))))
% 6.31/6.64 (assert (= tptp.arcsin (lambda ((Y6 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.sin_real X) Y6))))))))
% 6.31/6.64 (assert (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))) _let_1)))))))))))))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 6.31/6.64 (assert (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex))
% 6.31/6.64 (assert (forall ((L tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R2))) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.31/6.64 (assert (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) K)) (or (@ _let_1 K) (= R2 tptp.zero_zero_int))))))
% 6.31/6.64 (assert (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L) (@ tptp.sgn_sgn_int R2))) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.31/6.64 (assert (forall ((R2 tptp.int) (L tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R2)) L)) K) (and (@ (@ tptp.dvd_dvd_int L) K) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.31/6.64 (assert (forall ((K tptp.int)) (not (forall ((N tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (= tptp.sgn_sgn_int (lambda ((I5 tptp.int)) (@ (@ (@ tptp.if_int (= I5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I5)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((R2 tptp.int) (L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L)) R2)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q2) R2)))))))
% 6.31/6.64 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 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 (= A1 K3) (= A22 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 ((R5 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q4) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q4) L2)) R5))))))))
% 6.31/6.64 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A33) (=> (=> (= A23 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q3) A23)))))) (not (forall ((R3 tptp.int) (Q3 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A23)) R3)))))))))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real))))))
% 6.31/6.64 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real)))))))
% 6.31/6.64 (assert (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N2))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))))))))))))))))
% 6.31/6.64 (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)))))))))))
% 6.31/6.64 (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))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (I3 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real I3)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I3))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I3)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I3)))))))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.semiri1314217659103216013at_int N2)) N2)))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.31/6.64 (assert (forall ((P Bool)) (= (@ tptp.nat2 (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.31/6.64 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((I3 tptp.int)) (= (= (@ tptp.nat2 I3) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I3) tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.31/6.64 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 6.31/6.64 (assert (forall ((Y tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2) Y))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_nat N2) (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int N2)) K))))
% 6.31/6.64 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) N2) (@ (@ tptp.dvd_dvd_int K) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))) A) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)) A))))
% 6.31/6.64 (assert (forall ((A tptp.int) (X2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X2)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X2)) N2)) A))))
% 6.31/6.64 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 6.31/6.64 (assert (= tptp.numeral_numeral_nat (lambda ((I5 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I5)))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X2) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y)))))
% 6.31/6.64 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z7)) (= Z Z7)))))))
% 6.31/6.64 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (forall ((X7 tptp.nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.nat Bool))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ P4 (@ tptp.nat2 X)))))))
% 6.31/6.64 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((X tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ P4 (@ tptp.nat2 X)))))))
% 6.31/6.64 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.31/6.64 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.31/6.64 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X2)) N2) (@ (@ tptp.ord_less_eq_int X2) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 6.31/6.64 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.31/6.64 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5))))))
% 6.31/6.64 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.31/6.64 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (@ (@ tptp.ord_less_eq_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X2))))))
% 6.31/6.64 (assert (= tptp.divide_divide_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5))))))
% 6.31/6.64 (assert (= tptp.sgn_sgn_real (lambda ((A5 tptp.real)) (@ (@ (@ tptp.if_real (= A5 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A5)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.31/6.64 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.31/6.64 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.31/6.64 (assert (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (I3 tptp.int)) (= (@ P (@ tptp.nat2 I3)) (and (forall ((N3 tptp.nat)) (=> (= I3 (@ tptp.semiri1314217659103216013at_int N3)) (@ P N3))) (=> (@ (@ tptp.ord_less_int I3) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 6.31/6.64 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) K)))))
% 6.31/6.64 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))))
% 6.31/6.64 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 6.31/6.64 (assert (= tptp.suc (lambda ((A5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) tptp.one_one_int)))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X2) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y))))))))
% 6.31/6.64 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z7) (=> (@ (@ tptp.ord_less_eq_int Z7) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z7)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y))))))
% 6.31/6.64 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X2) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y))))))
% 6.31/6.64 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X2) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X2)) (@ tptp.nat2 Y))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X2)) A) (@ (@ tptp.ord_less_eq_nat X2) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))))
% 6.31/6.64 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K))))))
% 6.31/6.64 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.31/6.64 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((A tptp.real) (N2 tptp.nat) (X2 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) X2) (=> (= X2 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 6.31/6.64 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.31/6.64 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) X2) (=> (@ (@ tptp.ord_less_real X2) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X2)) N2)))))
% 6.31/6.64 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z7))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z7)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z7) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 6.31/6.64 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.31/6.64 (assert (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z6)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z6) tptp.one_one_int)))))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (N2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X2))) (let ((_let_2 (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N2)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N2)))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (not (= X2 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X2)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.one_one_complex))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X2))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X2) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X2) tptp.ring_1_Ints_real))))
% 6.31/6.64 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.zero_zero_real))))
% 6.31/6.64 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.one_one_real))))
% 6.31/6.64 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N3) (@ (@ (@ tptp.if_nat (= N3 tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N3) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1))))))))))
% 6.31/6.64 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N3)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N3) _let_1)))))))))
% 6.31/6.64 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z6)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z6) tptp.one_one_int)))))))))
% 6.31/6.64 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ _let_1 K)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N2) L))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.31/6.64 (assert (= tptp.sgn_sgn_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (= A5 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A5)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.31/6.64 (assert (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) N2) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2))))))
% 6.31/6.64 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 6.31/6.64 (assert (forall ((R2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R2) (not (forall ((S tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R2 (@ (@ tptp.plus_plus_rat S) T3)))))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N2) K)))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X2) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X2) Y)))))))
% 6.31/6.64 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.31/6.64 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N3) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.31/6.64 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.31/6.64 (assert (= tptp.bit_concat_bit (lambda ((N3 tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N3) K3)) (@ (@ tptp.bit_se545348938243370406it_int N3) L2)))))
% 6.31/6.64 (assert (= tptp.bit_concat_bit (lambda ((N3 tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N3) K3)) (@ (@ tptp.bit_se545348938243370406it_int N3) L2)))))
% 6.31/6.64 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int)))))
% 6.31/6.64 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.64 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N3 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X2) (=> (@ (@ tptp.ord_less_int X2) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X2) Y)) _let_1)))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (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)))))))))))))
% 6.31/6.64 (assert (forall ((A3 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (@ (@ tptp.member_nat N2) A3)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N2) A3)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.nat_set_encode A3)))))))
% 6.31/6.64 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A5 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 A5)) B5)) (@ tptp.abs_abs_int A5))))) (@ tptp.quotient_of P2)))))
% 6.31/6.64 (assert (forall ((Q2 tptp.int) (P2 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P2)) (@ tptp.uminus_uminus_int Q2)))))))
% 6.31/6.64 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T2)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((P2 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.31/6.64 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.64 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (I3 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I3)))))))
% 6.31/6.64 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ F N))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) U)))))))
% 6.31/6.64 (assert (= tptp.divide_divide_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q4) (@ tptp.inverse_inverse_rat R5)))))
% 6.31/6.64 (assert (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N9) (@ (@ tptp.ord_less_eq_nat X) M6)))))))
% 6.31/6.64 (assert (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N9) (@ (@ tptp.ord_less_nat X) M6)))))))
% 6.31/6.64 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N4) (@ (@ tptp.ord_less_nat X5) N2))) (@ tptp.finite_finite_nat N4))))
% 6.31/6.64 (assert (= tptp.minus_minus_rat (lambda ((Q4 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q4) (@ tptp.uminus_uminus_rat R5)))))
% 6.31/6.64 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.31/6.64 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L2))))))
% 6.31/6.64 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B5 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int C2) B5))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.31/6.64 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B5 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) B5)) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.31/6.64 (assert (forall ((A3 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A3)) (= (@ tptp.nat_set_encode A3) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.31/6.64 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.31/6.64 (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)))
% 6.31/6.64 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B5 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int B5) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.31/6.64 (assert (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P2) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B5 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int B5) C2))) (@ (@ tptp.times_times_int C2) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P2)))))
% 6.31/6.64 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N3) tptp.one_one_int))))))
% 6.31/6.64 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L2))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L2)))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M)))))))
% 6.31/6.64 (assert (forall ((R2 tptp.rat) (P2 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R2) (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.31/6.64 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N4))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int K)) (not (@ _let_1 K))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int)))
% 6.31/6.64 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.31/6.64 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) _let_1))))
% 6.31/6.64 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N2) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N2))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N2) M))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.zero_zero_int)))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((R2 tptp.product_prod_int_int) (P2 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R2) (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.31/6.64 (assert (forall ((Q2 tptp.int) (S2 tptp.int) (P2 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R2) S2))) (= (@ (@ tptp.times_times_int P2) S2) (@ (@ tptp.times_times_int R2) Q2)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.31/6.64 (assert (= tptp.ord_less_rat (lambda ((P6 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B5 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int C2) B5)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P6)))))
% 6.31/6.64 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P6 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P6)))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_rat (lambda ((P6 tptp.rat) (Q4 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C2 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B5 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A5) D2)) (@ (@ tptp.times_times_int C2) B5)))) (@ tptp.quotient_of Q4)))) (@ tptp.quotient_of P6)))))
% 6.31/6.64 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A3)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A3))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) K))))))
% 6.31/6.64 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat N3) K))))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I5) (@ (@ tptp.ord_less_eq_int I5) B)))))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_int A) I5) (@ (@ tptp.ord_less_int I5) B)))))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_int A) I5) (@ (@ tptp.ord_less_eq_int I5) B)))))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I5) (@ (@ tptp.ord_less_int I5) B)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))))))
% 6.31/6.64 (assert (forall ((I3 tptp.int)) (=> (not (= I3 tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (@ (@ tptp.dvd_dvd_int D2) I3)))))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 6.31/6.64 (assert (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N2) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N2)))))) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X2) X2)))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X2) tptp.zero_zero_real)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ _let_1 X2) (@ _let_1 Y)) (= X2 Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X2) tptp.zero_zero_real) (= X2 tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X2) Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X2) Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X2) tptp.one_one_real) (= X2 tptp.one_one_real)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) tptp.one_one_real) tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X2)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X2) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_real X2) tptp.one_one_real)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X2)) N2) X2)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X2 tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N2)) X2) (@ (@ tptp.root M) (@ (@ tptp.root N2) X2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (= (@ _let_1 (@ (@ tptp.times_times_real X2) Y)) (@ (@ tptp.times_times_real (@ _let_1 X2)) (@ _let_1 Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X2) Y) (@ (@ tptp.ord_less_real (@ _let_1 X2)) (@ _let_1 Y)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real X2) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X2)) (@ _let_1 Y)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.power_power_real X2) K)) (@ (@ tptp.power_power_real (@ _let_1 X2)) K))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ tptp.abs_abs_real X2)) (@ tptp.abs_abs_real (@ _let_1 X2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N2) X2)) (@ tptp.sgn_sgn_real X2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.root N2) X2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X2)) (@ (@ tptp.root N2) X2)))))))
% 6.31/6.64 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.abs_abs_real (@ (@ tptp.root N2) (@ (@ tptp.power_power_real Y) N2))) (@ tptp.abs_abs_real Y)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N2) X2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X2)) (@ (@ tptp.root N4) X2))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X2)) (@ (@ tptp.root N2) X2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X2)) N2) X2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N2) X2) (= (@ (@ tptp.root N2) X2) Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X2) N2)) X2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X2) N2)) X2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (= (@ (@ tptp.power_power_real Y) N2) X2) (= (@ (@ tptp.root N2) X2) Y)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X2)) N2) X2))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X2)) (@ (@ tptp.root N4) X2))))))))
% 6.31/6.64 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2))) Y))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ (@ tptp.root N2) X2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N2)) X2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N2) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N2) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (B tptp.real) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N2) B)) X2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) X2)))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.real Bool)) (N2 tptp.nat) (X2 tptp.real)) (= (@ P (@ (@ tptp.root N2) X2)) (and (=> (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (forall ((Y6 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N2)) X2) (@ P Y6))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= (@ (@ tptp.root N2) X2) (@ (@ tptp.powr_real X2) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M6 tptp.int)) (exists ((N3 tptp.int)) (and (@ (@ tptp.ord_less_int M6) (@ tptp.abs_abs_int N3)) (@ (@ tptp.member_int N3) S3)))))))
% 6.31/6.64 (assert (forall ((S3 tptp.set_int)) (= (not (@ tptp.finite_finite_int S3)) (forall ((M6 tptp.int)) (exists ((N3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N3)) (@ (@ tptp.member_int N3) S3)))))))
% 6.31/6.64 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N3) (@ (@ tptp.member_nat N3) S3)))))))
% 6.31/6.64 (assert (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M3) (exists ((N8 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N8) (@ (@ tptp.member_nat N8) S3))))) (not (@ tptp.finite_finite_nat S3)))))
% 6.31/6.64 (assert (forall ((S3 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S3)) (forall ((M6 tptp.nat)) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N3) (@ (@ tptp.member_nat N3) S3)))))))
% 6.31/6.64 (assert (forall ((T2 tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T2) D) (@ (@ tptp.vEBT_invar_vebt T2) D))))
% 6.31/6.64 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.31/6.64 (assert (forall ((T2 tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) D) (@ (@ tptp.vEBT_VEBT_valid T2) D))))
% 6.31/6.64 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X4 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N3) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X4 M6)) (@ X4 N3)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X))))))
% 6.31/6.64 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 6.31/6.64 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat N2) (@ _let_1 N2))))))
% 6.31/6.64 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N4))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N2) (@ _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K)))) (let ((_let_3 (@ tptp.pred_numeral K))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ A I2)) (@ A J2))))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I2))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I5)) (@ B I5)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.31/6.64 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.31/6.64 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q4 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q4))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)))
% 6.31/6.64 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.31/6.64 (assert (forall ((L tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L) L)))
% 6.31/6.64 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.31/6.64 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_real (@ tptp.re X2)) (@ tptp.re Y)))))
% 6.31/6.64 (assert (forall ((R2 tptp.real) (X2 tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R2) X2)) (@ (@ tptp.times_times_real R2) (@ tptp.re X2)))))
% 6.31/6.64 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 6.31/6.64 (assert (= tptp.zero_zero_int tptp.zero_zero_int))
% 6.31/6.64 (assert (= tptp.one_one_int tptp.one_one_int))
% 6.31/6.64 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.re Z))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2)))))
% 6.31/6.64 (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)))))))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.im Z))) (= (@ tptp.im (@ tptp.csqrt Z)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_1 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_1))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.31/6.64 (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))))))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.im X2))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X2)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X2)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X2)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.re X2))) (=> (= (@ tptp.im X2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X2) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.31/6.64 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int Xa2) X2)))))
% 6.31/6.64 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_int Xa2) X2))))
% 6.31/6.64 (assert (= tptp.zero_z3403309356797280102nteger (@ tptp.code_integer_of_int tptp.zero_zero_int)))
% 6.31/6.64 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.31/6.64 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 6.31/6.64 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa2) X2)))))
% 6.31/6.64 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa2) X2)))))
% 6.31/6.64 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 6.31/6.64 (assert (forall ((Xa2 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X2)) (@ (@ tptp.ord_less_eq_int Xa2) X2))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_real (@ tptp.im X2)) (@ tptp.im Y)))))
% 6.31/6.64 (assert (forall ((R2 tptp.real) (X2 tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R2) X2)) (@ (@ tptp.times_times_real R2) (@ tptp.im X2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X2) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) (@ tptp.im Y))) (@ (@ tptp.times_times_real (@ tptp.im X2)) (@ tptp.re Y))))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X2) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X2)) (@ tptp.im Y))))))
% 6.31/6.64 (assert (= tptp.plus_plus_complex (lambda ((X tptp.complex) (Y6 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y6))) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y6))))))
% 6.31/6.64 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X))) (@ _let_1 (@ tptp.im X)))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N2)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.cos_real (@ tptp.im Z))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.sin_real (@ tptp.im Z))))))
% 6.31/6.64 (assert (forall ((A tptp.complex)) (= A (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.re A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.im A)))))))
% 6.31/6.64 (assert (= tptp.times_times_complex (lambda ((X tptp.complex) (Y6 tptp.complex)) (let ((_let_1 (@ tptp.re Y6))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X)))) (let ((_let_3 (@ tptp.im Y6))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X)))) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_4 _let_1)) (@ _let_2 _let_3))) (@ (@ tptp.plus_plus_real (@ _let_4 _let_3)) (@ _let_2 _let_1))))))))))
% 6.31/6.64 (assert (= tptp.exp_complex (lambda ((Z6 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z6)))) (@ tptp.cis (@ tptp.im Z6))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1))))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X2) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X2))) (@ tptp.im X2))))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X2) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)) tptp.zero_zero_real)))))
% 6.31/6.64 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z6 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z6)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z6)) _let_1)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X2))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X2)) _let_1))))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.31/6.64 (assert (forall ((X2 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 X2) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.31/6.64 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.re W))) (=> (= (@ (@ tptp.power_power_complex W) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im W)))) (= (@ tptp.csqrt Z) W))))))
% 6.31/6.64 (assert (forall ((B tptp.complex)) (let ((_let_1 (@ tptp.re B))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B)))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X2))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X2)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.31/6.64 (assert (forall ((X2 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 X2) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X2)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X2)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))))
% 6.31/6.64 (assert (= tptp.invers8013647133539491842omplex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (let ((_let_3 (@ tptp.re X))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 6.31/6.64 (assert (= tptp.divide1717551699836669952omplex (lambda ((X 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 X)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 6.31/6.64 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R2))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.64 (assert (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R2) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R2) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R2)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.64 (assert (forall ((Y tptp.complex) (X2 tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X2) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y) X2) (and (= X2 tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.31/6.64 (assert (forall ((Y tptp.complex) (X2 tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X2) tptp.real_V2521375963428798218omplex) (= (= X2 (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X2 tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X2) Y)) (@ (@ tptp.times_times_complex (@ tptp.cnj X2)) (@ tptp.cnj Y)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 6.31/6.64 (assert (= (@ tptp.cnj tptp.one_one_complex) tptp.one_one_complex))
% 6.31/6.64 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X2) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X2)) (@ tptp.cnj Y)))))
% 6.31/6.64 (assert (= (@ tptp.code_int_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_int))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.31/6.64 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X2) Xa2)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X2) Xa2)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 6.31/6.64 (assert (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int))
% 6.31/6.64 (assert (forall ((X2 tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.divide6298287555418463151nteger X2) Xa2)) (@ (@ tptp.divide_divide_int (@ tptp.code_int_of_integer X2)) (@ tptp.code_int_of_integer Xa2)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 6.31/6.64 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 6.31/6.64 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z6 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z6) (@ tptp.cnj Z6)))))))
% 6.31/6.64 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.31/6.64 (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)))))))))
% 6.31/6.64 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z) (@ tptp.cnj Z)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z)))) tptp.imaginary_unit))))
% 6.31/6.64 (assert (= tptp.divide1717551699836669952omplex (lambda ((A5 tptp.complex) (B5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A5) (@ tptp.cnj B5))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B5)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.31/6.64 (assert (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z) (@ tptp.cnj W)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z)) W)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (= (@ tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat))
% 6.31/6.64 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.31/6.64 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.31/6.64 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S4))) (= S4 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.ord_less_nat I5) N2)))) N2)))
% 6.31/6.64 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I5) N2)))) (@ tptp.suc N2))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((M7 tptp.set_nat) (I3 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I3)))))) tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((M7 tptp.set_nat) (I3 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I3)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I3))))))))))
% 6.31/6.64 (assert (forall ((M7 tptp.set_nat) (I3 tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I3))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I3))))))))))
% 6.31/6.64 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 6.31/6.64 (assert (forall ((A3 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A3))))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) _let_1) (= A3 _let_1)))))
% 6.31/6.64 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N2))))
% 6.31/6.64 (assert (forall ((S3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S3)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) S3))))
% 6.31/6.64 (assert (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) C)))) N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z6 tptp.complex)) (= (@ (@ tptp.power_power_complex Z6) N2) tptp.one_one_complex)))) N2))))
% 6.31/6.64 (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 ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ 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 ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ 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))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.bezw X2) tptp.zero_zero_nat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.31/6.64 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M4)))) M)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M4 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M4) N2)))) M)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N2))))))
% 6.31/6.64 (assert (= tptp.binomial (lambda ((N3 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) N3))) (= (@ tptp.finite_card_nat K7) K3))))))))
% 6.31/6.64 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M6 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M6) K3)) (@ (@ tptp.product_Pair_nat_nat M6) (@ (@ tptp.minus_minus_nat K3) M6))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M6) _let_1)))))))
% 6.31/6.64 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) (@ _let_1 K)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N2) _let_1) _let_1))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.divide_divide_nat M) N2))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.modulo_modulo_nat M) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N2) M)) K)))))
% 6.31/6.64 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N3 tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)))))
% 6.31/6.64 (assert (forall ((R2 tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R2)))))
% 6.31/6.64 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X2) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X2) 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 X2) Y)))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) 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 X2) Xa2))))))))))))))
% 6.31/6.64 (assert (= tptp.bezw (lambda ((X tptp.nat) (Y6 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y6) (@ (@ tptp.modulo_modulo_nat X) 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 X) Y6)))))))))))
% 6.31/6.64 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N3 tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)))))
% 6.31/6.64 (assert (forall ((P2 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P2)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P2)))) tptp.one_one_int))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N2)))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N2))))))))
% 6.31/6.64 (assert (= tptp.adjust_mod (lambda ((L2 tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R5)))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X2) Xa2) 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 X2) Xa2)))))))) (not _let_1)))))))))))
% 6.31/6.64 (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)))))))))))))
% 6.31/6.64 (assert (forall ((M tptp.int)) (= (@ (@ tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.64 (assert (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N2)) (or (not (= M tptp.zero_zero_int)) (not (= N2 tptp.zero_zero_int))))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.gcd_gcd_int X2))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num) (X2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X2) (@ (@ tptp.gcd_gcd_int _let_1) X2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.gcd_gcd_int X2) tptp.zero_zero_int) (@ tptp.abs_abs_int X2))))
% 6.31/6.64 (assert (forall ((X2 tptp.int)) (= (@ (@ tptp.gcd_gcd_int tptp.zero_zero_int) X2) (@ tptp.abs_abs_int X2))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X2) Y))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (exists ((U3 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X2)) (@ (@ tptp.times_times_int V2) Y)) (@ (@ tptp.gcd_gcd_int X2) Y)))))
% 6.31/6.64 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K)) (@ (@ tptp.gcd_gcd_int M) N2)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X2))) (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 X2)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X2) 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 X2))) (=> (=> _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)))))))))))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((Y tptp.int) (X2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X2) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X2) Y))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (@ tptp.suc X2))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X2))) (=> (= (@ (@ tptp.nat_prod_decode_aux X2) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X2) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.31/6.64 (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 ((N8 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N8) (@ tptp.finite_card_nat S3)) (@ (@ tptp.member_nat (@ R3 N8)) S3))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) X2) X2)))
% 6.31/6.64 (assert (forall ((X2 tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat X2) tptp.zero_zero_nat) X2)))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A) tptp.zero_zero_nat) A)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) A) A)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N2)) (or (not (= M tptp.zero_zero_nat)) (not (= N2 tptp.zero_zero_nat))))))
% 6.31/6.64 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N2)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N2)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N2) M)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa2) Y) (and (=> _let_1 (= Y X2)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2)))))))))
% 6.31/6.64 (assert (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y6 tptp.zero_zero_nat)) X) (@ (@ tptp.gcd_gcd_nat Y6) (@ (@ tptp.modulo_modulo_nat X) Y6))))))
% 6.31/6.64 (assert (forall ((Y tptp.nat) (X2 tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X2) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X2) Y))))))
% 6.31/6.64 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y3)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.31/6.64 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X5 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y3))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X5))) (let ((_let_6 (@ _let_4 Y3))) (let ((_let_7 (@ _let_2 X5))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X2) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X2) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X2))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X2) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X2) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X2)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X2) Xa2))))) (not _let_1)))))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)) K)))))
% 6.31/6.64 (assert (forall ((K tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N2)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X2)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))))
% 6.31/6.64 (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 ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ 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))))))))))
% 6.31/6.64 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y6) X))) (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.ord_less_nat Y6) X))))
% 6.31/6.64 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.31/6.64 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M6 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M6) N3) (not (= M6 N3))))))
% 6.31/6.64 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.31/6.64 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.31/6.64 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (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 X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X2)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.int Bool)) (X2 tptp.int)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (@ P (@ tptp.abs_Integ Y3))) (@ P X2))))
% 6.31/6.64 (assert (forall ((Z tptp.int)) (not (forall ((X5 tptp.nat) (Y3 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X5) Y3))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X2)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X2))))
% 6.31/6.64 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N3 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N3) tptp.zero_zero_nat)))))
% 6.31/6.64 (assert (forall ((X2 tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X))) X2)))))
% 6.31/6.64 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.31/6.64 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (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 X) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0))) Xa2) X2))))
% 6.31/6.64 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (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 X) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0))) Xa2) X2))))
% 6.31/6.64 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (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 X) U2)) (@ (@ tptp.plus_plus_nat Y6) V4)))) __flatten_var_0))) Xa2) X2)))))
% 6.31/6.64 (assert (forall ((Xa2 tptp.product_prod_nat_nat) (X2 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa2)) (@ tptp.abs_Integ X2)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (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 X) V4)) (@ (@ tptp.plus_plus_nat Y6) U2)))) __flatten_var_0))) Xa2) X2)))))
% 6.31/6.64 (assert (forall ((M7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M7) (= (@ tptp.gcd_Gcd_nat M7) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M7) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 6.31/6.64 (assert (forall ((N4 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N4) (= (@ tptp.gcd_Gcd_nat N4) tptp.one_one_nat))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_int (lambda ((X 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 X)) (@ tptp.rep_Integ Xa4)))))
% 6.31/6.64 (assert (= tptp.ord_less_int (lambda ((X 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 X)) (@ tptp.rep_Integ Xa4)))))
% 6.31/6.64 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.31/6.64 (assert (= tptp.nat2 (lambda ((X tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X)))))
% 6.31/6.64 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N3))) M6)))))
% 6.31/6.64 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X tptp.nat) (Y6 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y6) X))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M))))
% 6.31/6.64 (assert (= tptp.times_times_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (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 X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.31/6.64 (assert (= tptp.minus_minus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (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 X) V4)) (@ (@ tptp.plus_plus_nat Y6) U2)))) __flatten_var_0))))))
% 6.31/6.64 (assert (= tptp.plus_plus_int (@ (@ (@ tptp.map_fu4960017516451851995nt_int tptp.rep_Integ) (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ)) (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (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 X) U2)) (@ (@ tptp.plus_plus_nat Y6) V4)))) __flatten_var_0))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N2)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N2)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.31/6.64 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.31/6.64 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N2) N2)) (@ tptp.bit0 (@ tptp.num_of_nat N2))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N2))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I3))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I3) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I3) N2))))))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X2)))))
% 6.31/6.64 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N2))))))
% 6.31/6.64 (assert (= tptp.sqr (lambda ((X tptp.num)) (@ (@ tptp.times_times_num X) X))))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X2))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N2)) N2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I3)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I3) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I3) N2))))))
% 6.31/6.64 (assert (forall ((C tptp.nat) (Y tptp.nat) (X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X2) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X2) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X2) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (assert (forall ((M7 tptp.set_nat) (N4 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N4) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N4))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I3) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I3)) (@ tptp.suc J)))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I3) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I3)) (@ tptp.suc J)))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A) B)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B))))))
% 6.31/6.64 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.zero_zero_int) tptp.zero_zero_rat)))
% 6.31/6.64 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract tptp.zero_zero_int) K) tptp.zero_zero_rat)))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))))
% 6.31/6.64 (assert (forall ((A3 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A3)))))
% 6.31/6.64 (assert (forall ((A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.fract tptp.zero_zero_int))) (= (@ _let_1 A) (@ _let_1 C)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A4 tptp.int) (B3 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B3) (@ P (@ (@ tptp.fract A4) B3)))) (@ P Q2))))
% 6.31/6.64 (assert (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))))
% 6.31/6.64 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= tptp.one_one_rat (@ (@ tptp.fract tptp.one_one_int) tptp.one_one_int)))
% 6.31/6.64 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.one_one_int) (@ tptp.ring_1_of_int_rat K))))
% 6.31/6.64 (assert (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)))
% 6.31/6.64 (assert (= tptp.numeral_numeral_rat (lambda ((K3 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K3)) tptp.one_one_int))))
% 6.31/6.64 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2))))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.31/6.64 (assert (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M) N2)) N2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M) N2)) tptp.one_one_rat)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.31/6.64 (assert (= tptp.comple4887499456419720421f_real (lambda ((X4 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X4))))))
% 6.31/6.64 (assert (= tptp.ord_less_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (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 X) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0))))))
% 6.31/6.64 (assert (= tptp.ord_less_eq_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (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 X) V4)) (@ (@ tptp.plus_plus_nat U2) Y6)))) __flatten_var_0))))))
% 6.31/6.64 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.31/6.64 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.31/6.64 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.31/6.64 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.31/6.64 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A)) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))))
% 6.31/6.64 (assert (not (@ tptp.finite_finite_int tptp.top_top_set_int)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.member_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int))))
% 6.31/6.64 (assert (= tptp.root (lambda ((N3 tptp.nat) (X tptp.real)) (@ (@ (@ tptp.if_real (= N3 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y6 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y6)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y6)) N3)))) X)))))
% 6.31/6.64 (assert (= (@ tptp.finite_card_char tptp.top_top_set_char) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))
% 6.31/6.64 (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)))))))))))))
% 6.31/6.64 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.31/6.64 (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))))))))))))
% 6.31/6.64 (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))))))))))))
% 6.31/6.64 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 6.31/6.64 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((C tptp.char)) (= (@ tptp.comm_s629917340098488124ar_nat (@ tptp.ascii_of C)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ tptp.comm_s629917340098488124ar_nat C)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I3))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I3) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I3))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I3) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.31/6.64 (assert (= tptp.upto_aux (lambda ((I5 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I5)) Js) (@ (@ (@ tptp.upto_aux I5) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.31/6.64 (assert (forall ((X2 tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X2) Y) (=> (=> (= X2 tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X2 (@ (@ tptp.cons_nat X5) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2)))))))))))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I3) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I3) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.31/6.64 (assert (forall ((J tptp.int) (I3 tptp.int)) (=> (@ (@ tptp.ord_less_int J) I3) (= (@ (@ tptp.upto I3) J) tptp.nil_int))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I3) J)) (@ (@ tptp.ord_less_int J) I3))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I3) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I3))))
% 6.31/6.64 (assert (forall ((I3 tptp.int)) (= (@ (@ tptp.upto I3) I3) (@ (@ tptp.cons_int I3) tptp.nil_int))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I3) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I3) J)) K) _let_1)))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I3) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I3)) tptp.one_one_int)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.31/6.64 (assert (= tptp.upto_aux (lambda ((I5 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I5) J3)) __flatten_var_0))))
% 6.31/6.64 (assert (= tptp.upto (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I5) J3) tptp.nil_int))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I3) J))))
% 6.31/6.64 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I5) J3)))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I3))) (=> (@ (@ tptp.ord_less_eq_int I3) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I3))) (=> (@ (@ tptp.ord_less_eq_int I3) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 6.31/6.64 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I5) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.31/6.64 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 6.31/6.64 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3)))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X2) Xa2))) (=> (= (@ (@ tptp.upto X2) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.31/6.64 (assert (= tptp.upto (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I5) J3)) (@ (@ tptp.cons_int I5) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) J) (= (@ (@ tptp.upto I3) J) (@ (@ tptp.cons_int I3) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J))))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I3))) (=> (@ (@ tptp.ord_less_eq_int I3) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 6.31/6.64 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I3))) (=> (@ (@ tptp.ord_less_eq_int I3) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X2) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X2) (@ tptp.nat_list_encode Xs)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X2) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X2) Xa2))) (=> (= (@ (@ tptp.upto X2) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X2) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))))))
% 6.31/6.64 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F _let_1)))))))))))))
% 6.31/6.64 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real) (S3 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) S3)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X2) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S3) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X2)))))))))))))
% 6.31/6.64 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X2)) (@ F (@ (@ tptp.plus_plus_real X2) H4))))))))))))
% 6.31/6.64 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X2 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X2) H4))) (@ F X2)))))))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X5) (=> (@ (@ tptp.ord_less_eq_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F4 Z3)))))))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X2)) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real) (S2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X2) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X2) S2))))
% 6.31/6.64 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ G X)) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ G X2)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) M)) _let_1)))))
% 6.31/6.64 (assert (forall ((Z tptp.real) (R2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z6 tptp.real)) (@ (@ tptp.powr_real Z6) R2))) (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R2) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X2))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.31/6.64 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) R2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R2) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R2) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.31/6.64 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X2 tptp.real) (F (-> tptp.real tptp.real)) (R2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))) (let ((_let_2 (@ G X2))) (let ((_let_3 (@ F X2))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R2) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) (@ F X)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R2) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X2))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.31/6.64 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F4 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F4 X0))) (=> (forall ((N tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ F X) N))) (@ (@ F4 X0) N)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X5)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N tptp.nat) (X5 tptp.real) (Y3 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X5) _let_1) (=> (@ (@ tptp.member_real Y3) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X5) N)) (@ (@ F Y3) N)))) (@ (@ tptp.times_times_real (@ L5 N)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X5) Y3)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (@ F X)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A3))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X2)))) (=> (not (= X2 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X2) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X2) A3)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) A3)))))
% 6.31/6.64 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N3)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) (@ (@ tptp.power_power_real X5) N3)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ F N3)) (@ (@ tptp.power_power_real X) (@ tptp.suc N3))))))) (@ tptp.suminf_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N3)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) (@ (@ tptp.power_power_real X0) N3))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X2) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real))))))
% 6.31/6.64 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N2 tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))))))))
% 6.31/6.64 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X2 tptp.real) (N2 tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2))))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (X2 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (not (= X2 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X2)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))))
% 6.31/6.64 (assert (forall ((H2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ 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) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))))
% 6.31/6.64 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ 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) H2) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2)))))))))))
% 6.31/6.64 (assert (forall ((H2 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real H2) 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 H2) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H2) N2))))))))))))
% 6.31/6.64 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X2 tptp.zero_zero_real)) (=> (forall ((M3 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real T3))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) (@ tptp.abs_abs_real X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2)))))))))))))
% 6.31/6.64 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X2 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X2))) (@ (@ (@ 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 X2)) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X2) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X2) N2))))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ 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 X2) (=> (@ (@ tptp.ord_less_eq_real X2) B) (=> (not (= X2 C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X2))) (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 X2))) (= (@ F X2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X2) C)) N2))))))))))))))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ 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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N2)))))))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ 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 ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N2)))))))))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B4 tptp.real)) (=> (forall ((M3 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M3)) (@ (@ Diff (@ tptp.suc M3)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N2 (@ tptp.suc K)) (forall ((M2 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N2) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) 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 M2) 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 B4) (@ (@ 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 M2)) 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 B4) (@ (@ 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))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((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 X2) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q4)))))) (@ (@ tptp.bit_take_bit_num _let_1) N2))))))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.31/6.64 (assert (forall ((R2 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N2) M)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))))
% 6.31/6.64 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M)))))
% 6.31/6.64 (assert (forall ((R2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R2)) M))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N3 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q4 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q4)))) (@ (@ tptp.bit_take_bit_num N3) M)))) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N2) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N3 tptp.nat)) (@ tptp.some_num tptp.one))) N2))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N3 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N3) M))))) N2))))
% 6.31/6.64 (assert (= tptp.bit_take_bit_num (lambda ((N3 tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N3) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))))
% 6.31/6.64 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))))
% 6.31/6.64 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.31/6.64 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num tptp.one))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N2)) tptp.none_num)))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int Q2)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N2) M)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.31/6.64 (assert (= tptp.bit_take_bit_num (lambda ((N3 tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A5 tptp.nat) (X tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((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))))) X))) A5))) (@ (@ tptp.product_Pair_nat_num N3) M6)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arccos)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X2) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) F)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z3) (=> (@ (@ tptp.ord_less_eq_real Z3) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) G)))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (=> (forall ((Z3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z3) (=> (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 Z3)) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real))))) (exists ((C3 tptp.real)) (and (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C3)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F4 C3))))))))))))
% 6.31/6.64 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 6.31/6.64 (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 ((N8 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.31/6.64 (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 ((N8 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.31/6.64 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.31/6.64 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.root N3) (@ tptp.semiri5074537144036343181t_real N3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.31/6.64 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N)) (@ F (@ tptp.suc N)))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N))) (@ G N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N)) (@ G N))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N3)) (@ G N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N8)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N8))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.31/6.64 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R3 tptp.real)) (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N) (@ (@ tptp.ord_less_real R3) (@ X8 N)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.31/6.64 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.31/6.64 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.root N3) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.31/6.64 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.31/6.64 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N)) (@ F (@ tptp.suc N)))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N)) L)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N8)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_real X2) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X2)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X2) N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.31/6.64 (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))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X2) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X2) N3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.plus_plus_real R2) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X2) (@ tptp.semiri5074537144036343181t_real N3)))) N3))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_nat)))
% 6.31/6.64 (assert (forall ((R2 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real R2) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))))))) (@ tptp.topolo2815343760600316023s_real R2)) tptp.at_top_nat)))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ A N3))))))))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N))) (@ A N))) (@ tptp.summable_real (lambda ((N3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N3)) (@ A N3)))))))))
% 6.31/6.64 (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)))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X2)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X2) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N))) (@ A N))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat))))))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N))) (@ A N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))))))))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N))) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) _let_1) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N8)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat)))))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N))) (@ A N))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat))))))
% 6.31/6.64 (assert (forall ((A (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N))) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N))) (@ A N))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat)))))))))
% 6.31/6.64 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F3 (-> tptp.real tptp.real))) (exists ((C2 tptp.real)) (= F3 (lambda ((X tptp.real)) (@ (@ tptp.times_times_real X) C2)))))))
% 6.31/6.64 (assert (forall ((X2 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 X2) Y6))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y6)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.31/6.64 (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))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.31/6.64 (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))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N2))) tptp.at_bot_real) F5))))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N2))) tptp.at_top_real) F5))))))
% 6.31/6.64 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 6.31/6.64 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.31/6.64 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.31/6.64 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.31/6.64 (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))))
% 6.31/6.64 (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))))))
% 6.31/6.64 (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)))))
% 6.31/6.64 (assert (forall ((X2 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 X2) Y6))) Y6))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X2))) tptp.at_top_real)))
% 6.31/6.64 (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)))))
% 6.31/6.64 (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))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) F))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X5) (@ (@ tptp.ord_less_real X5) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)) G))) (=> (forall ((X5 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X5) (@ (@ tptp.ord_less_real X5) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C3) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C3) (@ (@ tptp.ord_less_real C3) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I5 tptp.nat)) (@ P (@ tptp.suc I5)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N3 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N3) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I5 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I5) K)))) tptp.at_top_nat))))
% 6.31/6.64 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X5) (@ P X5))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N9 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N3) (@ P N3)))))))
% 6.31/6.64 (assert (forall ((F5 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F5) tptp.at_top_nat) (forall ((N9 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N9)) F5)))))
% 6.31/6.64 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ P (@ (@ tptp.plus_plus_real X) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.31/6.64 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_1 tptp.nat)) (@ P X_1)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.31/6.64 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.31/6.64 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList) Summary)) Deg4) (and (= Deg Deg4) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I5))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima2)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (= Y (not (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X2 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X2 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2)) (not (and (= Deg2 Xa2) (forall ((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 ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (= Y (= Xa2 tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X2 _let_1) (=> (= Y (and (= Deg2 Xa2) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X2) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (= Deg2 Xa2) (forall ((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 ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima)))))))))))))))
% 6.31/6.64 (assert (= tptp.complete_Sup_Sup_int (lambda ((X4 tptp.set_int)) (@ tptp.the_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) X4) (forall ((Y6 tptp.int)) (=> (@ (@ tptp.member_int Y6) X4) (@ (@ tptp.ord_less_eq_int Y6) X)))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X2) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X2) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X2 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList2) Summary2))) (=> (= X2 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (= Deg2 Xa2) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X4))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X4)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X4 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X4)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) Ma3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi3) X) (@ (@ tptp.ord_less_eq_nat X) Ma3)))))))))))))) Mima))))))))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (@ (@ tptp.ord_less_eq_real X2) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X2)) tptp.at_top_nat)))))
% 6.31/6.64 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z3 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z3) (@ (@ tptp.ord_less_real Z3) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z3) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.31/6.64 (assert (forall ((A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A3) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A3) tptp.arcosh_real))))
% 6.31/6.64 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A3))) (=> (@ _let_1 F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X5)))) (@ _let_1 (lambda ((X tptp.real)) (@ tptp.arcosh_real (@ F X)))))))))
% 6.31/6.64 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.31/6.64 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.31/6.64 (assert (forall ((A3 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A3) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A3) tptp.artanh_real))))
% 6.31/6.64 (assert (forall ((A3 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A3))) (=> (@ _let_1 F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) A3) (@ (@ tptp.member_real (@ F X5)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X tptp.real)) (@ tptp.artanh_real (@ F X)))))))))
% 6.31/6.64 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 6.31/6.64 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M6)) M6))))))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X2) Xa2) Y) (=> (=> _let_2 (=> (= Xa2 tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N tptp.num)) (= Xa2 (@ tptp.bit0 N))) (not (= Y (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N tptp.num)) (= Xa2 (@ tptp.bit1 N))) _let_1)) (=> (forall ((M3 tptp.num)) (let ((_let_1 (@ tptp.bit0 M3))) (=> (= X2 _let_1) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit0 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit0 N)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N)))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit0 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit1 N)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N)))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit1 M3)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit1 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit0 N)) (not (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M3) N)))))))) (not (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit1 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit1 N)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M3) N))))))))))))))))))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa2 tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X2) Xa2) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N tptp.num)) (= Xa2 (@ tptp.bit0 N))) _let_4)) (=> (=> _let_5 (=> (exists ((N tptp.num)) (= Xa2 (@ tptp.bit1 N))) _let_1)) (=> (=> (exists ((M3 tptp.num)) (= X2 (@ tptp.bit0 M3))) (=> _let_2 _let_4)) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit0 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit0 N)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N)))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit0 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit1 N)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N)))))))) (=> (=> (exists ((M3 tptp.num)) (= X2 (@ tptp.bit1 M3))) _let_3) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit1 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit0 N)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N)))))))) (not (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit1 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit1 N)) (not (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M3) N)))))))))))))))))))))))))
% 6.31/6.64 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num tptp.one))))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N2)) tptp.none_num)))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (Xa2 tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X2 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X2) Xa2) Y) (=> (=> _let_1 (=> (= Xa2 tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit0 N)) (not (= Y (@ tptp.some_num (@ tptp.bit1 N))))))) (=> (=> _let_1 (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit1 N)) (not (= Y (@ tptp.some_num (@ tptp.bit0 N))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit0 M3)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit0 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit0 N)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M3) N)))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit0 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit1 N)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M3) N))))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit1 M3)) (=> (= Xa2 tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M3))))))) (=> (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit1 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit0 N)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M3) N))))))))) (not (forall ((M3 tptp.num)) (=> (= X2 (@ tptp.bit1 M3)) (forall ((N tptp.num)) (=> (= Xa2 (@ tptp.bit1 N)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M3) N)))))))))))))))))))))
% 6.31/6.64 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.31/6.64 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.31/6.64 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num (@ tptp.bit0 N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num (@ tptp.bit1 N2)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))))
% 6.31/6.64 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.31/6.64 (assert (= (@ (@ tptp.image_int_int tptp.abs_abs_int) tptp.top_top_set_int) tptp.semiring_1_Nats_int))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ 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)) N2)))) tptp.top_top_set_real))))
% 6.31/6.64 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.31/6.64 (assert (forall ((N4 tptp.set_nat) (K tptp.nat)) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.member_nat N) N4) (@ (@ tptp.ord_less_eq_nat K) N))) (@ (@ tptp.inj_on_nat_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat N3) K))) N4))))
% 6.31/6.64 (assert (forall ((N4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N4)))
% 6.31/6.64 (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))))))))))))
% 6.31/6.64 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I5 tptp.int) (N3 tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I5)) (@ tptp.semiri5074537144036343181t_real N3))) (not (= N3 tptp.zero_zero_nat))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X2)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X2) tptp.field_5140801741446780682s_real))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X2) X5)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X5) X2)))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X2) X5) (@ (@ tptp.ord_less_real X5) Y))))))
% 6.31/6.64 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I5 tptp.int) (J3 tptp.int)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I5)) (@ tptp.ring_1_of_int_real J3))) (not (= J3 tptp.zero_zero_int))))))))
% 6.31/6.64 (assert (= tptp.sup_sup_int tptp.ord_max_int))
% 6.31/6.64 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I3))) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X2) (=> (or (not (= X2 tptp.zero_zero_real)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2)) (= (@ (@ tptp.powr_real X2) (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.power_int_real X2) N2))))))
% 6.31/6.64 (assert (forall ((M tptp.nat)) (= (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I5) J3)) M)))) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.set_ord_atMost_nat M)) (lambda ((R5 tptp.nat)) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat M) R5)))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N2))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I3) J)) (@ (@ tptp.minus_minus_nat J) I3))))
% 6.31/6.64 (assert (forall ((J tptp.nat) (I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I3) (= (@ (@ tptp.upt I3) J) tptp.nil_nat))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.upt M) N2))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I3) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I3)))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I3) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I3) J)) K) _let_1)))))
% 6.31/6.64 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N2)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat I5) N2))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N2) (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I3) J))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N2) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat)) (= (@ (@ tptp.upt I3) tptp.zero_zero_nat) tptp.nil_nat)))
% 6.31/6.64 (assert (= tptp.set_ord_lessThan_nat (lambda ((N3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N3)))))
% 6.31/6.64 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I5) J3)))))
% 6.31/6.64 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N3 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N3)) (@ tptp.suc M6))))))
% 6.31/6.64 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N3 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N3)) M6)))))
% 6.31/6.64 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N3 tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N3) (@ tptp.suc M6))))))
% 6.31/6.64 (assert (= tptp.set_ord_atMost_nat (lambda ((N3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N3))))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (= (@ (@ tptp.upt I3) J) (@ (@ tptp.cons_nat I3) (@ (@ tptp.upt (@ tptp.suc I3)) J))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N3 tptp.nat)) (@ (@ tptp.minus_minus_nat N3) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.upt M) N2))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I3))) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat) (X2 tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I3) J) (@ (@ tptp.cons_nat X2) Xs)) (and (@ (@ tptp.ord_less_nat I3) J) (= I3 X2) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat)) J) Xs)))))
% 6.31/6.64 (assert (= tptp.upt (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I5) J3)) (@ (@ tptp.cons_nat I5) (@ (@ tptp.upt (@ tptp.suc I5)) J3))) tptp.nil_nat))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I3))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I3) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I3))) (=> (@ (@ tptp.ord_less_eq_nat I3) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 6.31/6.64 (assert (forall ((X2 tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X2) Y) (=> (@ _let_1 X2) (=> (=> (= X2 tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X5) Xs2))) (=> (= X2 _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N4))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N4)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N4))))))))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N4 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N4))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N4) M)) tptp.one_one_nat)) N4))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N2))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N2))))
% 6.31/6.64 (assert (forall ((Ns tptp.list_nat) (I3 tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I3) (@ (@ tptp.nth_nat Ns) I3))))))
% 6.31/6.64 (assert (forall ((I3 tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I3) J))))
% 6.31/6.64 (assert (forall ((M tptp.int) (N2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N2))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.upt (@ tptp.suc M)) N2))))
% 6.31/6.64 (assert (forall ((I3 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I3) J)) I3))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N2)))))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.31/6.64 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) (@ tptp.pred_numeral K))))))
% 6.31/6.64 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N2)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N2) K) L)) R2) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N2)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N2)) L) R2)))))
% 6.31/6.64 (assert (forall ((M tptp.nat) (I3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I3)) (@ (@ tptp.minus_minus_nat N2) I3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N2)) I3))))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X2) Y) Y)))
% 6.31/6.64 (assert (forall ((X2 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X2) Y) X2)))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X2) Y) Y)))
% 6.31/6.64 (assert (forall ((X2 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X2) Y) X2)))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X2) Y) Y)))
% 6.31/6.64 (assert (forall ((X2 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X2) Y) X2)))
% 6.31/6.64 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X2) Y) Y)))
% 6.31/6.64 (assert (forall ((X2 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X2) Y) X2)))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X2) Y) Y)))
% 6.31/6.64 (assert (forall ((X2 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X2) Y) X2)))
% 6.31/6.64 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X2) Y) Y)))
% 6.31/6.64 (assert (forall ((X2 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (@ (@ (@ tptp.if_VEBT_VEBT true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((X2 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X2) Y) X2)))
% 6.31/6.65 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 6.31/6.65 (assert (forall ((X2 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X2) Y) Y)))
% 6.31/6.65 (assert (forall ((X2 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X2) Y) X2)))
% 6.31/6.65 (assert (not (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.ya)))
% 6.31/6.65 (set-info :filename cvc5---1.0.5_13355)
% 6.31/6.65 (check-sat-assuming ( true ))
% 6.31/6.65 ------- get file name : TPTP file name is ITP230^1
% 6.31/6.65 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_13355.smt2...
% 6.31/6.65 --- Run --ho-eli/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 13738 Alarm clock ( read result; case "$result" in
% 299.68/300.16 unsat)
% 299.68/300.16 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.68/300.16 ;;
% 299.68/300.16 sat)
% 299.68/300.16 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.68/300.16 ;;
% 299.68/300.16 esac; exit 1 )
% 299.68/300.17 Alarm clock
% 299.68/300.17 % cvc5---1.0.5 exiting
% 299.68/300.17 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------